From 26ab465c133f61d2e70be6e16357abf8f5bc1dc6bd760f4b145740a909fb6751 Mon Sep 17 00:00:00 2001 From: Martin Pluskal Date: Thu, 16 Jul 2020 11:52:52 +0000 Subject: [PATCH] Accepting request 820999 from home:badshah400:branches:science - Add insighttoolkit-drop-netlib-triangle-files.patch: Drop netlib triangle files and any linking to them due to licensing issues; patch from upstream [gh#InsightSoftwareConsortium/ITK#1913]. OBS-URL: https://build.opensuse.org/request/show/820999 OBS-URL: https://build.opensuse.org/package/show/Application:Geo/insighttoolkit?expand=0&rev=23 --- ...httoolkit-drop-netlib-triangle-files.patch | 20032 ++++++++++++++++ insighttoolkit.changes | 7 + insighttoolkit.spec | 9 +- 3 files changed, 20047 insertions(+), 1 deletion(-) create mode 100644 insighttoolkit-drop-netlib-triangle-files.patch diff --git a/insighttoolkit-drop-netlib-triangle-files.patch b/insighttoolkit-drop-netlib-triangle-files.patch new file mode 100644 index 0000000..69c2d41 --- /dev/null +++ b/insighttoolkit-drop-netlib-triangle-files.patch @@ -0,0 +1,20032 @@ +commit 7f95961fa74175981ff41eddfd8b1b1af83f315e +Author: Matt McCormick +Date: Mon Jul 13 13:34:04 2020 -0400 + + BUG: Remove netnlib triangle classes + + These are incompatible with ITK's license per Issue #1913. + +diff --git a/Modules/ThirdParty/VNL/CMakeLists.txt b/Modules/ThirdParty/VNL/CMakeLists.txt +index 0fffeb4022..c655dcdf80 100644 +--- a/Modules/ThirdParty/VNL/CMakeLists.txt ++++ b/Modules/ThirdParty/VNL/CMakeLists.txt +@@ -58,7 +58,7 @@ else() + ${ITKVNL_BINARY_DIR}/src/vxl/vcl + ${ITKVNL_BINARY_DIR}/src/vxl/core + ) +- set(ITKVNL_LIBRARIES itkvnl_algo itkvnl itkv3p_netlib itknetlib itkvcl) ++ set(ITKVNL_LIBRARIES itkvnl_algo itkvnl itkv3p_netlib itkvcl) + + if(ITK_TEMPLATE_VISIBILITY_DEFAULT) + add_definitions( "-DVNL_TEMPLATE_EXPORT=__attribute__((visibility(\"default\")))") +diff --git a/Modules/ThirdParty/VNL/src/CMakeLists.txt b/Modules/ThirdParty/VNL/src/CMakeLists.txt +index 75633c5ab5..c6200aa1a3 100644 +--- a/Modules/ThirdParty/VNL/src/CMakeLists.txt ++++ b/Modules/ThirdParty/VNL/src/CMakeLists.txt +@@ -18,7 +18,7 @@ add_subdirectory(vxl) + # Retrive the variable type to CACHE. + set(BUILD_EXAMPLES ${BUILD_EXAMPLES} CACHE BOOL "Build the examples from the ITK Software Guide." FORCE) + +-foreach(lib itkvcl itkv3p_netlib itktestlib itkvnl itkvnl_algo itknetlib) ++foreach(lib itkvcl itkv3p_netlib itktestlib itkvnl itkvnl_algo) + itk_module_target(${lib} NO_INSTALL) + endforeach() + +diff --git a/Modules/ThirdParty/VNL/src/vxl/config/cmake/Modules/FindNetlib.cmake b/Modules/ThirdParty/VNL/src/vxl/config/cmake/Modules/FindNetlib.cmake +index c953a8bbc3..0fba6dddf2 100644 +--- a/Modules/ThirdParty/VNL/src/vxl/config/cmake/Modules/FindNetlib.cmake ++++ b/Modules/ThirdParty/VNL/src/vxl/config/cmake/Modules/FindNetlib.cmake +@@ -9,4 +9,4 @@ + set( NETLIB_FOUND "YES" ) + set( NETLIB_INCLUDE_DIR ${VXL_ROOT_SOURCE_DIR}/v3p/netlib ) + set( NETLIB_INSTALL_INCLUDE_DIR ${CMAKE_INSTALL_PREFIX}/include/vxl/v3p/netlib ) +-set( NETLIB_LIBRARIES ${VXL_LIB_PREFIX}netlib ${VXL_LIB_PREFIX}v3p_netlib ) ++set( NETLIB_LIBRARIES ${VXL_LIB_PREFIX}v3p_netlib ) +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/CMakeLists.txt b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/CMakeLists.txt +index 726a25a834..310a47597c 100644 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/CMakeLists.txt ++++ b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/CMakeLists.txt +@@ -2,6 +2,8 @@ + + project( netlib C ) + ++# Incompatible with ITK's License ++if(0) + set(netlib_sources + # The "Triangle" program of Jonathan Richard Shewchuk + triangle.c triangle.h +@@ -13,6 +15,8 @@ vxl_add_library(LIBRARY_NAME ${VXL_LIB_PREFIX}netlib + if(UNIX) + target_link_libraries( ${VXL_LIB_PREFIX}netlib m ) + endif() ++# Incompatible with ITK's License ++endif() + + # Allow sources in subdirectories to see the include files. + include_directories(${netlib_SOURCE_DIR}) +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/examples/showme.c b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/examples/showme.c +deleted file mode 100644 +index 815d63a0fd..0000000000 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/examples/showme.c ++++ /dev/null +@@ -1,3392 +0,0 @@ +-/*****************************************************************************/ +-/* */ +-/* ,d88^^o 888 o o */ +-/* 8888 888o^88, o88^^o Y88b o / d8b d8b o88^^8o */ +-/* "Y88b 888 888 d888 b Y88b d8b / d888bdY88b d888 88b */ +-/* "Y88b, 888 888 8888 8 Y888/Y88b/ / Y88Y Y888b 8888oo888 */ +-/* o 8888 888 888 q888 p Y8/ Y8/ / YY Y888b q888 */ +-/* "oo88P" 888 888 "88oo" Y Y / Y888b "88oooo" */ +-/* */ +-/* A Display Program for Meshes and More. */ +-/* (showme.c) */ +-/* */ +-/* Version 1.3 */ +-/* July 20, 1996 */ +-/* */ +-/* Copyright 1996 */ +-/* Jonathan Richard Shewchuk */ +-/* School of Computer Science */ +-/* Carnegie Mellon University */ +-/* 5000 Forbes Avenue */ +-/* Pittsburgh, Pennsylvania 15213-3891 */ +-/* jrs@cs.cmu.edu */ +-/* */ +-/* This program may be freely redistributed under the condition that the */ +-/* copyright notices (including this entire header and the copyright */ +-/* notice printed when the `-h' switch is selected) are not removed, and */ +-/* no compensation is received. Private, research, and institutional */ +-/* use is free. You may distribute modified versions of this code UNDER */ +-/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ +-/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ +-/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ +-/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ +-/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ +-/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ +-/* customer, and you are instead telling them how they can obtain it for */ +-/* free, then you are not required to make any arrangement with me.) */ +-/* */ +-/* Hypertext instructions for Triangle are available on the Web at */ +-/* */ +-/* http://www.cs.cmu.edu/~quake/showme.html */ +-/* */ +-/* Show Me was created as part of the Archimedes project in the School of */ +-/* Computer Science at Carnegie Mellon University. Archimedes is a */ +-/* system for compiling parallel finite element solvers. For further */ +-/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */ +-/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */ +-/* and Shang-Hua Teng. "Automated Parallel Solution of Unstructured PDE */ +-/* Problems." To appear in Communications of the ACM, we hope. */ +-/* */ +-/* If you make any improvements to this code, please please please let me */ +-/* know, so that I may obtain the improvements. Even if you don't change */ +-/* the code, I'd still love to hear what it's being used for. */ +-/* */ +-/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ +-/* whatsoever. Use at your own risk. */ +-/* */ +-/*****************************************************************************/ +- +-/* For single precision (which will save some memory and reduce paging), */ +-/* write "#define SINGLE" below. */ +-/* */ +-/* For double precision (which will allow you to display triangulations of */ +-/* a finer resolution), leave SINGLE undefined. */ +- +-/* #define SINGLE */ +- +-#ifdef SINGLE +-#define REAL float +-#else +-#define REAL double +-#endif +- +-/* Maximum number of characters in a file name (including the null). */ +- +-#define FILENAMESIZE 1024 +- +-/* Maximum number of characters in a line read from a file (including the */ +-/* null). */ +- +-#define INPUTLINESIZE 512 +- +-#define STARTWIDTH 414 +-#define STARTHEIGHT 414 +-#define MINWIDTH 50 +-#define MINHEIGHT 50 +-#define BUTTONHEIGHT 21 +-#define BUTTONROWS 3 +-#define PANELHEIGHT (BUTTONHEIGHT * BUTTONROWS) +-#define MAXCOLORS 64 +- +-#define IMAGE_TYPES 7 +-#define NOTHING -1 +-#define NODE 0 +-#define POLY 1 +-#define ELE 2 +-#define EDGE 3 +-#define PART 4 +-#define ADJ 5 +-#define VORO 6 +- +-#define STARTEXPLOSION 0.5 +- +-#include +-#include +-#include +-#include +-#include +-#include +- +-/* The following obscenity seems to be necessary to ensure that this program */ +-/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */ +-/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */ +-/* exit() may or may not already be defined at this point. I declare these */ +-/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */ +- +-#if !defined(_STDLIB_H_) && !defined(_STDLIB_H) && defined(__need_malloc_and_calloc) +-extern char *malloc(); +-extern void free(); +-extern void exit(); +-extern double strtod(); +-extern long strtol(); +-#endif +- +-/* A necessary forward declaration. */ +- +-int load_image(); +- +-Display *display; +-int screen; +-Window rootwindow; +-Window mainwindow; +-Window quitwin; +-Window leftwin; +-Window rightwin; +-Window upwin; +-Window downwin; +-Window resetwin; +-Window pswin; +-Window epswin; +-Window expwin; +-Window exppluswin; +-Window expminuswin; +-Window widthpluswin; +-Window widthminuswin; +-Window versionpluswin; +-Window versionminuswin; +-Window fillwin; +-Window nodewin[2]; +-Window polywin[2]; +-Window elewin[2]; +-Window edgewin[2]; +-Window partwin[2]; +-Window adjwin[2]; +-Window voronoiwin[2]; +- +-int windowdepth; +-XEvent event; +-Colormap rootmap; +-XFontStruct *font; +-int width, height; +-int black, white; +-int showme_foreground; +-GC fontgc; +-GC blackfontgc; +-GC linegc; +-GC trianglegc; +-int colors[MAXCOLORS]; +-XColor rgb[MAXCOLORS]; +-int color; +- +-int start_image, current_image; +-int start_inc, current_inc; +-int loweriteration; +-int line_width; +-int loaded[2][IMAGE_TYPES]; +-REAL xlo[2][IMAGE_TYPES], ylo[2][IMAGE_TYPES]; +-REAL xhi[2][IMAGE_TYPES], yhi[2][IMAGE_TYPES]; +-REAL xscale, yscale; +-REAL xoffset, yoffset; +-int zoom; +- +-int nodes[2], node_dim[2]; +-REAL *nodeptr[2]; +-int polynodes[2], poly_dim[2], polyedges[2], polyholes[2]; +-REAL *polynodeptr[2], *polyholeptr[2]; +-int *polyedgeptr[2]; +-int elems[2], ele_corners[2]; +-int *eleptr[2]; +-int edges[2]; +-int *edgeptr[2]; +-REAL *normptr[2]; +-int subdomains[2]; +-int *partpart[2]; +-REAL *partcenter[2], *partshift[2]; +-int adjsubdomains[2]; +-int *adjptr[2]; +-int vnodes[2], vnode_dim[2]; +-REAL *vnodeptr[2]; +-int vedges[2]; +-int *vedgeptr[2]; +-REAL *vnormptr[2]; +-int firstnumber[2]; +- +-int quiet, fillelem, bw_ps, explode; +-REAL explosion; +- +-char filename[FILENAMESIZE]; +-char nodefilename[2][FILENAMESIZE]; +-char polyfilename[2][FILENAMESIZE]; +-char elefilename[2][FILENAMESIZE]; +-char edgefilename[2][FILENAMESIZE]; +-char partfilename[2][FILENAMESIZE]; +-char adjfilename[2][FILENAMESIZE]; +-char vnodefilename[2][FILENAMESIZE]; +-char vedgefilename[2][FILENAMESIZE]; +- +-const +-char *colorname[] = {"aquamarine", "red", "green yellow", "magenta", +- "yellow", "green", "orange", "blue", +- "white", "sandy brown", "cyan", "moccasin", +- "cadet blue", "coral", "cornflower blue", "sky blue", +- "firebrick", "forest green", "gold", "goldenrod", +- "gray", "hot pink", "chartreuse", "pale violet red", +- "indian red", "khaki", "lavender", "light blue", +- "light gray", "light steel blue", "lime green", "azure", +- "maroon", "medium aquamarine", "dodger blue", "honeydew", +- "medium orchid", "medium sea green", "moccasin", +- "medium slate blue", "medium spring green", +- "medium turquoise", "medium violet red", +- "orange red", "chocolate", "light goldenrod", +- "orchid", "pale green", "pink", "plum", +- "purple", "salmon", "sea green", +- "sienna", "slate blue", "spring green", +- "steel blue", "tan", "thistle", "turquoise", +- "violet", "violet red", "wheat", +- "yellow green"}; +- +-void syntax() +-{ +- printf("showme [-bfw_Qh] input_file\n"); +- printf(" -b Black and white PostScript (default is color).\n"); +- printf(" -f Fill triangles of partitioned mesh with color.\n"); +- printf(" -w Set line width to some specified number.\n"); +- printf(" -Q Quiet: No terminal output except errors.\n"); +- printf(" -h Help: Detailed instructions for Show Me.\n"); +- exit(0); +-} +- +-void info() +-{ +- printf("Show Me\n"); +- printf("A Display Program for Meshes and More.\n"); +- printf("Version 1.3\n\n"); +- printf( +-"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n" +-); +- printf("School of Computer Science / Carnegie Mellon University\n"); +- printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n"); +- printf( +-"Created as part of the Archimedes project (tools for parallel FEM).\n"); +- printf( +-"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); +- printf("There is no warranty whatsoever. Use at your own risk.\n"); +-#ifdef SINGLE +- printf("This executable is compiled for single precision arithmetic.\n\n\n"); +-#else +- printf("This executable is compiled for double precision arithmetic.\n\n\n"); +-#endif +- printf( +-"Show Me graphically displays the contents of geometric files, especially\n"); +- printf( +-"those generated by Triangle, my two-dimensional quality mesh generator and\n" +-); +- printf( +-"Delaunay triangulator. Show Me can also write images in PostScript form.\n"); +- printf( +-"Show Me is also useful for checking the consistency of the files you create\n" +-); +- printf( +-"as input to Triangle; Show Me does these checks more thoroughly than\n"); +- printf("Triangle does. The command syntax is:\n\n"); +- printf("showme [-bfw_Qh] input_file\n\n"); +- printf( +-"The underscore indicates that a number should follow the -w switch.\n"); +- printf( +-"input_file may be one of several types of file. It must have extension\n"); +- printf( +-".node, .poly, .ele, .edge, .part, or .adj. If no extension is provided,\n"); +- printf( +-"Show Me will assume the extension .ele. A .node file represents a set of\n"); +- printf( +-"points; a .poly file represents a Planar Straight Line Graph; an .ele file\n" +-); +- printf( +-"(coupled with a .node file) represents the elements of a mesh or the\n"); +- printf( +-"triangles of a triangulation; an .edge file (coupled with a .node file)\n"); +- printf( +-"represents a set of edges; a .part file specifies a partition of a mesh;\n"); +- printf( +-"and a .adj file represents the adjacency graph defined by a partition.\n"); +- printf("\n"); +- printf("Command Line Switches:\n"); +- printf("\n"); +- printf( +-" -b Makes all PostScript output black and white. If this switch is not\n" +-); +- printf( +-" selected, color PostScript is used for partitioned meshes and\n"); +- printf(" adjacency graphs (.part and .adj files).\n"); +- printf( +-" -f On color displays and in color PostScript, displays partitioned\n"); +- printf( +-" meshes by filling triangles with color, rather than by coloring the\n" +-); +- printf( +-" edges. This switch will result in a clearer picture if all\n"); +- printf( +-" triangles are reasonably large, and a less clear picture if small\n"); +- printf( +-" triangles are present. (There is also a button to toggle this\n"); +- printf(" behavior.)\n"); +- printf( +-" -w Followed by an integer, specifies the line width used in all\n"); +- printf( +-" images. (There are also buttons to change the line width.)\n"); +- printf( +-" -Q Quiet: Suppresses all explanation of what Show Me is doing, unless\n" +-); +- printf(" an error occurs.\n"); +- printf(" -h Help: Displays these instructions.\n"); +- printf("\n"); +- printf("Controls:\n"); +- printf("\n"); +- printf( +-" To zoom in on an image, point at the location where you want a closer\n"); +- printf( +-" look, and click the left mouse button. To zoom out, click the right\n"); +- printf( +-" mouse button. In either case, the point you click on will be centered in\n" +-); +- printf( +-" the window. If you want to know the coordinates of a point, click the\n"); +- printf( +-" middle mouse button; the coordinates will be printed on the terminal you\n" +-); +- printf(" invoked Show Me from.\n\n"); +- printf( +-" If you resize the window, the image will grow or shrink to match.\n"); +- printf("\n"); +- printf( +-" There is a panel of control buttons at the bottom of the Show Me window:\n" +-); +- printf("\n"); +- printf(" Quit: Shuts down Show Me.\n"); +- printf(" <, >, ^, v: Moves the image in the indicated direction.\n"); +- printf( +-" Reset: Unzooms and centers the image in the window. When you switch from\n" +-); +- printf( +-" one image to another, the viewing region does not change, so you may\n"); +- printf( +-" need to reset the new image to make it fully visible. This often is\n"); +- printf( +-" the case when switching between Delaunay triangulations and their\n"); +- printf( +-" corresponding Voronoi diagrams, as Voronoi vertices can be far from the\n" +-); +- printf(" initial point set.\n"); +- printf( +-" Width+, -: Increases or decreases the width of all lines and points.\n"); +- printf( +-" Exp, +, -: These buttons appear only when you are viewing a partitioned\n" +-); +- printf( +-" mesh (.part file). `Exp' toggles between an exploded and non-exploded\n" +-); +- printf( +-" image of the mesh. The non-exploded image will not show the partition\n" +-); +- printf( +-" on a black and white monitor. `+' and `-' allow you to adjust the\n"); +- printf( +-" spacing between pieces of the mesh to better distinguish them.\n"); +- printf( +-" Fill: This button appears only when you are viewing a partitioned mesh\n"); +- printf( +-" (.part file). It toggles between color-filled triangles and colored\n"); +- printf( +-" edges (as the -f switch does). Filled triangles look better when all\n"); +- printf( +-" triangles are reasonably large; colored edges look better when there\n"); +- printf(" are very small triangles present.\n"); +- printf( +-" PS: Creates a PostScript file containing the image you are viewing. If\n" +-); +- printf( +-" the -b switch is selected, all PostScript output will be black and\n"); +- printf( +-" white; otherwise, .part.ps and .adj.ps files will be color, independent\n" +-); +- printf( +-" of whether you are using a color monitor. Normally the output will\n"); +- printf( +-" preserve the properties of the image you see on the screen, including\n"); +- printf( +-" zoom and line width; however, if black and white output is selected (-b\n" +-); +- printf( +-" switch), partitioned meshes will always be drawn exploded. The output\n" +-); +- printf( +-" file name depends on the image being viewed. If you want several\n"); +- printf( +-" different snapshots (zooming in on different parts) of the same object,\n" +-); +- printf( +-" you'll have to rename each file after Show Me creates it so that it\n"); +- printf(" isn't overwritten by the next snapshot.\n"); +- printf( +-" EPS: Creates an encapsulated PostScript file, suitable for inclusion in\n" +-); +- printf( +-" documents. Otherwise, this button is just like the PS button. (The\n"); +- printf( +-" main difference is that .eps files lack a `showpage' command at the\n"); +- printf(" end.)\n\n"); +- printf( +-" There are two nearly-identical rows of buttons that load different images\n" +-); +- printf(" from disk. Each row contains the following buttons:\n\n"); +- printf(" node: Loads a .node file.\n"); +- printf( +-" poly: Loads a .poly file (and possibly an associated .node file).\n"); +- printf(" ele: Loads an .ele file (and associated .node file).\n"); +- printf(" edge: Loads an .edge file (and associated .node file).\n"); +- printf( +-" part: Loads a .part file (and associated .node and .ele files).\n"); +- printf( +-" adj: Loads an .adj file (and associated .node, .ele, and .part files).\n"); +- printf(" voro: Loads a .v.node and .v.edge file for a Voronoi diagram.\n"); +- printf("\n"); +- printf( +-" Each row represents a different iteration number of the geometry files.\n"); +- printf( +-" For a full explanation of iteration numbers, read the instructions for\n"); +- printf( +-" Triangle. Briefly, iteration numbers are used to allow a user to easily\n" +-); +- printf( +-" represent a sequence of related triangulations. Iteration numbers are\n"); +- printf( +-" used in the names of geometry files; for instance, mymesh.3.ele is a\n"); +- printf( +-" triangle file with iteration number three, and mymesh.ele has an implicit\n" +-); +- printf(" iteration number of zero.\n\n"); +- printf( +-" The control buttons at the right end of each row display the two\n"); +- printf( +-" iterations currently under view. These buttons can be clicked to\n"); +- printf( +-" increase or decrease the iteration numbers, and thus conveniently view\n"); +- printf(" a sequence of meshes.\n\n"); +- printf( +-" Show Me keeps each file in memory after loading it, but you can force\n"); +- printf( +-" Show Me to reread a set of files (for one iteration number) by reclicking\n" +-); +- printf( +-" the button that corresponds to the current image. This is convenient if\n" +-); +- printf(" you have changed a geometry file.\n\n"); +- printf("File Formats:\n\n"); +- printf( +-" All files may contain comments prefixed by the character '#'. Points,\n"); +- printf( +-" segments, holes, triangles, edges, and subdomains must be numbered\n"); +- printf( +-" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); +- printf( +-" input files must be consistent (for any single iteration number); if the\n" +-); +- printf( +-" nodes are numbered from 1, so must be all other objects. Show Me\n"); +- printf( +-" automatically detects your choice while reading a .node (or .poly) file.\n" +-); +- printf(" Examples of these file formats are given below.\n\n"); +- printf(" .node files:\n"); +- printf( +-" First line: <# of points> <# of attributes>\n"); +- printf( +-" <# of boundary markers (0 or 1)>\n" +-); +- printf( +-" Remaining lines: [attributes] [boundary marker]\n"); +- printf("\n"); +- printf( +-" The attributes, which are typically floating-point values of physical\n"); +- printf( +-" quantities (such as mass or conductivity) associated with the nodes of\n" +-); +- printf( +-" a finite element mesh, are ignored by Show Me. Show Me also ignores\n"); +- printf( +-" boundary markers. See the instructions for Triangle to find out what\n"); +- printf(" attributes and boundary markers are.\n\n"); +- printf(" .poly files:\n"); +- printf( +-" First line: <# of points> <# of attributes>\n"); +- printf( +-" <# of boundary markers (0 or 1)>\n" +-); +- printf( +-" Following lines: [attributes] [boundary marker]\n"); +- printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); +- printf( +-" Following lines: [boundary marker]\n"); +- printf(" One line: <# of holes>\n"); +- printf(" Following lines: \n"); +- printf(" [Optional additional lines that are ignored]\n\n"); +- printf( +-" A .poly file represents a Planar Straight Line Graph (PSLG), an idea\n"); +- printf( +-" familiar to computational geometers. By definition, a PSLG is just a\n"); +- printf( +-" list of points and edges. A .poly file also contains some additional\n"); +- printf(" information.\n\n"); +- printf( +-" The first section lists all the points, and is identical to the format\n" +-); +- printf( +-" of .node files. <# of points> may be set to zero to indicate that the\n" +-); +- printf( +-" points are listed in a separate .node file; .poly files produced by\n"); +- printf( +-" Triangle always have this format. When Show Me reads such a file, it\n"); +- printf(" also reads the corresponding .node file.\n\n"); +- printf( +-" The second section lists the segments. Segments are edges whose\n"); +- printf( +-" presence in a triangulation produced from the PSLG is enforced. Each\n"); +- printf( +-" segment is specified by listing the indices of its two endpoints. This\n" +-); +- printf( +-" means that its endpoints must be included in the point list. Each\n"); +- printf( +-" segment, like each point, may have a boundary marker, which is ignored\n" +-); +- printf(" by Show Me.\n\n"); +- printf( +-" The third section lists holes and concavities that are desired in any\n"); +- printf( +-" triangulation generated from the PSLG. Holes are specified by\n"); +- printf(" identifying a point inside each hole.\n\n"); +- printf(" .ele files:\n"); +- printf( +-" First line: <# of triangles> <# of attributes>\n"); +- printf( +-" Remaining lines: ... [attributes]\n" +-); +- printf("\n"); +- printf( +-" Points are indices into the corresponding .node file. Show Me ignores\n" +-); +- printf( +-" all but the first three points of each triangle; these should be the\n"); +- printf( +-" corners listed in counterclockwise order around the triangle. The\n"); +- printf(" attributes are ignored by Show Me.\n\n"); +- printf(" .edge files:\n"); +- printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); +- printf( +-" Following lines: [boundary marker]\n"); +- printf("\n"); +- printf( +-" Endpoints are indices into the corresponding .node file. The boundary\n" +-); +- printf(" markers are ignored by Show Me.\n\n"); +- printf( +-" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); +- printf( +-" infinite ray with only one endpoint. For these edges, a different\n"); +- printf(" format is used:\n\n"); +- printf(" -1 \n\n"); +- printf( +-" The `direction' is a floating-point vector that indicates the direction\n" +-); +- printf(" of the infinite ray.\n\n"); +- printf(" .part files:\n"); +- printf(" First line: <# of triangles> <# of subdomains>\n"); +- printf(" Remaining lines: \n\n"); +- printf( +-" The set of triangles is partitioned by a .part file; each triangle is\n"); +- printf(" mapped to a subdomain.\n\n"); +- printf(" .adj files:\n"); +- printf(" First line: <# of subdomains>\n"); +- printf(" Remaining lines: \n\n"); +- printf( +-" An .adj file represents adjacencies between subdomains (presumably\n"); +- printf(" computed by a partitioner). The first line is followed by\n"); +- printf( +-" (subdomains X subdomains) lines, each containing one entry of the\n"); +- printf( +-" adjacency matrix. A nonzero entry indicates that two subdomains are\n"); +- printf(" adjacent (share a point).\n\n"); +- printf("Example:\n\n"); +- printf( +-" Here is a sample file `box.poly' describing a square with a square hole:\n" +-); +- printf("\n"); +- printf( +-" # A box with eight points in 2D, no attributes, no boundary marker.\n"); +- printf(" 8 2 0 0\n"); +- printf(" # Outer box has these vertices:\n"); +- printf(" 1 0 0\n"); +- printf(" 2 0 3\n"); +- printf(" 3 3 0\n"); +- printf(" 4 3 3\n"); +- printf(" # Inner square has these vertices:\n"); +- printf(" 5 1 1\n"); +- printf(" 6 1 2\n"); +- printf(" 7 2 1\n"); +- printf(" 8 2 2\n"); +- printf(" # Five segments without boundary markers.\n"); +- printf(" 5 0\n"); +- printf(" 1 1 2 # Left side of outer box.\n"); +- printf(" 2 5 7 # Segments 2 through 5 enclose the hole.\n"); +- printf(" 3 7 8\n"); +- printf(" 4 8 6\n"); +- printf(" 5 6 5\n"); +- printf(" # One hole in the middle of the inner square.\n"); +- printf(" 1\n"); +- printf(" 1 1.5 1.5\n\n"); +- printf( +-" After this PSLG is triangulated by Triangle, the resulting triangulation\n" +-); +- printf( +-" consists of a .node and .ele file. Here is the former, `box.1.node',\n"); +- printf(" which duplicates the points of the PSLG:\n\n"); +- printf(" 8 2 0 0\n"); +- printf(" 1 0 0\n"); +- printf(" 2 0 3\n"); +- printf(" 3 3 0\n"); +- printf(" 4 3 3\n"); +- printf(" 5 1 1\n"); +- printf(" 6 1 2\n"); +- printf(" 7 2 1\n"); +- printf(" 8 2 2\n"); +- printf(" # Generated by triangle -pcBev box\n"); +- printf("\n"); +- printf(" Here is the triangulation file, `box.1.ele'.\n"); +- printf("\n"); +- printf(" 8 3 0\n"); +- printf(" 1 1 5 6\n"); +- printf(" 2 5 1 3\n"); +- printf(" 3 2 6 8\n"); +- printf(" 4 6 2 1\n"); +- printf(" 5 7 3 4\n"); +- printf(" 6 3 7 5\n"); +- printf(" 7 8 4 2\n"); +- printf(" 8 4 8 7\n"); +- printf(" # Generated by triangle -pcBev box\n\n"); +- printf(" Here is the edge file for the triangulation, `box.1.edge'.\n\n"); +- printf(" 16 0\n"); +- printf(" 1 1 5\n"); +- printf(" 2 5 6\n"); +- printf(" 3 6 1\n"); +- printf(" 4 1 3\n"); +- printf(" 5 3 5\n"); +- printf(" 6 2 6\n"); +- printf(" 7 6 8\n"); +- printf(" 8 8 2\n"); +- printf(" 9 2 1\n"); +- printf(" 10 7 3\n"); +- printf(" 11 3 4\n"); +- printf(" 12 4 7\n"); +- printf(" 13 7 5\n"); +- printf(" 14 8 4\n"); +- printf(" 15 4 2\n"); +- printf(" 16 8 7\n"); +- printf(" # Generated by triangle -pcBev box\n"); +- printf("\n"); +- printf( +-" Here's a file `box.1.part' that partitions the mesh into four subdomains.\n" +-); +- printf("\n"); +- printf(" 8 4\n"); +- printf(" 1 3\n"); +- printf(" 2 3\n"); +- printf(" 3 4\n"); +- printf(" 4 4\n"); +- printf(" 5 1\n"); +- printf(" 6 1\n"); +- printf(" 7 2\n"); +- printf(" 8 2\n"); +- printf(" # Generated by slice -s4 box.1\n\n"); +- printf( +-" Here's a file `box.1.adj' that represents the resulting adjacencies.\n"); +- printf("\n"); +- printf(" 4\n"); +- printf(" 9\n"); +- printf(" 2\n"); +- printf(" 2\n"); +- printf(" 0\n"); +- printf(" 2\n"); +- printf(" 9\n"); +- printf(" 0\n"); +- printf(" 2\n"); +- printf(" 2\n"); +- printf(" 0\n"); +- printf(" 9\n"); +- printf(" 2\n"); +- printf(" 0\n"); +- printf(" 2\n"); +- printf(" 2\n"); +- printf(" 9\n"); +- printf("\n"); +- printf("Display Speed:\n"); +- printf("\n"); +- printf( +-" It is worthwhile to note that .edge files typically plot and print twice\n" +-); +- printf( +-" as quickly as .ele files, because .ele files cause each internal edge to\n" +-); +- printf( +-" be drawn twice. For the same reason, PostScript files created from edge\n" +-); +- printf(" sets are smaller than those created from triangulations.\n\n"); +- printf("Show Me on the Web:\n\n"); +- printf( +-" To see an illustrated, updated version of these instructions, check out\n"); +- printf("\n"); +- printf(" http://www.cs.cmu.edu/~quake/showme.html\n"); +- printf("\n"); +- printf("A Brief Plea:\n"); +- printf("\n"); +- printf( +-" If you use Show Me (or Triangle), and especially if you use it to\n"); +- printf( +-" accomplish real work, I would like very much to hear from you. A short\n"); +- printf( +-" letter or email (to jrs@cs.cmu.edu) describing how you use Show Me (and\n"); +- printf( +-" its sister programs) will mean a lot to me. The more people I know\n"); +- printf( +-" are using my programs, the more easily I can justify spending time on\n"); +- printf( +-" improvements, which in turn will benefit you. Also, I can put you\n"); +- printf( +-" on a list to receive email whenever new versions are available.\n"); +- printf("\n"); +- printf( +-" If you use a PostScript file generated by Show Me in a publication,\n"); +- printf(" please include an acknowledgment as well.\n\n"); +- exit(0); +-} +- +-void set_filenames(filename, lowermeshnumber) +-char *filename; +-int lowermeshnumber; +-{ +- char numberstring[100]; +- int i; +- +- for (i = 0; i < 2; i++) { +- strcpy(nodefilename[i], filename); +- strcpy(polyfilename[i], filename); +- strcpy(elefilename[i], filename); +- strcpy(edgefilename[i], filename); +- strcpy(partfilename[i], filename); +- strcpy(adjfilename[i], filename); +- strcpy(vnodefilename[i], filename); +- strcpy(vedgefilename[i], filename); +- +- if (lowermeshnumber + i > 0) { +- sprintf(numberstring, ".%d", lowermeshnumber + i); +- strcat(nodefilename[i], numberstring); +- strcat(polyfilename[i], numberstring); +- strcat(elefilename[i], numberstring); +- strcat(edgefilename[i], numberstring); +- strcat(partfilename[i], numberstring); +- strcat(adjfilename[i], numberstring); +- strcat(vnodefilename[i], numberstring); +- strcat(vedgefilename[i], numberstring); +- } +- +- strcat(nodefilename[i], ".node"); +- strcat(polyfilename[i], ".poly"); +- strcat(elefilename[i], ".ele"); +- strcat(edgefilename[i], ".edge"); +- strcat(partfilename[i], ".part"); +- strcat(adjfilename[i], ".adj"); +- strcat(vnodefilename[i], ".v.node"); +- strcat(vedgefilename[i], ".v.edge"); +- } +-} +- +-#if 1 /* This function is already in netlib.lib, see triangle.c */ +-void parsecommandline(int argc, char **argv); +-#else +-void parsecommandline(argc, argv) +-int argc; +-char **argv; +-{ +- int increment; +- int meshnumber; +- int i, j; +- +- quiet = 0; +- fillelem = 0; +- line_width = 1; +- bw_ps = 0; +- start_image = ELE; +- filename[0] = '\0'; +- for (i = 1; i < argc; i++) { +- if (argv[i][0] == '-') { +- for (j = 1; argv[i][j] != '\0'; j++) { +- if (argv[i][j] == 'f') { +- fillelem = 1; +- } +- if (argv[i][j] == 'w') { +- if ((argv[i][j + 1] >= '1') && (argv[i][j + 1] <= '9')) { +- line_width = 0; +- while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { +- j++; +- line_width = line_width * 10 + (int) (argv[i][j] - '0'); +- } +- if (line_width > 100) { +- printf("Error: Line width cannot exceed 100.\n"); +- line_width = 1; +- } +- } +- } +- if (argv[i][j] == 'b') { +- bw_ps = 1; +- } +- if (argv[i][j] == 'Q') { +- quiet = 1; +- } +- if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || +- (argv[i][j] == '?')) { +- info(); +- } +- } +- } else { +- strcpy(filename, argv[i]); +- } +- } +- if (filename[0] == '\0') { +- syntax(); +- } +- if (!strcmp(&filename[strlen(filename) - 5], ".node")) { +- filename[strlen(filename) - 5] = '\0'; +- start_image = NODE; +- } +- if (!strcmp(&filename[strlen(filename) - 5], ".poly")) { +- filename[strlen(filename) - 5] = '\0'; +- start_image = POLY; +- } +- if (!strcmp(&filename[strlen(filename) - 4], ".ele")) { +- filename[strlen(filename) - 4] = '\0'; +- start_image = ELE; +- } +- if (!strcmp(&filename[strlen(filename) - 5], ".edge")) { +- filename[strlen(filename) - 5] = '\0'; +- start_image = EDGE; +- } +- if (!strcmp(&filename[strlen(filename) - 5], ".part")) { +- filename[strlen(filename) - 5] = '\0'; +- start_image = PART; +- } +- if (!strcmp(&filename[strlen(filename) - 4], ".adj")) { +- filename[strlen(filename) - 4] = '\0'; +- start_image = ADJ; +- } +- +- increment = 0; +- j = 1; +- while (filename[j] != '\0') { +- if ((filename[j] == '.') && (filename[j + 1] != '\0')) { +- increment = j + 1; +- } +- j++; +- } +- meshnumber = 0; +- if (increment > 0) { +- j = increment; +- do { +- if ((filename[j] >= '0') && (filename[j] <= '9')) { +- meshnumber = meshnumber * 10 + (int) (filename[j] - '0'); +- } else { +- increment = 0; +- } +- j++; +- } while (filename[j] != '\0'); +- } +- if (increment > 0) { +- filename[increment - 1] = '\0'; +- } +- +- if (meshnumber == 0) { +- start_inc = 0; +- loweriteration = 0; +- } else { +- start_inc = 1; +- loweriteration = meshnumber - 1; +- } +- set_filenames(filename, loweriteration); +-} +-#endif /* 0 */ +- +-void free_inc(inc) +-int inc; +-{ +- if (loaded[inc][NODE]) { +- free(nodeptr[inc]); +- } +- if (loaded[inc][POLY]) { +- if (polynodes[inc] > 0) { +- free(polynodeptr[inc]); +- } +- free(polyedgeptr[inc]); +- free(polyholeptr[inc]); +- } +- if (loaded[inc][ELE]) { +- free(eleptr[inc]); +- } +- if (loaded[inc][PART]) { +- free(partpart[inc]); +- free(partcenter[inc]); +- free(partshift[inc]); +- } +- if (loaded[inc][EDGE]) { +- free(edgeptr[inc]); +- free(normptr[inc]); +- } +- if (loaded[inc][ADJ]) { +- free(adjptr[inc]); +- } +- if (loaded[inc][VORO]) { +- free(vnodeptr[inc]); +- free(vedgeptr[inc]); +- free(vnormptr[inc]); +- } +-} +- +-void move_inc(inc) +-int inc; +-{ +- int i; +- +- free_inc(1 - inc); +- for (i = 0; i < IMAGE_TYPES; i++) { +- loaded[1 - inc][i] = loaded[inc][i]; +- loaded[inc][i] = 0; +- xlo[1 - inc][i] = xlo[inc][i]; +- ylo[1 - inc][i] = ylo[inc][i]; +- xhi[1 - inc][i] = xhi[inc][i]; +- yhi[1 - inc][i] = yhi[inc][i]; +- } +- nodes[1 - inc] = nodes[inc]; +- node_dim[1 - inc] = node_dim[inc]; +- nodeptr[1 - inc] = nodeptr[inc]; +- polynodes[1 - inc] = polynodes[inc]; +- poly_dim[1 - inc] = poly_dim[inc]; +- polyedges[1 - inc] = polyedges[inc]; +- polyholes[1 - inc] = polyholes[inc]; +- polynodeptr[1 - inc] = polynodeptr[inc]; +- polyedgeptr[1 - inc] = polyedgeptr[inc]; +- polyholeptr[1 - inc] = polyholeptr[inc]; +- elems[1 - inc] = elems[inc]; +- ele_corners[1 - inc] = ele_corners[inc]; +- eleptr[1 - inc] = eleptr[inc]; +- edges[1 - inc] = edges[inc]; +- edgeptr[1 - inc] = edgeptr[inc]; +- normptr[1 - inc] = normptr[inc]; +- subdomains[1 - inc] = subdomains[inc]; +- partpart[1 - inc] = partpart[inc]; +- partcenter[1 - inc] = partcenter[inc]; +- partshift[1 - inc] = partshift[inc]; +- adjsubdomains[1 - inc] = adjsubdomains[inc]; +- adjptr[1 - inc] = adjptr[inc]; +- vnodes[1 - inc] = vnodes[inc]; +- vnode_dim[1 - inc] = vnode_dim[inc]; +- vnodeptr[1 - inc] = vnodeptr[inc]; +- vedges[1 - inc] = vedges[inc]; +- vedgeptr[1 - inc] = vedgeptr[inc]; +- vnormptr[1 - inc] = vnormptr[inc]; +- firstnumber[1 - inc] = firstnumber[inc]; +- firstnumber[inc] = -1; +-} +- +-void unload_inc(inc) +-int inc; +-{ +- int i; +- +- current_image = NOTHING; +- for (i = 0; i < IMAGE_TYPES; i++) { +- loaded[inc][i] = 0; +- firstnumber[inc] = -1; +- } +-} +- +-void showme_init() +-{ +- current_image = NOTHING; +- current_inc = 0; +- explosion = STARTEXPLOSION; +- unload_inc(0); +- unload_inc(1); +-} +- +-char *readline(string, infile, infilename) +-char *string; +-FILE *infile; +-char *infilename; +-{ +- char *result; +- +- do { +- result = fgets(string, INPUTLINESIZE, infile); +- if (result == (char *) NULL) { +- printf(" Error: Unexpected end of file in %s.\n", +- infilename); +- exit(1); +- } +- while ((*result != '\0') && (*result != '#') +- && (*result != '.') && (*result != '+') && (*result != '-') +- && ((*result < '0') || (*result > '9'))) { +- result++; +- } +- } while ((*result == '#') || (*result == '\0')); +- return result; +-} +- +-char *findfield(string) +-char *string; +-{ +- char *result; +- +- result = string; +- while ((*result != '\0') && (*result != '#') +- && (*result != ' ') && (*result != '\t')) { +- result++; +- } +- while ((*result != '\0') && (*result != '#') +- && (*result != '.') && (*result != '+') && (*result != '-') +- && ((*result < '0') || (*result > '9'))) { +- result++; +- } +- if (*result == '#') { +- *result = '\0'; +- } +- return result; +-} +- +-int load_node(fname, firstnumber, nodes, dim, ptr, xmin, ymin, xmax, ymax) +-char *fname; +-int *firstnumber; +-int *nodes; +-int *dim; +-REAL **ptr; +-REAL *xmin; +-REAL *ymin; +-REAL *xmax; +-REAL *ymax; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int extras; +- int nodemarks; +- int index; +- int nodenumber; +- int i, j; +- int smallerr; +- REAL x, y; +- +- *xmin = *ymin = 0.0; +- *xmax = *ymax = 1.0; +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- *nodes = (int) strtol (stringptr, &stringptr, 0); +- if (*nodes < 3) { +- printf(" Error: %s contains %d points.\n", fname, *nodes); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- *dim = 2; +- } else { +- *dim = (int) strtol (stringptr, &stringptr, 0); +- } +- if (*dim < 1) { +- printf(" Error: %s has dimensionality %d.\n", fname, *dim); +- return 1; +- } +- if (*dim != 2) { +- printf(" I only understand two-dimensional meshes.\n"); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- extras = 0; +- } else { +- extras = (int) strtol (stringptr, &stringptr, 0); +- } +- if (extras < 0) { +- printf(" Error: %s has negative value for number of attributes.\n", +- fname); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- nodemarks = 0; +- } else { +- nodemarks = (int) strtol (stringptr, &stringptr, 0); +- } +- if (nodemarks < 0) { +- printf(" Warning: %s has negative value for number of point markers.\n", +- fname); +- } +- if (nodemarks > 1) { +- printf( +- " Warning: %s has value greater than one for number of point markers.\n", +- fname); +- } +- *ptr = (REAL *) malloc((*nodes + 1) * *dim * sizeof(REAL)); +- if (*ptr == (REAL *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- index = *dim; +- smallerr = 1; +- for (i = 0; i < *nodes; i++) { +- stringptr = readline(inputline, infile, fname); +- nodenumber = (int) strtol (stringptr, &stringptr, 0); +- if ((i == 0) && (*firstnumber == -1)) { +- if (nodenumber == 0) { +- *firstnumber = 0; +- } else { +- *firstnumber = 1; +- } +- } +- if ((nodenumber != *firstnumber + i) && (smallerr)) { +- printf(" Warning: Points in %s are not numbered correctly\n", fname); +- printf(" (starting with point %d).\n", *firstnumber + i); +- smallerr = 0; +- } +- for (j = 0; j < *dim; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Point %d is missing a coordinate in %s.\n", +- *firstnumber + i, fname); +- free(*ptr); +- return 1; +- } +- (*ptr)[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- } +- fclose(infile); +- index = *dim; +- *xmin = *xmax = (*ptr)[index]; +- *ymin = *ymax = (*ptr)[index + 1]; +- for (i = 2; i <= *nodes; i++) { +- index += *dim; +- x = (*ptr)[index]; +- y = (*ptr)[index + 1]; +- if (x < *xmin) { +- *xmin = x; +- } +- if (y < *ymin) { +- *ymin = y; +- } +- if (x > *xmax) { +- *xmax = x; +- } +- if (y > *ymax) { +- *ymax = y; +- } +- } +- if (*xmin == *xmax) { +- *xmin -= 0.5; +- *xmax += 0.5; +- } +- if (*ymin == *ymax) { +- *ymin -= 0.5; +- *ymax += 0.5; +- } +- return 0; +-} +- +-int load_poly(inc, fname, firstnumber, pnodes, dim, edges, holes, nodeptr, +- edgeptr, holeptr, xmin, ymin, xmax, ymax) +-int inc; +-char *fname; +-int *firstnumber; +-int *pnodes; +-int *dim; +-int *edges; +-int *holes; +-REAL **nodeptr; +-int **edgeptr; +-REAL **holeptr; +-REAL *xmin; +-REAL *ymin; +-REAL *xmax; +-REAL *ymax; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int extras; +- int nodemarks; +- int segmentmarks; +- int index; +- int nodenumber, edgenumber, holenumber; +- int maxnode; +- int i, j; +- int smallerr; +- REAL x, y; +- +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- *pnodes = (int) strtol (stringptr, &stringptr, 0); +- if (*pnodes == 0) { +- if (!loaded[inc][NODE]) { +- if (load_image(inc, NODE)) { +- return 1; +- } +- } +- maxnode = nodes[inc]; +- *xmin = xlo[inc][NODE]; +- *ymin = ylo[inc][NODE]; +- *xmax = xhi[inc][NODE]; +- *ymax = yhi[inc][NODE]; +- } else { +- if (*pnodes < 1) { +- printf(" Error: %s contains %d points.\n", fname, *pnodes); +- return 1; +- } +- maxnode = *pnodes; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- *dim = 2; +- } else { +- *dim = (int) strtol (stringptr, &stringptr, 0); +- } +- if (*dim < 1) { +- printf(" Error: %s has dimensionality %d.\n", fname, *dim); +- return 1; +- } +- if (*dim != 2) { +- printf(" I only understand two-dimensional meshes.\n"); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- extras = 0; +- } else { +- extras = (int) strtol (stringptr, &stringptr, 0); +- } +- if (extras < 0) { +- printf(" Error: %s has negative value for number of attributes.\n", +- fname); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- nodemarks = 0; +- } else { +- nodemarks = (int) strtol (stringptr, &stringptr, 0); +- } +- if (nodemarks < 0) { +- printf(" Warning: %s has negative value for number of point markers.\n", +- fname); +- } +- if (nodemarks > 1) { +- printf( +- " Warning: %s has value greater than one for number of point markers.\n", +- fname); +- } +- if (*pnodes > 0) { +- *nodeptr = (REAL *) malloc((*pnodes + 1) * *dim * sizeof(REAL)); +- if (*nodeptr == (REAL *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- index = *dim; +- smallerr = 1; +- for (i = 0; i < *pnodes; i++) { +- stringptr = readline(inputline, infile, fname); +- nodenumber = (int) strtol (stringptr, &stringptr, 0); +- if ((i == 0) && (*firstnumber == -1)) { +- if (nodenumber == 0) { +- *firstnumber = 0; +- } else { +- *firstnumber = 1; +- } +- } +- if ((nodenumber != *firstnumber + i) && (smallerr)) { +- printf(" Warning: Points in %s are not numbered correctly.\n", +- fname); +- printf(" (starting with point %d).\n", *firstnumber + i); +- smallerr = 0; +- } +- for (j = 0; j < *dim; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Point %d is missing a coordinate in %s.\n", +- *firstnumber + i, fname); +- free(*nodeptr); +- return 1; +- } +- (*nodeptr)[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- } +- } +- stringptr = readline(inputline, infile, fname); +- *edges = (int) strtol (stringptr, &stringptr, 0); +- if (*edges < 0) { +- printf(" Error: %s contains %d segments.\n", fname, *edges); +- free(*nodeptr); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- segmentmarks = 0; +- } else { +- segmentmarks = (int) strtol (stringptr, &stringptr, 0); +- } +- if (segmentmarks < 0) { +- printf(" Error: %s has negative value for number of segment markers.\n", +- fname); +- free(*nodeptr); +- return 1; +- } +- if (segmentmarks > 1) { +- printf( +- " Error: %s has value greater than one for number of segment markers.\n", +- fname); +- free(*nodeptr); +- return 1; +- } +- *edgeptr = (int *) malloc(((*edges + 1) << 1) * sizeof(int)); +- if (*edgeptr == (int *) NULL) { +- printf(" Out of memory.\n"); +- free(*nodeptr); +- return 1; +- } +- index = 2; +- smallerr = 1; +- for (i = *firstnumber; i < *firstnumber + *edges; i++) { +- stringptr = readline(inputline, infile, fname); +- edgenumber = (int) strtol (stringptr, &stringptr, 0); +- if ((edgenumber != i) && (smallerr)) { +- printf(" Warning: Segments in %s are not numbered correctly.\n", +- fname); +- printf(" (starting with segment %d).\n", i); +- smallerr = 0; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %d is missing its endpoints in %s.\n", i, fname); +- free(*nodeptr); +- free(*edgeptr); +- return 1; +- } +- (*edgeptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - +- *firstnumber; +- if (((*edgeptr)[index] < 1) || ((*edgeptr)[index] > maxnode)) { +- printf("Error: Segment %d has invalid endpoint in %s.\n", i, fname); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %d is missing an endpoint in %s.\n", i, fname); +- free(*nodeptr); +- free(*edgeptr); +- return 1; +- } +- (*edgeptr)[index + 1] = (int) strtol (stringptr, &stringptr, 0) + 1 - +- *firstnumber; +- if (((*edgeptr)[index + 1] < 1) || ((*edgeptr)[index + 1] > maxnode)) { +- printf("Error: Segment %d has invalid endpoint in %s.\n", i, fname); +- return 1; +- } +- index += 2; +- } +- stringptr = readline(inputline, infile, fname); +- *holes = (int) strtol (stringptr, &stringptr, 0); +- if (*holes < 0) { +- printf(" Error: %s contains %d holes.\n", fname, *holes); +- free(*nodeptr); +- free(*edgeptr); +- return 1; +- } +- *holeptr = (REAL *) malloc((*holes + 1) * *dim * sizeof(REAL)); +- if (*holeptr == (REAL *) NULL) { +- printf(" Out of memory.\n"); +- free(*nodeptr); +- free(*edgeptr); +- return 1; +- } +- index = *dim; +- smallerr = 1; +- for (i = *firstnumber; i < *firstnumber + *holes; i++) { +- stringptr = readline(inputline, infile, fname); +- holenumber = (int) strtol (stringptr, &stringptr, 0); +- if ((holenumber != i) && (smallerr)) { +- printf(" Warning: Holes in %s are not numbered correctly.\n", fname); +- printf(" (starting with hole %d).\n", i); +- smallerr = 0; +- } +- for (j = 0; j < *dim; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Hole %d is missing a coordinate in %s.\n", i, +- fname); +- free(*nodeptr); +- free(*edgeptr); +- free(*holeptr); +- return 1; +- } +- (*holeptr)[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- } +- fclose(infile); +- if (*pnodes > 0) { +- index = *dim; +- *xmin = *xmax = (*nodeptr)[index]; +- *ymin = *ymax = (*nodeptr)[index + 1]; +- for (i = 2; i <= *pnodes; i++) { +- index += *dim; +- x = (*nodeptr)[index]; +- y = (*nodeptr)[index + 1]; +- if (x < *xmin) { +- *xmin = x; +- } +- if (y < *ymin) { +- *ymin = y; +- } +- if (x > *xmax) { +- *xmax = x; +- } +- if (y > *ymax) { +- *ymax = y; +- } +- } +- } +- index = *dim; +- for (i = 1; i <= *holes; i++) { +- x = (*holeptr)[index]; +- y = (*holeptr)[index + 1]; +- if (x < *xmin) { +- *xmin = x; +- } +- if (y < *ymin) { +- *ymin = y; +- } +- if (x > *xmax) { +- *xmax = x; +- } +- if (y > *ymax) { +- *ymax = y; +- } +- index += *dim; +- } +- return 0; +-} +- +-int load_ele(fname, firstnumber, nodes, elems, corners, ptr) +-char *fname; +-int firstnumber; +-int nodes; +-int *elems; +-int *corners; +-int **ptr; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int extras; +- int index; +- int elemnumber; +- int i, j; +- int smallerr; +- +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- *elems = (int) strtol (stringptr, &stringptr, 0); +- if (*elems < 1) { +- printf(" Error: %s contains %d triangles.\n", fname, *elems); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- *corners = 3; +- } else { +- *corners = (int) strtol (stringptr, &stringptr, 0); +- } +- if (*corners < 3) { +- printf(" Error: Triangles in %s have only %d corners.\n", fname, +- *corners); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- extras = 0; +- } else { +- extras = (int) strtol (stringptr, &stringptr, 0); +- } +- if (extras < 0) { +- printf(" Error: %s has negative value for extra fields.\n", fname); +- return 1; +- } +- *ptr = (int *) malloc((*elems + 1) * 3 * sizeof(int)); +- if (*ptr == (int *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- index = 3; +- smallerr = 1; +- for (i = firstnumber; i < firstnumber + *elems; i++) { +- stringptr = readline(inputline, infile, fname); +- elemnumber = (int) strtol (stringptr, &stringptr, 0); +- if ((elemnumber != i) && (smallerr)) { +- printf(" Warning: Triangles in %s are not numbered correctly.\n", +- fname); +- printf(" (starting with triangle %d).\n", i); +- smallerr = 0; +- } +- for (j = 0; j < 3; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Triangle %d is missing a corner in %s.\n", i, fname); +- free(*ptr); +- return 1; +- } +- (*ptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - +- firstnumber; +- if (((*ptr)[index] < 1) || ((*ptr)[index] > nodes)) { +- printf("Error: Triangle %d has invalid corner in %s.\n", i, fname); +- return 1; +- } +- index++; +- } +- } +- fclose(infile); +- return 0; +-} +- +-int load_edge(fname, firstnumber, nodes, edges, edgeptr, normptr) +-char *fname; +-int firstnumber; +-int nodes; +-int *edges; +-int **edgeptr; +-REAL **normptr; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int index; +- int edgenumber; +- int edgemarks; +- int i; +- int smallerr; +- +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- *edges = (int) strtol (stringptr, &stringptr, 0); +- if (*edges < 1) { +- printf(" Error: %s contains %d edges.\n", fname, *edges); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- edgemarks = 0; +- } else { +- edgemarks = (int) strtol (stringptr, &stringptr, 0); +- } +- if (edgemarks < 0) { +- printf(" Error: %s has negative value for number of edge markers.\n", +- fname); +- return 1; +- } +- if (edgemarks > 1) { +- printf( +- " Error: %s has value greater than one for number of edge markers.\n", +- fname); +- return 1; +- } +- *edgeptr = (int *) malloc(((*edges + 1) << 1) * sizeof(int)); +- if (*edgeptr == (int *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- *normptr = (REAL *) malloc(((*edges + 1) << 1) * sizeof(REAL)); +- if (*normptr == (REAL *) NULL) { +- printf(" Out of memory.\n"); +- free(*edgeptr); +- return 1; +- } +- index = 2; +- smallerr = 1; +- for (i = firstnumber; i < firstnumber + *edges; i++) { +- stringptr = readline(inputline, infile, fname); +- edgenumber = (int) strtol (stringptr, &stringptr, 0); +- if ((edgenumber != i) && (smallerr)) { +- printf(" Warning: Edges in %s are not numbered correctly.\n", fname); +- printf(" (starting with edge %d).\n", i); +- smallerr = 0; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Edge %d is missing its endpoints in %s.\n", i, fname); +- free(*edgeptr); +- free(*normptr); +- return 1; +- } +- (*edgeptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - +- firstnumber; +- if (((*edgeptr)[index] < 1) || ((*edgeptr)[index] > nodes)) { +- printf("Error: Edge %d has invalid endpoint in %s.\n", i, fname); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Edge %d is missing an endpoint in %s.\n", i, fname); +- free(*edgeptr); +- free(*normptr); +- return 1; +- } +- (*edgeptr)[index + 1] = (int) strtol (stringptr, &stringptr, 0); +- if ((*edgeptr)[index + 1] == -1) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Edge %d is missing its direction in %s.\n", i, fname); +- free(*edgeptr); +- free(*normptr); +- return 1; +- } +- (*normptr)[index] = (REAL) strtod(stringptr, &stringptr); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Edge %d is missing a direction coordinate in %s.\n", +- i, fname); +- free(*edgeptr); +- free(*normptr); +- return 1; +- } +- (*normptr)[index + 1] = (REAL) strtod(stringptr, &stringptr); +- } else { +- (*edgeptr)[index + 1] += 1 - firstnumber; +- if (((*edgeptr)[index + 1] < 1) || ((*edgeptr)[index + 1] > nodes)) { +- printf("Error: Edge %d has invalid endpoint in %s.\n", i, fname); +- return 1; +- } +- } +- index += 2; +- } +- fclose(infile); +- return 0; +-} +- +-int load_part(fname, dim, firstnumber, elems, nodeptr, eleptr, parts, +- partition, partcenter, partshift) +-char *fname; +-int dim; +-int firstnumber; +-int elems; +-REAL *nodeptr; +-int *eleptr; +-int *parts; +-int **partition; +-REAL **partcenter; +-REAL **partshift; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int partelems; +- int index; +- int elemnumber; +- int i, j; +- int smallerr; +- int *partsize; +- +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- partelems = (int) strtol (stringptr, &stringptr, 0); +- if (partelems != elems) { +- printf( +- " Error: .ele and .part files do not agree on number of triangles.\n"); +- return 1; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- *parts = 1; +- } else { +- *parts = (int) strtol (stringptr, &stringptr, 0); +- } +- if (*parts < 1) { +- printf(" Error: %s specifies %d subdomains.\n", fname, *parts); +- return 1; +- } +- *partition = (int *) malloc((elems + 1) * sizeof(int)); +- if (*partition == (int *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- smallerr = 1; +- for (i = firstnumber; i < firstnumber + partelems; i++) { +- stringptr = readline(inputline, infile, fname); +- elemnumber = (int) strtol (stringptr, &stringptr, 0); +- if ((elemnumber != i) && (smallerr)) { +- printf(" Warning: Triangles in %s are not numbered correctly.\n", +- fname); +- printf(" (starting with triangle %d).\n", i); +- smallerr = 0; +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Triangle %d has no subdomain in %s.\n", i, fname); +- free(*partition); +- return 1; +- } +- (*partition)[i] = (int) strtol (stringptr, &stringptr, 0) - firstnumber; +- if (((*partition)[i] >= *parts) || ((*partition)[i] < 0)) { +- printf(" Error: Triangle %d of %s has an invalid subdomain.\n", +- i, fname); +- free(*partition); +- return 1; +- } +- } +- fclose(infile); +- *partcenter = (REAL *) malloc(((*parts + 1) << 1) * sizeof(REAL)); +- if (*partcenter == (REAL *) NULL) { +- printf("Error: Out of memory.\n"); +- free(*partition); +- return 1; +- } +- *partshift = (REAL *) malloc((*parts << 1) * sizeof(REAL)); +- if (*partshift == (REAL *) NULL) { +- printf("Error: Out of memory.\n"); +- free(*partition); +- free(*partcenter); +- return 1; +- } +- partsize = (int *) malloc((*parts + 1) * sizeof(int)); +- if (partsize == (int *) NULL) { +- printf("Error: Out of memory.\n"); +- free(*partition); +- free(*partcenter); +- free(*partshift); +- return 1; +- } +- index = 3; +- for (i = 0; i <= *parts; i++) { +- partsize[i] = 0; +- (*partcenter)[i << 1] = 0.0; +- (*partcenter)[(i << 1) + 1] = 0.0; +- } +- for (i = 1; i <= elems; i++) { +- partsize[(*partition)[i]] += 3; +- for (j = 0; j < 3; j++) { +- (*partcenter)[(*partition)[i] << 1] += +- nodeptr[eleptr[index] * dim]; +- (*partcenter)[((*partition)[i] << 1) + 1] += +- nodeptr[eleptr[index++] * dim + 1]; +- } +- } +- for (i = 0; i < *parts; i++) { +- (*partcenter)[i << 1] /= (REAL) partsize[i]; +- (*partcenter)[(i << 1) + 1] /= (REAL) partsize[i]; +- (*partcenter)[*parts << 1] += (*partcenter)[i << 1]; +- (*partcenter)[(*parts << 1) + 1] += (*partcenter)[(i << 1) + 1]; +- } +- (*partcenter)[*parts << 1] /= (REAL) *parts; +- (*partcenter)[(*parts << 1) + 1] /= (REAL) *parts; +- free(partsize); +- return 0; +-} +- +-int load_adj(fname, subdomains, ptr) +-char *fname; +-int *subdomains; +-int **ptr; +-{ +- FILE *infile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int i, j; +- +- if (!quiet) { +- printf("Opening %s.\n", fname); +- } +- infile = fopen(fname, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", fname); +- return 1; +- } +- stringptr = readline(inputline, infile, fname); +- *subdomains = (int) strtol (stringptr, &stringptr, 0); +- if (*subdomains < 1) { +- printf(" Error: %s contains %d subdomains.\n", fname, *subdomains); +- return 1; +- } +- *ptr = (int *) malloc(*subdomains * *subdomains * sizeof(int)); +- if (*ptr == (int *) NULL) { +- printf(" Out of memory.\n"); +- return 1; +- } +- for (i = 0; i < *subdomains; i++) { +- for (j = 0; j < *subdomains; j++) { +- stringptr = readline(inputline, infile, fname); +- (*ptr)[i * *subdomains + j] = (int) strtol (stringptr, &stringptr, 0); +- } +- } +- return 0; +-} +- +-void findpartshift(parts, explosion, partcenter, partshift) +-int parts; +-REAL explosion; +-REAL *partcenter; +-REAL *partshift; +-{ +- int i; +- +- for (i = 0; i < parts; i++) { +- partshift[i << 1] = explosion * +- (partcenter[i << 1] - partcenter[parts << 1]); +- partshift[(i << 1) + 1] = explosion * +- (partcenter[(i << 1) + 1] - partcenter[(parts << 1) + 1]); +- } +-} +- +-int load_image(inc, image) +-int inc; +-int image; +-{ +- int error; +- +- switch (image) { +- case NODE: +- error = load_node(nodefilename[inc], &firstnumber[inc], &nodes[inc], +- &node_dim[inc], &nodeptr[inc], &xlo[inc][NODE], +- &ylo[inc][NODE], &xhi[inc][NODE], &yhi[inc][NODE]); +- break; +- case POLY: +- error = load_poly(inc, polyfilename[inc], &firstnumber[inc], +- &polynodes[inc], &poly_dim[inc], &polyedges[inc], +- &polyholes[inc], &polynodeptr[inc], &polyedgeptr[inc], +- &polyholeptr[inc], +- &xlo[inc][POLY], &ylo[inc][POLY], +- &xhi[inc][POLY], &yhi[inc][POLY]); +- break; +- case ELE: +- error = load_ele(elefilename[inc], firstnumber[inc], nodes[inc], +- &elems[inc], &ele_corners[inc], &eleptr[inc]); +- xlo[inc][ELE] = xlo[inc][NODE]; +- ylo[inc][ELE] = ylo[inc][NODE]; +- xhi[inc][ELE] = xhi[inc][NODE]; +- yhi[inc][ELE] = yhi[inc][NODE]; +- break; +- case EDGE: +- error = load_edge(edgefilename[inc], firstnumber[inc], nodes[inc], +- &edges[inc], &edgeptr[inc], &normptr[inc]); +- xlo[inc][EDGE] = xlo[inc][NODE]; +- ylo[inc][EDGE] = ylo[inc][NODE]; +- xhi[inc][EDGE] = xhi[inc][NODE]; +- yhi[inc][EDGE] = yhi[inc][NODE]; +- break; +- case PART: +- error = load_part(partfilename[inc], node_dim[inc], firstnumber[inc], +- elems[inc], nodeptr[inc], eleptr[inc], +- &subdomains[inc], &partpart[inc], &partcenter[inc], +- &partshift[inc]); +- if (!error) { +- findpartshift(subdomains[inc], explosion, partcenter[inc], +- partshift[inc]); +- } +- xlo[inc][PART] = xlo[inc][NODE]; +- ylo[inc][PART] = ylo[inc][NODE]; +- xhi[inc][PART] = xhi[inc][NODE]; +- yhi[inc][PART] = yhi[inc][NODE]; +- break; +- case ADJ: +- error = load_adj(adjfilename[inc], &adjsubdomains[inc], &adjptr[inc]); +- xlo[inc][ADJ] = xlo[inc][NODE]; +- ylo[inc][ADJ] = ylo[inc][NODE]; +- xhi[inc][ADJ] = xhi[inc][NODE]; +- yhi[inc][ADJ] = yhi[inc][NODE]; +- break; +- case VORO: +- error = load_node(vnodefilename[inc], &firstnumber[inc], &vnodes[inc], +- &vnode_dim[inc], &vnodeptr[inc], &xlo[inc][VORO], +- &ylo[inc][VORO], &xhi[inc][VORO], &yhi[inc][VORO]); +- if (!error) { +- error = load_edge(vedgefilename[inc], firstnumber[inc], vnodes[inc], +- &vedges[inc], &vedgeptr[inc], &vnormptr[inc]); +- } +- break; +- default: +- error = 1; +- } +- if (!error) { +- loaded[inc][image] = 1; +- } +- return error; +-} +- +-void choose_image(inc, image) +-int inc; +-int image; +-{ +- if (!loaded[inc][image]) { +- if ((image == ELE) || (image == EDGE) || (image == PART) +- || (image == ADJ)) { +- if (!loaded[inc][NODE]) { +- if (load_image(inc, NODE)) { +- return; +- } +- } +- } +- if ((image == PART) || (image == ADJ)) { +- if (!loaded[inc][ELE]) { +- if (load_image(inc, ELE)) { +- return; +- } +- } +- } +- if (image == ADJ) { +- if (!loaded[inc][PART]) { +- if (load_image(inc, PART)) { +- return; +- } +- } +- } +- if (load_image(inc, image)) { +- return; +- } +- } +- current_inc = inc; +- current_image = image; +-} +- +-Window make_button(name, x, y, width) +-char *name; +-int x; +-int y; +-int width; +-{ +- XSetWindowAttributes attr; +- XSizeHints hints; +- Window button; +- +- attr.background_pixel = black; +- attr.border_pixel = white; +- attr.backing_store = NotUseful; +- attr.event_mask = ExposureMask | ButtonReleaseMask | ButtonPressMask; +- attr.bit_gravity = SouthWestGravity; +- attr.win_gravity = SouthWestGravity; +- attr.save_under = False; +- button = XCreateWindow(display, mainwindow, x, y, width, BUTTONHEIGHT - 4, +- 2, 0, InputOutput, CopyFromParent, +- CWBackPixel | CWBorderPixel | CWEventMask | +- CWBitGravity | CWWinGravity | CWBackingStore | +- CWSaveUnder, &attr); +- hints.width = width; +- hints.height = BUTTONHEIGHT - 4; +- hints.min_width = 0; +- hints.min_height = BUTTONHEIGHT - 4; +- hints.max_width = width; +- hints.max_height = BUTTONHEIGHT - 4; +- hints.width_inc = 1; +- hints.height_inc = 1; +- hints.flags = PMinSize | PMaxSize | PSize | PResizeInc; +- XSetStandardProperties(display, button, name, "showme", None, (char **) NULL, +- 0, &hints); +- return button; +-} +- +-void make_buttons(y) +-int y; +-{ +- int i; +- +- for (i = 1; i >= 0; i--) { +- nodewin[i] = make_button("node", 0, y + (1 - i) * BUTTONHEIGHT, 42); +- XMapWindow(display, nodewin[i]); +- polywin[i] = make_button("poly", 44, y + (1 - i) * BUTTONHEIGHT, 42); +- XMapWindow(display, polywin[i]); +- elewin[i] = make_button("ele", 88, y + (1 - i) * BUTTONHEIGHT, 33); +- XMapWindow(display, elewin[i]); +- edgewin[i] = make_button("edge", 123, y + (1 - i) * BUTTONHEIGHT, 42); +- XMapWindow(display, edgewin[i]); +- partwin[i] = make_button("part", 167, y + (1 - i) * BUTTONHEIGHT, 42); +- XMapWindow(display, partwin[i]); +- adjwin[i] = make_button("adj", 211, y + (1 - i) * BUTTONHEIGHT, 33); +- XMapWindow(display, adjwin[i]); +- voronoiwin[i] = make_button("voro", 246, y + (1 - i) * BUTTONHEIGHT, 42); +- XMapWindow(display, voronoiwin[i]); +- } +- versionpluswin = make_button(" +", 290, y, 52); +- XMapWindow(display, versionpluswin); +- versionminuswin = make_button(" -", 290, y + BUTTONHEIGHT, 52); +- XMapWindow(display, versionminuswin); +- +- quitwin = make_button("Quit", 0, y + 2 * BUTTONHEIGHT, 42); +- XMapWindow(display, quitwin); +- leftwin = make_button("<", 44, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, leftwin); +- rightwin = make_button(">", 60, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, rightwin); +- upwin = make_button("^", 76, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, upwin); +- downwin = make_button("v", 92, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, downwin); +- resetwin = make_button("Reset", 108, y + 2 * BUTTONHEIGHT, 52); +- XMapWindow(display, resetwin); +- widthpluswin = make_button("Width+", 162, y + 2 * BUTTONHEIGHT, 61); +- XMapWindow(display, widthpluswin); +- widthminuswin = make_button("-", 225, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, widthminuswin); +- expwin = make_button("Exp", 241, y + 2 * BUTTONHEIGHT, 33); +- XMapWindow(display, expwin); +- exppluswin = make_button("+", 276, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, exppluswin); +- expminuswin = make_button("-", 292, y + 2 * BUTTONHEIGHT, 14); +- XMapWindow(display, expminuswin); +- fillwin = make_button("Fill", 308, y + 2 * BUTTONHEIGHT, 41); +- XMapWindow(display, fillwin); +- pswin = make_button("PS", 351, y + 2 * BUTTONHEIGHT, 24); +- XMapWindow(display, pswin); +- epswin = make_button("EPS", 377, y + 2 * BUTTONHEIGHT, 33); +- XMapWindow(display, epswin); +-} +- +-void fill_button(button) +-Window button; +-{ +- int x, y; +- unsigned int w, h, d, b; +- Window rootw; +- +- XGetGeometry(display, button, &rootw, &x, &y, &w, &h, &d, &b); +- XFillRectangle(display, button, fontgc, 0, 0, w, h); +-} +- +-void draw_buttons() +-{ +- char numberstring[32]; +- char buttonstring[6]; +- int i; +- +- for (i = 1; i >= 0; i--) { +- if ((current_image == NODE) && (current_inc == i)) { +- fill_button(nodewin[i]); +- XDrawString(display, nodewin[i], blackfontgc, 2, 13, "node", 4); +- } else { +- XClearWindow(display, nodewin[i]); +- XDrawString(display, nodewin[i], fontgc, 2, 13, "node", 4); +- } +- if ((current_image == POLY) && (current_inc == i)) { +- fill_button(polywin[i]); +- XDrawString(display, polywin[i], blackfontgc, 2, 13, "poly", 4); +- } else { +- XClearWindow(display, polywin[i]); +- XDrawString(display, polywin[i], fontgc, 2, 13, "poly", 4); +- } +- if ((current_image == ELE) && (current_inc == i)) { +- fill_button(elewin[i]); +- XDrawString(display, elewin[i], blackfontgc, 2, 13, "ele", 3); +- } else { +- XClearWindow(display, elewin[i]); +- XDrawString(display, elewin[i], fontgc, 2, 13, "ele", 3); +- } +- if ((current_image == EDGE) && (current_inc == i)) { +- fill_button(edgewin[i]); +- XDrawString(display, edgewin[i], blackfontgc, 2, 13, "edge", 4); +- } else { +- XClearWindow(display, edgewin[i]); +- XDrawString(display, edgewin[i], fontgc, 2, 13, "edge", 4); +- } +- if ((current_image == PART) && (current_inc == i)) { +- fill_button(partwin[i]); +- XDrawString(display, partwin[i], blackfontgc, 2, 13, "part", 4); +- } else { +- XClearWindow(display, partwin[i]); +- XDrawString(display, partwin[i], fontgc, 2, 13, "part", 4); +- } +- if ((current_image == ADJ) && (current_inc == i)) { +- fill_button(adjwin[i]); +- XDrawString(display, adjwin[i], blackfontgc, 2, 13, "adj", 3); +- } else { +- XClearWindow(display, adjwin[i]); +- XDrawString(display, adjwin[i], fontgc, 2, 13, "adj", 3); +- } +- if ((current_image == VORO) && (current_inc == i)) { +- fill_button(voronoiwin[i]); +- XDrawString(display, voronoiwin[i], blackfontgc, 2, 13, "voro", 4); +- } else { +- XClearWindow(display, voronoiwin[i]); +- XDrawString(display, voronoiwin[i], fontgc, 2, 13, "voro", 4); +- } +- } +- +- XClearWindow(display, versionpluswin); +- sprintf(numberstring, "%d", loweriteration + 1); +- sprintf(buttonstring, "%-4.4s+", numberstring); +- XDrawString(display, versionpluswin, fontgc, 2, 13, buttonstring, 5); +- XClearWindow(display, versionminuswin); +- sprintf(numberstring, "%d", loweriteration); +- if (loweriteration == 0) { +- sprintf(buttonstring, "%-4.4s", numberstring); +- } else { +- sprintf(buttonstring, "%-4.4s-", numberstring); +- } +- XDrawString(display, versionminuswin, fontgc, 2, 13, buttonstring, 5); +- +- XClearWindow(display, quitwin); +- XDrawString(display, quitwin, fontgc, 2, 13, "Quit", 4); +- XClearWindow(display, leftwin); +- XDrawString(display, leftwin, fontgc, 2, 13, "<", 1); +- XClearWindow(display, rightwin); +- XDrawString(display, rightwin, fontgc, 2, 13, ">", 1); +- XClearWindow(display, upwin); +- XDrawString(display, upwin, fontgc, 2, 13, "^", 1); +- XClearWindow(display, downwin); +- XDrawString(display, downwin, fontgc, 2, 13, "v", 1); +- XClearWindow(display, resetwin); +- XDrawString(display, resetwin, fontgc, 2, 13, "Reset", 6); +- XClearWindow(display, widthpluswin); +- if (line_width < 100) { +- XDrawString(display, widthpluswin, fontgc, 2, 13, "Width+", 6); +- } else { +- XDrawString(display, widthpluswin, fontgc, 2, 13, "Width ", 6); +- } +- XClearWindow(display, widthminuswin); +- if (line_width > 1) { +- XDrawString(display, widthminuswin, fontgc, 2, 13, "-", 1); +- } +- XClearWindow(display, expwin); +- XClearWindow(display, exppluswin); +- XClearWindow(display, expminuswin); +- XClearWindow(display, fillwin); +- if (current_image == PART) { +- if (explode) { +- fill_button(expwin); +- XDrawString(display, expwin, blackfontgc, 2, 13, "Exp", 3); +- } else { +- XDrawString(display, expwin, fontgc, 2, 13, "Exp", 3); +- } +- XDrawString(display, exppluswin, fontgc, 2, 13, "+", 1); +- XDrawString(display, expminuswin, fontgc, 2, 13, "-", 1); +- if (fillelem) { +- fill_button(fillwin); +- XDrawString(display, fillwin, blackfontgc, 2, 13, "Fill", 4); +- } else { +- XDrawString(display, fillwin, fontgc, 2, 13, "Fill", 4); +- } +- } +- XClearWindow(display, pswin); +- XDrawString(display, pswin, fontgc, 2, 13, "PS", 2); +- XClearWindow(display, epswin); +- XDrawString(display, epswin, fontgc, 2, 13, "EPS", 3); +-} +- +-void showme_window(argc, argv) +-int argc; +-char **argv; +-{ +- XSetWindowAttributes attr; +- XSizeHints hints; +- XGCValues fontvalues, linevalues; +- XColor alloc_color, exact_color; +- int i; +- +- display = XOpenDisplay((char *) NULL); +- if (!display) { +- printf("Error: Cannot open display.\n"); +- exit(1); +- } +- screen = DefaultScreen(display); +- rootwindow = DefaultRootWindow(display); +- black = BlackPixel(display, screen); +- white = WhitePixel(display, screen); +- windowdepth = DefaultDepth(display, screen); +- rootmap = DefaultColormap(display, screen); +- width = STARTWIDTH; +- height = STARTHEIGHT; +- attr.background_pixel = black; +- attr.border_pixel = white; +- attr.backing_store = NotUseful; +- attr.event_mask = ExposureMask | ButtonReleaseMask | ButtonPressMask | +- StructureNotifyMask; +- attr.bit_gravity = NorthWestGravity; +- attr.win_gravity = NorthWestGravity; +- attr.save_under = False; +- mainwindow = XCreateWindow(display, rootwindow, 0, 0, width, +- height + PANELHEIGHT, 3, 0, +- InputOutput, CopyFromParent, +- CWBackPixel | CWBorderPixel | CWEventMask | +- CWBitGravity | CWWinGravity | CWBackingStore | +- CWSaveUnder, &attr); +- hints.width = width; +- hints.height = height + PANELHEIGHT; +- hints.min_width = MINWIDTH; +- hints.min_height = MINHEIGHT + PANELHEIGHT; +- hints.width_inc = 1; +- hints.height_inc = 1; +- hints.flags = PMinSize | PSize | PResizeInc; +- XSetStandardProperties(display, mainwindow, "Show Me", "showme", None, +- argv, argc, &hints); +- +- static const unsigned char temp_show_me_achimedes_local[18] = {'s','h','o','w','m','e','\0','A','r','c','h','i','m','e','d','e','s','\0'}; +- XChangeProperty(display, mainwindow, XA_WM_CLASS, XA_STRING, 8, +- PropModeReplace, temp_show_me_achimedes_local, 18U); +- XClearWindow(display, mainwindow); +- XMapWindow(display, mainwindow); +- if ((windowdepth > 1) && +- XAllocNamedColor(display, rootmap, "yellow", &alloc_color, +- &exact_color)) { +- color = 1; +- explode = bw_ps; +- fontvalues.foreground = alloc_color.pixel; +- linevalues.foreground = alloc_color.pixel; +- showme_foreground = alloc_color.pixel; +- for (i = 0; i < 64; i++) { +- if (XAllocNamedColor(display, rootmap, colorname[i], &alloc_color, +- &rgb[i])) { +- colors[i] = alloc_color.pixel; +- } else { +- colors[i] = white; +- rgb[i].red = alloc_color.red; +- rgb[i].green = alloc_color.green; +- rgb[i].blue = alloc_color.blue; +- if (!quiet) { +- printf("Warning: I could not allocate %s.\n", colorname[i]); +- } +- } +- } +- } else { +- color = 0; +- fillelem = 0; +- explode = 1; +- fontvalues.foreground = white; +- linevalues.foreground = white; +- showme_foreground = white; +- } +- font = XLoadQueryFont(display, "9x15"); +- fontvalues.background = black; +- fontvalues.font = font->fid; +- fontvalues.fill_style = FillSolid; +- fontvalues.line_width = 2; +- fontgc = XCreateGC(display, rootwindow, GCForeground | GCBackground | +- GCFont | GCLineWidth | GCFillStyle, &fontvalues); +- fontvalues.foreground = black; +- blackfontgc = XCreateGC(display, rootwindow, GCForeground | GCBackground | +- GCFont | GCLineWidth | GCFillStyle, &fontvalues); +- linevalues.background = black; +- linevalues.line_width = line_width; +- linevalues.cap_style = CapRound; +- linevalues.join_style = JoinRound; +- linevalues.fill_style = FillSolid; +- linegc = XCreateGC(display, rootwindow, GCForeground | GCBackground | +- GCLineWidth | GCCapStyle | GCJoinStyle | GCFillStyle, +- &linevalues); +- trianglegc = XCreateGC(display, rootwindow, GCForeground | GCBackground | +- GCLineWidth | GCCapStyle | GCJoinStyle | GCFillStyle, +- &linevalues); +- make_buttons(height); +- XFlush(display); +-} +- +-void draw_node(nodes, dim, ptr, xscale, yscale, xoffset, yoffset) +-int nodes; +-int dim; +-REAL *ptr; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i; +- int index; +- +- index = dim; +- for (i = 1; i <= nodes; i++) { +- XFillRectangle(display, mainwindow, linegc, +- (int) (ptr[index] * xscale + xoffset) - (line_width >> 1), +- (int) (ptr[index + 1] * yscale + yoffset) - +- (line_width >> 1), line_width, line_width); +- index += dim; +- } +-} +- +-void draw_poly(nodes, dim, edges, holes, nodeptr, edgeptr, holeptr, +- xscale, yscale, xoffset, yoffset) +-int nodes; +-int dim; +-int edges; +-int holes; +-REAL *nodeptr; +-int *edgeptr; +-REAL *holeptr; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i; +- int index; +- REAL *point1, *point2; +- int x1, y1, x2, y2; +- +- index = dim; +- for (i = 1; i <= nodes; i++) { +- XFillRectangle(display, mainwindow, linegc, +- (int) (nodeptr[index] * xscale + xoffset) - +- (line_width >> 1), +- (int) (nodeptr[index + 1] * yscale + yoffset) - +- (line_width >> 1), line_width, line_width); +- index += dim; +- } +- index = 2; +- for (i = 1; i <= edges; i++) { +- point1 = &nodeptr[edgeptr[index++] * dim]; +- point2 = &nodeptr[edgeptr[index++] * dim]; +- XDrawLine(display, mainwindow, linegc, +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +- index = dim; +- if (color) { +- XSetForeground(display, linegc, colors[0]); +- } +- for (i = 1; i <= holes; i++) { +- x1 = (int) (holeptr[index] * xscale + xoffset) - 3; +- y1 = (int) (holeptr[index + 1] * yscale + yoffset) - 3; +- x2 = x1 + 6; +- y2 = y1 + 6; +- XDrawLine(display, mainwindow, linegc, x1, y1, x2, y2); +- XDrawLine(display, mainwindow, linegc, x1, y2, x2, y1); +- index += dim; +- } +- XSetForeground(display, linegc, showme_foreground); +-} +- +-void draw_ele(inc, elems, corners, ptr, partition, shift, +- xscale, yscale, xoffset, yoffset) +-int inc; +-int elems; +-int corners; /* unused */ +-int *ptr; +-int *partition; +-REAL *shift; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i, j; +- int index; +- REAL shiftx = 0.0, shifty = 0.0; +- REAL *prevpoint, *nowpoint; +- XPoint *vertices = (XPoint *) NULL; +- +- if (color && fillelem && (partition != (int *) NULL)) { +- vertices = (XPoint *) malloc(3 * sizeof(XPoint)); +- if (vertices == (XPoint *) NULL) { +- printf("Error: Out of memory.\n"); +- exit(1); +- } +- } +- index = 3; +- for (i = 1; i <= elems; i++) { +- if ((partition != (int *) NULL) && explode) { +- shiftx = shift[partition[i] << 1]; +- shifty = shift[(partition[i] << 1) + 1]; +- } +- if (color && (partition != (int *) NULL)) { +- if (fillelem) { +- XSetForeground(display, trianglegc, colors[partition[i] & 63]); +- } else { +- XSetForeground(display, linegc, colors[partition[i] & 63]); +- } +- } +- if (color && fillelem && (partition != (int *) NULL)) { +- if ((partition != (int *) NULL) && explode) { +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[inc][ptr[index + j] * node_dim[inc]]; +- vertices[j].x = (nowpoint[0] + shiftx) * xscale + xoffset; +- vertices[j].y = (nowpoint[1] + shifty) * yscale + yoffset; +- } +- } else { +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[inc][ptr[index + j] * node_dim[inc]]; +- vertices[j].x = nowpoint[0] * xscale + xoffset; +- vertices[j].y = nowpoint[1] * yscale + yoffset; +- } +- } +- XFillPolygon(display, mainwindow, trianglegc, vertices, 3, +- Convex, CoordModeOrigin); +- } +- prevpoint = &nodeptr[inc][ptr[index + 2] * node_dim[inc]]; +- if ((partition != (int *) NULL) && explode) { +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[inc][ptr[index++] * node_dim[inc]]; +- XDrawLine(display, mainwindow, linegc, +- (int) ((prevpoint[0] + shiftx) * xscale + xoffset), +- (int) ((prevpoint[1] + shifty) * yscale + yoffset), +- (int) ((nowpoint[0] + shiftx) * xscale + xoffset), +- (int) ((nowpoint[1] + shifty) * yscale + yoffset)); +- prevpoint = nowpoint; +- } +- } else { +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[inc][ptr[index++] * node_dim[inc]]; +- XDrawLine(display, mainwindow, linegc, +- (int) (prevpoint[0] * xscale + xoffset), +- (int) (prevpoint[1] * yscale + yoffset), +- (int) (nowpoint[0] * xscale + xoffset), +- (int) (nowpoint[1] * yscale + yoffset)); +- prevpoint = nowpoint; +- } +- } +- } +- if (color && fillelem && (partition != (int *) NULL)) { +- free(vertices); +- } +- XSetForeground(display, linegc, showme_foreground); +-} +- +-void draw_edge(nodes, dim, edges, nodeptr, edgeptr, normptr, +- xscale, yscale, xoffset, yoffset) +-int nodes; /* unused */ +-int dim; +-int edges; +-REAL *nodeptr; +-int *edgeptr; +-REAL *normptr; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i; +- int index; +- REAL *point1, *point2; +- REAL normx, normy; +- REAL normmult, normmultx, normmulty; +- REAL windowxmin, windowymin, windowxmax, windowymax; +- +- index = 2; +- for (i = 1; i <= edges; i++) { +- point1 = &nodeptr[edgeptr[index++] * dim]; +- if (edgeptr[index] == -1) { +- normx = normptr[index - 1]; +- normy = normptr[index++]; +- normmultx = 0.0; +- if (normx > 0) { +- windowxmax = (width - 1 - xoffset) / xscale; +- normmultx = (windowxmax - point1[0]) / normx; +- } else if (normx < 0) { +- windowxmin = -xoffset / xscale; +- normmultx = (windowxmin - point1[0]) / normx; +- } +- normmulty = 0.0; +- if (normy > 0) { +- windowymax = -yoffset / yscale; +- normmulty = (windowymax - point1[1]) / normy; +- } else if (normy < 0) { +- windowymin = (height - 1 - yoffset) / yscale; +- normmulty = (windowymin - point1[1]) / normy; +- } +- if (normmultx == 0.0) { +- normmult = normmulty; +- } else if (normmulty == 0.0) { +- normmult = normmultx; +- } else if (normmultx < normmulty) { +- normmult = normmultx; +- } else { +- normmult = normmulty; +- } +- if (normmult > 0.0) { +- XDrawLine(display, mainwindow, linegc, +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- (int) ((point1[0] + normmult * normx) * xscale + xoffset), +- (int) ((point1[1] + normmult * normy) * yscale + yoffset)); +- } +- } else { +- point2 = &nodeptr[edgeptr[index++] * dim]; +- XDrawLine(display, mainwindow, linegc, +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +- } +-} +- +-void draw_adj(dim, subdomains, ptr, center, xscale, yscale, +- xoffset, yoffset) +-int dim; +-int subdomains; +-int *ptr; +-REAL *center; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i, j; +- REAL *point1, *point2; +- +- for (i = 0; i < subdomains; i++) { +- for (j = i + 1; j < subdomains; j++) { +- if (ptr[i * subdomains + j]) { +- point1 = ¢er[i * dim]; +- point2 = ¢er[j * dim]; +- XDrawLine(display, mainwindow, linegc, +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +- } +- } +- for (i = 0; i < subdomains; i++) { +- point1 = ¢er[i * dim]; +- if (color) { +- XSetForeground(display, linegc, colors[i & 63]); +- } +- XFillArc(display, mainwindow, linegc, +- (int) (point1[0] * xscale + xoffset) - 5 - (line_width >> 1), +- (int) (point1[1] * yscale + yoffset) - 5 - (line_width >> 1), +- line_width + 10, line_width + 10, 0, 23040); +- } +- XSetForeground(display, linegc, showme_foreground); +-} +- +-void draw(inc, image, xmin, ymin, xmax, ymax) +-int inc; +-int image; +-REAL xmin; +-REAL ymin; +-REAL xmax; +-REAL ymax; +-{ +- draw_buttons(); +- XClearWindow(display, mainwindow); +- if (image == NOTHING) { +- return; +- } +- if (!loaded[inc][image]) { +- return; +- } +- if ((image == PART) && explode) { +- xmin += (xmin - partcenter[inc][subdomains[inc] << 1]) * explosion; +- xmax += (xmax - partcenter[inc][subdomains[inc] << 1]) * explosion; +- ymin += (ymin - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; +- ymax += (ymax - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; +- } +- xscale = (REAL) (width - line_width - 4) / (xmax - xmin); +- yscale = (REAL) (height - line_width - 4) / (ymax - ymin); +- if (xscale > yscale) { +- xscale = yscale; +- } else { +- yscale = xscale; +- } +- xoffset = 0.5 * ((REAL) width - xscale * (xmax - xmin)) - +- xscale * xmin; +- yoffset = (REAL) height - 0.5 * ((REAL) height - yscale * (ymax - ymin)) + +- yscale * ymin; +- yscale = - yscale; +- switch(image) { +- case NODE: +- draw_node(nodes[inc], node_dim[inc], nodeptr[inc], +- xscale, yscale, xoffset, yoffset); +- break; +- case POLY: +- if (polynodes[inc] > 0) { +- draw_poly(polynodes[inc], poly_dim[inc], polyedges[inc], +- polyholes[inc], polynodeptr[inc], polyedgeptr[inc], +- polyholeptr[inc], +- xscale, yscale, xoffset, yoffset); +- } else { +- draw_poly(nodes[inc], node_dim[inc], polyedges[inc], +- polyholes[inc], nodeptr[inc], polyedgeptr[inc], +- polyholeptr[inc], +- xscale, yscale, xoffset, yoffset); +- } +- break; +- case ELE: +- draw_ele(inc, elems[inc], ele_corners[inc], eleptr[inc], +- (int *) NULL, (REAL *) NULL, +- xscale, yscale, xoffset, yoffset); +- break; +- case EDGE: +- draw_edge(nodes[inc], node_dim[inc], edges[inc], +- nodeptr[inc], edgeptr[inc], normptr[inc], +- xscale, yscale, xoffset, yoffset); +- break; +- case PART: +- draw_ele(inc, elems[inc], ele_corners[inc], eleptr[inc], +- partpart[inc], partshift[inc], +- xscale, yscale, xoffset, yoffset); +- break; +- case ADJ: +- draw_adj(node_dim[inc], adjsubdomains[inc], adjptr[inc], partcenter[inc], +- xscale, yscale, xoffset, yoffset); +- break; +- case VORO: +- if (loaded[inc][NODE]) { +- draw_node(nodes[inc], node_dim[inc], nodeptr[inc], +- xscale, yscale, xoffset, yoffset); +- } +- draw_edge(vnodes[inc], vnode_dim[inc], vedges[inc], +- vnodeptr[inc], vedgeptr[inc], vnormptr[inc], +- xscale, yscale, xoffset, yoffset); +- break; +- default: +- break; +- } +-} +- +-void addps(instring, outstring, eps) +-char *instring; +-char *outstring; +-int eps; +-{ +- strcpy(outstring, instring); +- if (eps) { +- strcat(outstring, ".eps"); +- } else { +- strcat(outstring, ".ps"); +- } +-} +- +-int print_head(fname, file, llcornerx, llcornery, eps) +-char *fname; +-FILE **file; +-int llcornerx; +-int llcornery; +-int eps; +-{ +- if (!quiet) { +- printf("Writing %s\n", fname); +- } +- *file = fopen(fname, "w"); +- if (*file == (FILE *) NULL) { +- printf(" Error: Could not open %s\n", fname); +- return 1; +- } +- if (eps) { +- fprintf(*file, "%%!PS-Adobe-2.0 EPSF-2.0\n"); +- } else { +- fprintf(*file, "%%!PS-Adobe-2.0\n"); +- } +- fprintf(*file, "%%%%BoundingBox: %d %d %d %d\n", llcornerx, llcornery, +- 612 - llcornerx, 792 - llcornery); +- fprintf(*file, "%%%%Creator: Show Me\n"); +- fprintf(*file, "%%%%EndComments\n\n"); +- fprintf(*file, "1 setlinecap\n"); +- fprintf(*file, "1 setlinejoin\n"); +- fprintf(*file, "%d setlinewidth\n", line_width); +- fprintf(*file, "%d %d moveto\n", llcornerx, llcornery); +- fprintf(*file, "%d %d lineto\n", 612 - llcornerx, llcornery); +- fprintf(*file, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); +- fprintf(*file, "%d %d lineto\n", llcornerx, 792 - llcornery); +- fprintf(*file, "closepath\nclip\nnewpath\n"); +- return 0; +-} +- +-void print_node(nodefile, nodes, dim, ptr, xscale, yscale, +- xoffset, yoffset) +-FILE *nodefile; +-int nodes; +-int dim; +-REAL *ptr; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i; +- int index; +- +- index = dim; +- for (i = 1; i <= nodes; i++) { +- fprintf(nodefile, "%d %d %d 0 360 arc\nfill\n", +- (int) (ptr[index] * xscale + xoffset), +- (int) (ptr[index + 1] * yscale + yoffset), +- 1 + (line_width >> 1)); +- index += dim; +- } +-} +- +-void print_poly(polyfile, nodes, dim, edges, holes, nodeptr, edgeptr, holeptr, +- xscale, yscale, xoffset, yoffset) +-FILE *polyfile; +-int nodes; +-int dim; +-int edges; +-int holes; /* unused */ +-REAL *nodeptr; +-int *edgeptr; +-REAL *holeptr; /* unused */ +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-{ +- int i; +- int index; +- REAL *point1, *point2; +- +- index = dim; +- for (i = 1; i <= nodes; i++) { +- fprintf(polyfile, "%d %d %d 0 360 arc\nfill\n", +- (int) (nodeptr[index] * xscale + xoffset), +- (int) (nodeptr[index + 1] * yscale + yoffset), +- 1 + (line_width >> 1)); +- index += dim; +- } +- index = 2; +- for (i = 1; i <= edges; i++) { +- point1 = &nodeptr[edgeptr[index++] * dim]; +- point2 = &nodeptr[edgeptr[index++] * dim]; +- fprintf(polyfile, "%d %d moveto\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset)); +- fprintf(polyfile, "%d %d lineto\nstroke\n", +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +-} +- +-void print_ele(elefile, nodes, dim, elems, corners, nodeptr, eleptr, +- partition, shift, +- xscale, yscale, xoffset, yoffset, llcornerx, llcornery) +-FILE *elefile; +-int nodes; /* unused */ +-int dim; +-int elems; +-int corners; /* unused */ +-REAL *nodeptr; +-int *eleptr; +-int *partition; +-REAL *shift; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-int llcornerx; +-int llcornery; +-{ +- int i, j; +- int index, colorindex; +- REAL shiftx, shifty; +- REAL *nowpoint; +- +- index = 3; +- if ((partition != (int *) NULL) && !bw_ps) { +- fprintf(elefile, "0 0 0 setrgbcolor\n"); +- fprintf(elefile, "%d %d moveto\n", llcornerx, llcornery); +- fprintf(elefile, "%d %d lineto\n", 612 - llcornerx, llcornery); +- fprintf(elefile, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); +- fprintf(elefile, "%d %d lineto\n", llcornerx, 792 - llcornery); +- fprintf(elefile, "fill\n"); +- } +- for (i = 1; i <= elems; i++) { +- if ((partition != (int *) NULL) && !bw_ps) { +- colorindex = partition[i] & 63; +- fprintf(elefile, "%6.3f %6.3f %6.3f setrgbcolor\n", +- (REAL) rgb[colorindex].red / 65535.0, +- (REAL) rgb[colorindex].green / 65535.0, +- (REAL) rgb[colorindex].blue / 65535.0); +- } +- nowpoint = &nodeptr[eleptr[index + 2] * dim]; +- if ((partition != (int *) NULL) && (explode || bw_ps)) { +- shiftx = shift[partition[i] << 1]; +- shifty = shift[(partition[i] << 1) + 1]; +- fprintf(elefile, "%d %d moveto\n", +- (int) ((nowpoint[0] + shiftx) * xscale + xoffset), +- (int) ((nowpoint[1] + shifty) * yscale + yoffset)); +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[eleptr[index++] * dim]; +- fprintf(elefile, "%d %d lineto\n", +- (int) ((nowpoint[0] + shiftx) * xscale + xoffset), +- (int) ((nowpoint[1] + shifty) * yscale + yoffset)); +- } +- } else { +- fprintf(elefile, "%d %d moveto\n", +- (int) (nowpoint[0] * xscale + xoffset), +- (int) (nowpoint[1] * yscale + yoffset)); +- for (j = 0; j < 3; j++) { +- nowpoint = &nodeptr[eleptr[index++] * dim]; +- fprintf(elefile, "%d %d lineto\n", +- (int) (nowpoint[0] * xscale + xoffset), +- (int) (nowpoint[1] * yscale + yoffset)); +- } +- } +- if (fillelem && !bw_ps) { +- fprintf(elefile, "gsave\nfill\ngrestore\n1 1 0 setrgbcolor\n"); +- } +- fprintf(elefile, "stroke\n"); +- } +-} +- +-void print_edge(edgefile, nodes, dim, edges, nodeptr, edgeptr, normptr, +- xscale, yscale, xoffset, yoffset, llcornerx, llcornery) +-FILE *edgefile; +-int nodes; /* unused */ +-int dim; +-int edges; +-REAL *nodeptr; +-int *edgeptr; +-REAL *normptr; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-int llcornerx; +-int llcornery; +-{ +- int i; +- int index; +- REAL *point1, *point2; +- REAL normx, normy; +- REAL normmult, normmultx, normmulty; +- REAL windowxmin, windowymin, windowxmax, windowymax; +- +- index = 2; +- for (i = 1; i <= edges; i++) { +- point1 = &nodeptr[edgeptr[index++] * dim]; +- if (edgeptr[index] == -1) { +- normx = normptr[index - 1]; +- normy = normptr[index++]; +- normmultx = 0.0; +- if (normx > 0) { +- windowxmax = ((REAL) (612 - llcornerx) - xoffset) / xscale; +- normmultx = (windowxmax - point1[0]) / normx; +- } else if (normx < 0) { +- windowxmin = ((REAL) llcornerx - xoffset) / xscale; +- normmultx = (windowxmin - point1[0]) / normx; +- } +- normmulty = 0.0; +- if (normy > 0) { +- windowymax = ((REAL) (792 - llcornery) - yoffset) / yscale; +- normmulty = (windowymax - point1[1]) / normy; +- } else if (normy < 0) { +- windowymin = ((REAL) llcornery - yoffset) / yscale; +- normmulty = (windowymin - point1[1]) / normy; +- } +- if (normmultx == 0.0) { +- normmult = normmulty; +- } else if (normmulty == 0.0) { +- normmult = normmultx; +- } else if (normmultx < normmulty) { +- normmult = normmultx; +- } else { +- normmult = normmulty; +- } +- if (normmult > 0.0) { +- fprintf(edgefile, "%d %d moveto\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset)); +- fprintf(edgefile, "%d %d lineto\nstroke\n", +- (int) ((point1[0] + normmult * normx) * xscale + xoffset), +- (int) ((point1[1] + normmult * normy) * yscale + yoffset)); +- } +- } else { +- point2 = &nodeptr[edgeptr[index++] * dim]; +- fprintf(edgefile, "%d %d moveto\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset)); +- fprintf(edgefile, "%d %d lineto\nstroke\n", +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +- } +-} +- +-void print_adj(adjfile, dim, subdomains, ptr, center, xscale, yscale, +- xoffset, yoffset, llcornerx, llcornery) +-FILE *adjfile; +-int dim; +-int subdomains; +-int *ptr; +-REAL *center; +-REAL xscale; +-REAL yscale; +-REAL xoffset; +-REAL yoffset; +-int llcornerx; +-int llcornery; +-{ +- int i, j; +- REAL *point1, *point2; +- int colorindex; +- +- if (!bw_ps) { +- fprintf(adjfile, "0 0 0 setrgbcolor\n"); +- fprintf(adjfile, "%d %d moveto\n", llcornerx, llcornery); +- fprintf(adjfile, "%d %d lineto\n", 612 - llcornerx, llcornery); +- fprintf(adjfile, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); +- fprintf(adjfile, "%d %d lineto\n", llcornerx, 792 - llcornery); +- fprintf(adjfile, "fill\n"); +- fprintf(adjfile, "1 1 0 setrgbcolor\n"); +- } +- for (i = 0; i < subdomains; i++) { +- for (j = i + 1; j < subdomains; j++) { +- if (ptr[i * subdomains + j]) { +- point1 = ¢er[i * dim]; +- point2 = ¢er[j * dim]; +- fprintf(adjfile, "%d %d moveto\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset)); +- fprintf(adjfile, "%d %d lineto\nstroke\n", +- (int) (point2[0] * xscale + xoffset), +- (int) (point2[1] * yscale + yoffset)); +- } +- } +- } +- for (i = 0; i < subdomains; i++) { +- point1 = ¢er[i * dim]; +- if (!bw_ps) { +- colorindex = i & 63; +- fprintf(adjfile, "%6.3f %6.3f %6.3f setrgbcolor\n", +- (REAL) rgb[colorindex].red / 65535.0, +- (REAL) rgb[colorindex].green / 65535.0, +- (REAL) rgb[colorindex].blue / 65535.0); +- fprintf(adjfile, "%d %d %d 0 360 arc\nfill\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- 5 + (line_width >> 1)); +- } else { +- fprintf(adjfile, "%d %d %d 0 360 arc\nfill\n", +- (int) (point1[0] * xscale + xoffset), +- (int) (point1[1] * yscale + yoffset), +- 3 + (line_width >> 1)); +- } +- } +-} +- +-void print(inc, image, xmin, ymin, xmax, ymax, eps) +-int inc; +-int image; +-REAL xmin; +-REAL ymin; +-REAL xmax; +-REAL ymax; +-int eps; +-{ +- REAL xxscale, yyscale, xxoffset, yyoffset; +- char psfilename[FILENAMESIZE]; +- int llcornerx, llcornery; +- FILE *psfile; +- +- if (image == NOTHING) { +- return; +- } +- if (!loaded[inc][image]) { +- return; +- } +- if ((image == PART) && (explode || bw_ps)) { +- xmin += (xmin - partcenter[inc][subdomains[inc] << 1]) * explosion; +- xmax += (xmax - partcenter[inc][subdomains[inc] << 1]) * explosion; +- ymin += (ymin - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; +- ymax += (ymax - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; +- } +- xxscale = (460.0 - (REAL) line_width) / (xmax - xmin); +- yyscale = (640.0 - (REAL) line_width) / (ymax - ymin); +- if (xxscale > yyscale) { +- xxscale = yyscale; +- llcornerx = (604 - (int) (yyscale * (xmax - xmin)) - line_width) >> 1; +- llcornery = 72; +- } else { +- yyscale = xxscale; +- llcornerx = 72; +- llcornery = (784 - (int) (xxscale * (ymax - ymin)) - line_width) >> 1; +- } +- xxoffset = 0.5 * (612.0 - xxscale * (xmax - xmin)) - xxscale * xmin + +- (line_width >> 1); +- yyoffset = 0.5 * (792.0 - yyscale * (ymax - ymin)) - yyscale * ymin + +- (line_width >> 1); +- switch(image) { +- case NODE: +- addps(nodefilename[inc], psfilename, eps); +- break; +- case POLY: +- addps(polyfilename[inc], psfilename, eps); +- break; +- case ELE: +- addps(elefilename[inc], psfilename, eps); +- break; +- case EDGE: +- addps(edgefilename[inc], psfilename, eps); +- break; +- case PART: +- addps(partfilename[inc], psfilename, eps); +- break; +- case ADJ: +- addps(adjfilename[inc], psfilename, eps); +- break; +- case VORO: +- addps(vedgefilename[inc], psfilename, eps); +- break; +- default: +- break; +- } +- if (print_head(psfilename, &psfile, llcornerx, llcornery, eps)) { +- return; +- } +- switch (image) { +- case NODE: +- print_node(psfile, nodes[inc], node_dim[inc], nodeptr[inc], +- xxscale, yyscale, xxoffset, yyoffset); +- break; +- case POLY: +- if (polynodes[inc] > 0) { +- print_poly(psfile, polynodes[inc], poly_dim[inc], polyedges[inc], +- polyholes[inc], polynodeptr[inc], polyedgeptr[inc], +- polyholeptr[inc], xxscale, yyscale, xxoffset, yyoffset); +- } else { +- print_poly(psfile, nodes[inc], node_dim[inc], polyedges[inc], +- polyholes[inc], nodeptr[inc], polyedgeptr[inc], +- polyholeptr[inc], xxscale, yyscale, xxoffset, yyoffset); +- } +- break; +- case ELE: +- print_ele(psfile, nodes[inc], node_dim[inc], elems[inc], +- ele_corners[inc], nodeptr[inc], eleptr[inc], +- (int *) NULL, (REAL *) NULL, +- xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); +- break; +- case EDGE: +- print_edge(psfile, nodes[inc], node_dim[inc], edges[inc], +- nodeptr[inc], edgeptr[inc], normptr[inc], +- xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); +- break; +- case PART: +- print_ele(psfile, nodes[inc], node_dim[inc], elems[inc], +- ele_corners[inc], nodeptr[inc], eleptr[inc], +- partpart[inc], partshift[inc], +- xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); +- break; +- case ADJ: +- print_adj(psfile, node_dim[inc], adjsubdomains[inc], adjptr[inc], +- partcenter[inc], +- xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); +- break; +- case VORO: +- print_edge(psfile, vnodes[inc], vnode_dim[inc], vedges[inc], +- vnodeptr[inc], vedgeptr[inc], vnormptr[inc], +- xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); +- break; +- default: +- break; +- } +- if (!eps) { +- fprintf(psfile, "showpage\n"); +- } +- fclose(psfile); +-} +- +-int main(argc, argv) +-int argc; +-char **argv; +-{ +- REAL xmin = 0.0, ymin = 0.0, xmax = 0.0, ymax = 0.0; +- REAL xptr, yptr, xspan, yspan; +- int past_image; +- int new_image = 0; +- int new_inc = 0; +- +- parsecommandline(argc, argv); +- showme_init(); +- choose_image(start_inc, start_image); +- showme_window(argc, argv); +- +- if (current_image != NOTHING) { +- xmin = xlo[current_inc][current_image]; +- ymin = ylo[current_inc][current_image]; +- xmax = xhi[current_inc][current_image]; +- ymax = yhi[current_inc][current_image]; +- zoom = 0; +- } +- +- XMaskEvent(display, ExposureMask, &event); +- while (1) { +- switch (event.type) { +- case ButtonRelease: +- if (event.xany.window == quitwin) { +- XDestroyWindow(display, mainwindow); +- XCloseDisplay(display); +- return 0; +- } else if (event.xany.window == leftwin) { +- xspan = 0.25 * (xmax - xmin); +- xmin += xspan; +- xmax += xspan; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xany.window == rightwin) { +- xspan = 0.25 * (xmax - xmin); +- xmin -= xspan; +- xmax -= xspan; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xany.window == upwin) { +- yspan = 0.25 * (ymax - ymin); +- ymin -= yspan; +- ymax -= yspan; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xany.window == downwin) { +- yspan = 0.25 * (ymax - ymin); +- ymin += yspan; +- ymax += yspan; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xany.window == resetwin) { +- xmin = xlo[current_inc][current_image]; +- ymin = ylo[current_inc][current_image]; +- xmax = xhi[current_inc][current_image]; +- ymax = yhi[current_inc][current_image]; +- zoom = 0; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xany.window == widthpluswin) { +- if (line_width < 100) { +- line_width++; +- XSetLineAttributes(display, linegc, line_width, LineSolid, +- CapRound, JoinRound); +- XSetLineAttributes(display, trianglegc, line_width, LineSolid, +- CapRound, JoinRound); +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == widthminuswin) { +- if (line_width > 1) { +- line_width--; +- XSetLineAttributes(display, linegc, line_width, LineSolid, +- CapRound, JoinRound); +- XSetLineAttributes(display, trianglegc, line_width, LineSolid, +- CapRound, JoinRound); +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == expwin) { +- if ((current_image == PART) && loaded[current_inc][PART]) { +- explode = !explode; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == exppluswin) { +- if ((current_image == PART) && loaded[current_inc][PART] && explode) { +- explosion += 0.125; +- findpartshift(subdomains[current_inc], explosion, +- partcenter[current_inc], partshift[current_inc]); +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == expminuswin) { +- if ((current_image == PART) && loaded[current_inc][PART] && explode && +- (explosion >= 0.125)) { +- explosion -= 0.125; +- findpartshift(subdomains[current_inc], explosion, +- partcenter[current_inc], partshift[current_inc]); +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == fillwin) { +- if ((current_image == PART) && loaded[current_inc][PART]) { +- fillelem = !fillelem; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } +- } else if (event.xany.window == pswin) { +- fill_button(pswin); +- XFlush(display); +- print(current_inc, current_image, xmin, ymin, xmax, ymax, 0); +- XClearWindow(display, pswin); +- XDrawString(display, pswin, fontgc, 2, 13, "PS", 2); +- } else if (event.xany.window == epswin) { +- fill_button(epswin); +- XFlush(display); +- print(current_inc, current_image, xmin, ymin, xmax, ymax, 1); +- XClearWindow(display, epswin); +- XDrawString(display, epswin, fontgc, 2, 13, "EPS", 3); +- } else if (event.xany.window == versionpluswin) { +- move_inc(1); +- loweriteration++; +- set_filenames(filename, loweriteration); +- if (current_inc == 1) { +- current_inc = 0; +- } else { +- current_image = NOTHING; +- XClearWindow(display, mainwindow); +- } +- draw_buttons(); +- } else if (event.xany.window == versionminuswin) { +- if (loweriteration > 0) { +- move_inc(0); +- loweriteration--; +- set_filenames(filename, loweriteration); +- if (current_inc == 0) { +- current_inc = 1; +- } else { +- current_image = NOTHING; +- XClearWindow(display, mainwindow); +- } +- draw_buttons(); +- } +- } else if ((event.xany.window == nodewin[0]) || +- (event.xany.window == polywin[0]) || +- (event.xany.window == elewin[0]) || +- (event.xany.window == edgewin[0]) || +- (event.xany.window == partwin[0]) || +- (event.xany.window == adjwin[0]) || +- (event.xany.window == voronoiwin[0]) || +- (event.xany.window == nodewin[1]) || +- (event.xany.window == polywin[1]) || +- (event.xany.window == elewin[1]) || +- (event.xany.window == edgewin[1]) || +- (event.xany.window == partwin[1]) || +- (event.xany.window == adjwin[1]) || +- (event.xany.window == voronoiwin[1])) { +- if (event.xany.window == nodewin[0]) { +- new_inc = 0; +- new_image = NODE; +- } +- if (event.xany.window == polywin[0]) { +- new_inc = 0; +- new_image = POLY; +- } +- if (event.xany.window == elewin[0]) { +- new_inc = 0; +- new_image = ELE; +- } +- if (event.xany.window == edgewin[0]) { +- new_inc = 0; +- new_image = EDGE; +- } +- if (event.xany.window == partwin[0]) { +- new_inc = 0; +- new_image = PART; +- } +- if (event.xany.window == adjwin[0]) { +- new_inc = 0; +- new_image = ADJ; +- } +- if (event.xany.window == voronoiwin[0]) { +- new_inc = 0; +- new_image = VORO; +- } +- if (event.xany.window == nodewin[1]) { +- new_inc = 1; +- new_image = NODE; +- } +- if (event.xany.window == polywin[1]) { +- new_inc = 1; +- new_image = POLY; +- } +- if (event.xany.window == elewin[1]) { +- new_inc = 1; +- new_image = ELE; +- } +- if (event.xany.window == edgewin[1]) { +- new_inc = 1; +- new_image = EDGE; +- } +- if (event.xany.window == partwin[1]) { +- new_inc = 1; +- new_image = PART; +- } +- if (event.xany.window == adjwin[1]) { +- new_inc = 1; +- new_image = ADJ; +- } +- if (event.xany.window == voronoiwin[1]) { +- new_inc = 1; +- new_image = VORO; +- } +- past_image = current_image; +- if ((current_inc == new_inc) && (current_image == new_image)) { +- free_inc(new_inc); +- unload_inc(new_inc); +- } +- choose_image(new_inc, new_image); +- if ((past_image == NOTHING) && (current_image != NOTHING)) { +- xmin = xlo[current_inc][current_image]; +- ymin = ylo[current_inc][current_image]; +- xmax = xhi[current_inc][current_image]; +- ymax = yhi[current_inc][current_image]; +- zoom = 0; +- } +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else { +- xptr = ((REAL) event.xbutton.x - xoffset) / xscale; +- yptr = ((REAL) event.xbutton.y - yoffset) / yscale; +- if ((current_image == PART) && loaded[current_inc][PART] && explode) { +- xptr = (xptr + partcenter[current_inc] +- [subdomains[current_inc] << 1] +- * explosion) / (1.0 + explosion); +- yptr = (yptr + partcenter[current_inc] +- [(subdomains[current_inc] << 1) + 1] +- * explosion) / (1.0 + explosion); +- } +- if ((event.xbutton.button == Button1) +- || (event.xbutton.button == Button3)) { +- if (event.xbutton.button == Button1) { +- xspan = 0.25 * (xmax - xmin); +- yspan = 0.25 * (ymax - ymin); +- zoom++; +- } else { +- xspan = xmax - xmin; +- yspan = ymax - ymin; +- zoom--; +- } +- xmin = xptr - xspan; +- ymin = yptr - yspan; +- xmax = xptr + xspan; +- ymax = yptr + yspan; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- } else if (event.xbutton.button == Button2) { +- printf("x = %.4g, y = %.4g\n", xptr, yptr); +- } +- } +- break; +- case DestroyNotify: +- XDestroyWindow(display, mainwindow); +- XCloseDisplay(display); +- return 0; +- case ConfigureNotify: +- if ((width != event.xconfigure.width) || +- (height != event.xconfigure.height - PANELHEIGHT)) { +- width = event.xconfigure.width; +- height = event.xconfigure.height - PANELHEIGHT; +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- while (XCheckMaskEvent(display, ExposureMask, &event)); +- } +- break; +- case Expose: +- draw(current_inc, current_image, xmin, ymin, xmax, ymax); +- while (XCheckMaskEvent(display, ExposureMask, &event)); +- break; +- default: +- break; +- } +- XNextEvent(display, &event); +- } +-} +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/tests/CMakeLists.txt b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/tests/CMakeLists.txt +index d23be0c165..3b858454c2 100644 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/tests/CMakeLists.txt ++++ b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/tests/CMakeLists.txt +@@ -24,9 +24,13 @@ if(BUILD_TESTING) + add_test( NAME netlib_test_slamch COMMAND netlib_slamch_test ) + target_link_libraries(netlib_slamch_test ${VXL_LIB_PREFIX}v3p_netlib) + # test ++# Incompatibly with ITK's License ++if(0) + add_executable( netlib_tricall tricall.c ) + add_test( NAME netlib_test_tricall COMMAND netlib_tricall ) + target_link_libraries(netlib_tricall ${VXL_LIB_PREFIX}netlib) ++# Incompatible with ITK's License ++endif() + # test + add_executable( netlib_integral_test integral-test.c ) + add_test( NAME netlib_test_integral COMMAND netlib_integral_test ) +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.README b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.README +deleted file mode 100644 +index b33ea00948..0000000000 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.README ++++ /dev/null +@@ -1,198 +0,0 @@ +-Triangle +-A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. +-Version 1.6 +- +-Show Me +-A Display Program for Meshes and More. +-Version 1.6 +- +-Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk +-2360 Woolsey #H +-Berkeley, California 94705-1927 +-Please send bugs and comments to jrs@cs.berkeley.edu +- +-Created as part of the Quake project (tools for earthquake simulation). +-Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship. +-There is no warranty whatsoever. Use at your own risk. +- +- +-Triangle generates exact Delaunay triangulations, constrained Delaunay +-triangulations, conforming Delaunay triangulations, Voronoi diagrams, and +-high-quality triangular meshes. The latter can be generated with no small +-or large angles, and are thus suitable for finite element analysis. +-Show Me graphically displays the contents of the geometric files used by +-Triangle. Show Me can also write images in PostScript form. +- +-Information on the algorithms used by Triangle, including complete +-references, can be found in the comments at the beginning of the triangle.c +-source file. Another listing of these references, with PostScript copies +-of some of the papers, is available from the Web page +- +- http://www.cs.cmu.edu/~quake/triangle.research.html +- +------------------------------------------------------------------------------- +- +-These programs may be freely redistributed under the condition that the +-copyright notices (including the copy of this notice in the code comments +-and the copyright notice printed when the `-h' switch is selected) are +-not removed, and no compensation is received. Private, research, and +-institutional use is free. You may distribute modified versions of this +-code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT +-IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH +-SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND +-CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as +-part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT +-WITH THE AUTHOR. (If you are not directly supplying this code to a +-customer, and you are instead telling them how they can obtain it for +-free, then you are not required to make any arrangement with me.) +- +------------------------------------------------------------------------------- +- +-The files included in this distribution are: +- +- README The file you're reading now. +- triangle.c Complete C source code for Triangle. +- showme.c Complete C source code for Show Me. +- triangle.h Include file for calling Triangle from another program. +- tricall.c Sample program that calls Triangle. +- makefile Makefile for compiling Triangle and Show Me. +- A.poly A sample input file. +- +-Each of Triangle and Show Me is a single portable C file. The easiest way +-to compile them is to edit and use the included makefile. Before +-compiling, read the makefile, which describes your options, and edit it +-accordingly. You should specify: +- +- The source and binary directories. +- +- The C compiler and level of optimization. +- +- The "correct" directories for include files (especially X include files), +- if necessary. +- +- Do you want single precision or double? (The default is double.) Do you +- want to leave out some of Triangle's features to reduce the size of the +- executable file? Investigate the SINGLE, REDUCED, and CDT_ONLY symbols. +- +- If yours is not a Unix system, define the NO_TIMER symbol to remove the +- Unix-specific timing code. Also, don't try to compile Show Me; it only +- works with X Windows. +- +- If you are compiling on an Intel x86 CPU and using gcc w/Linux or +- Microsoft C, be sure to define the LINUX or CPU86 (for Microsoft) symbol +- during compilation so that the exact arithmetic works right. +- +-Once you've done this, type "make" to compile the programs. Alternatively, +-the files are usually easy to compile without a makefile: +- +- cc -O -o triangle triangle.c -lm +- cc -O -o showme showme.c -lX11 +- +-On some systems, the C compiler won't be able to find the X include files +-or libraries, and you'll need to specify an include path or library path: +- +- cc -O -I/usr/local/include -o showme showme.c -L/usr/local/lib -lX11 +- +-Some processors, including Intel x86 family and possibly Motorola 68xxx +-family chips, are IEEE conformant but have extended length internal +-floating-point registers that may defeat Triangle's exact arithmetic +-routines by failing to cause enough roundoff error! Typically, there is a +-way to set these internal registers so that they are rounded off to IEEE +-single or double precision format. I believe (but I'm not certain) that +-Triangle has the right incantations for x86 chips, if you have gcc running +-under Linux (define the LINUX compiler symbol) or Microsoft C (define the +-CPU86 compiler symbol). +- +-If you have a different processor or operating system, or if I got the +-incantations wrong, you should check your C compiler or system manuals to +-find out how to configure these internal registers to the precision you are +-using. Otherwise, the exact arithmetic routines won't be exact at all. +-See http://www.cs.cmu.edu/~quake/robust.pc.html for details. Triangle's +-exact arithmetic hasn't a hope of working on machines like the Cray C90 or +-Y-MP, which are not IEEE conformant and have inaccurate rounding. +- +-Triangle and Show Me have both text and HTML documentation. The latter is +-illustrated. Find it on the Web at +- +- http://www.cs.cmu.edu/~quake/triangle.html +- http://www.cs.cmu.edu/~quake/showme.html +- +-Complete text instructions are printed by invoking each program with the +-`-h' switch: +- +- triangle -h +- showme -h +- +-The instructions are long; you'll probably want to pipe the output to +-`more' or `lpr' or redirect it to a file. +- +-Both programs give a short list of command line options if they are invoked +-without arguments (that is, just type `triangle' or `showme'). +- +-Try out Triangle on the enclosed sample file, A.poly: +- +- triangle -p A +- showme A.poly & +- +-Triangle will read the Planar Straight Line Graph defined by A.poly, and +-write its constrained Delaunay triangulation to A.1.node and A.1.ele. +-Show Me will display the figure defined by A.poly. There are two buttons +-marked "ele" in the Show Me window; click on the top one. This will cause +-Show Me to load and display the triangulation. +- +-For contrast, try running +- +- triangle -pq A +- +-Now, click on the same "ele" button. A new triangulation will be loaded; +-this one having no angles smaller than 20 degrees. +- +-To see a Voronoi diagram, try this: +- +- cp A.poly A.node +- triangle -v A +- +-Click the "ele" button again. You will see the Delaunay triangulation of +-the points in A.poly, without the segments. Now click the top "voro" button. +-You will see the Voronoi diagram corresponding to that Delaunay triangulation. +-Click the "Reset" button to see the full extent of the diagram. +- +------------------------------------------------------------------------------- +- +-If you wish to call Triangle from another program, instructions for doing +-so are contained in the file `triangle.h' (but read Triangle's regular +-instructions first!). Also look at `tricall.c', which provides an example +-of how to call Triangle. +- +-Type "make trilibrary" to create triangle.o, a callable object file. +-Alternatively, the object file is usually easy to compile without a +-makefile: +- +- cc -DTRILIBRARY -O -c triangle.c +- +-Type "make distclean" to remove all the object and executable files created +-by make. +- +------------------------------------------------------------------------------- +- +-If you use Triangle, and especially if you use it to accomplish real work, +-I would like very much to hear from you. A short letter or email (to +-jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot to me. +-The more people I know are using this program, the more easily I can +-justify spending time on improvements and on the three-dimensional +-successor to Triangle, which in turn will benefit you. Also, I can put you +-on a list to receive email whenever a new version of Triangle is available. +- +-If you use a mesh generated by Triangle or plotted by Show Me in a +-publication, please include an acknowledgment as well. And please spell +-Triangle with a capital `T'! If you want to include a citation, use +-`Jonathan Richard Shewchuk, ``Triangle: Engineering a 2D Quality Mesh +-Generator and Delaunay Triangulator,'' in Applied Computational Geometry: +-Towards Geometric Engineering (Ming C. Lin and Dinesh Manocha, editors), +-volume 1148 of Lecture Notes in Computer Science, pages 203-222, +-Springer-Verlag, Berlin, May 1996. (From the First ACM Workshop on Applied +-Computational Geometry.)' +- +- +-Jonathan Richard Shewchuk +-July 27, 2005 +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.c b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.c +deleted file mode 100644 +index 017dbe1fae..0000000000 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.c ++++ /dev/null +@@ -1,16011 +0,0 @@ +-/*****************************************************************************/ +-/* */ +-/* 888888888 ,o, / 888 */ +-/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ +-/* 888 888 888 88b 888 888 888 888 888 d888 88b */ +-/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ +-/* 888 888 888 C888 888 888 888 / 888 q888 */ +-/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ +-/* "8oo8D */ +-/* */ +-/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ +-/* (triangle.c) */ +-/* */ +-/* Version 1.6 */ +-/* July 28, 2005 */ +-/* */ +-/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */ +-/* Jonathan Richard Shewchuk */ +-/* 2360 Woolsey #H */ +-/* Berkeley, California 94705-1927 */ +-/* jrs@cs.berkeley.edu */ +-/* */ +-/* This program may be freely redistributed under the condition that the */ +-/* copyright notices (including this entire header and the copyright */ +-/* notice printed when the `-h' switch is selected) are not removed, and */ +-/* no compensation is received. Private, research, and institutional */ +-/* use is free. You may distribute modified versions of this code UNDER */ +-/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ +-/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ +-/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ +-/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ +-/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ +-/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ +-/* customer, and you are instead telling them how they can obtain it for */ +-/* free, then you are not required to make any arrangement with me.) */ +-/* */ +-/* Hypertext instructions for Triangle are available on the Web at */ +-/* */ +-/* http://www.cs.cmu.edu/~quake/triangle.html */ +-/* */ +-/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ +-/* whatsoever. This code is provided "as-is". Use at your own risk. */ +-/* */ +-/* Some of the references listed below are marked with an asterisk. [*] */ +-/* These references are available for downloading from the Web page */ +-/* */ +-/* http://www.cs.cmu.edu/~quake/triangle.research.html */ +-/* */ +-/* Three papers discussing aspects of Triangle are available. A short */ +-/* overview appears in "Triangle: Engineering a 2D Quality Mesh */ +-/* Generator and Delaunay Triangulator," in Applied Computational */ +-/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */ +-/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */ +-/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */ +-/* Workshop on Applied Computational Geometry). [*] */ +-/* */ +-/* The algorithms are discussed in the greatest detail in "Delaunay */ +-/* Refinement Algorithms for Triangular Mesh Generation," Computational */ +-/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */ +-/* */ +-/* More detail about the data structures may be found in my dissertation: */ +-/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */ +-/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */ +-/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */ +-/* */ +-/* Triangle was created as part of the Quake Project in the School of */ +-/* Computer Science at Carnegie Mellon University. For further */ +-/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */ +-/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */ +-/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */ +-/* Media on Parallel Computers," Computer Methods in Applied Mechanics */ +-/* and Engineering 152(1-2):85-102, 22 January 1998. */ +-/* */ +-/* Triangle's Delaunay refinement algorithm for quality mesh generation is */ +-/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */ +-/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */ +-/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */ +-/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */ +-/* Annual Symposium on Computational Geometry (San Diego, California), */ +-/* pages 274-280, Association for Computing Machinery, May 1993, */ +-/* http://portal.acm.org/citation.cfm?id=161150 . */ +-/* */ +-/* The Delaunay refinement algorithm has been modified so that it meshes */ +-/* domains with small input angles well, as described in Gary L. Miller, */ +-/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */ +-/* Algorithm Works," Twelfth International Meshing Roundtable, pages */ +-/* 91-102, Sandia National Laboratories, September 2003. [*] */ +-/* */ +-/* My implementation of the divide-and-conquer and incremental Delaunay */ +-/* triangulation algorithms follows closely the presentation of Guibas */ +-/* and Stolfi, even though I use a triangle-based data structure instead */ +-/* of their quad-edge data structure. (In fact, I originally implemented */ +-/* Triangle using the quad-edge data structure, but the switch to a */ +-/* triangle-based data structure sped Triangle by a factor of two.) The */ +-/* mesh manipulation primitives and the two aforementioned Delaunay */ +-/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ +-/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ +-/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ +-/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/ +-/* */ +-/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */ +-/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */ +-/* Delaunay Triangulation," International Journal of Computer and */ +-/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */ +-/* divide-and-conquer algorithm by alternating between vertical and */ +-/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */ +-/* Conquer Algorithm for Constructing Delaunay Triangulations," */ +-/* Algorithmica 2(2):137-151, 1987. */ +-/* */ +-/* The incremental insertion algorithm was first proposed by C. L. Lawson, */ +-/* "Software for C1 Surface Interpolation," in Mathematical Software III, */ +-/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */ +-/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */ +-/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */ +-/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */ +-/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */ +-/* ACM, May 1996. [*] If I were to randomize the order of vertex */ +-/* insertion (I currently don't bother), their result combined with the */ +-/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */ +-/* Random Sampling in Computational Geometry II," Discrete & */ +-/* Computational Geometry 4(1):387-421, 1989, would yield an expected */ +-/* O(n^{4/3}) bound on running time. */ +-/* */ +-/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */ +-/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */ +-/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */ +-/* boundary of the triangulation are maintained in a splay tree for the */ +-/* purpose of point location. Splay trees are described by Daniel */ +-/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */ +-/* Trees," Journal of the ACM 32(3):652-686, July 1985, */ +-/* http://portal.acm.org/citation.cfm?id=3835 . */ +-/* */ +-/* The algorithms for exact computation of the signs of determinants are */ +-/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */ +-/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */ +-/* Computational Geometry 18(3):305-363, October 1997. (Also available */ +-/* as Technical Report CMU-CS-96-140, School of Computer Science, */ +-/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */ +-/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */ +-/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */ +-/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */ +-/* Many of the ideas for my exact arithmetic routines originate with */ +-/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */ +-/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */ +-/* Computer Society Press, 1991. [*] Many of the ideas for the correct */ +-/* evaluation of the signs of determinants are taken from Steven Fortune */ +-/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */ +-/* tional Geometry," Proceedings of the Ninth Annual Symposium on */ +-/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */ +-/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */ +-/* lations," International Journal of Computational Geometry & Applica- */ +-/* tions 5(1-2):193-213, March-June 1995. */ +-/* */ +-/* The method of inserting new vertices off-center (not precisely at the */ +-/* circumcenter of every poor-quality triangle) is from Alper Ungor, */ +-/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */ +-/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */ +-/* 2004 (Buenos Aires, Argentina), April 2004. */ +-/* */ +-/* For definitions of and results involving Delaunay triangulations, */ +-/* constrained and conforming versions thereof, and other aspects of */ +-/* triangular mesh generation, see the excellent survey by Marshall Bern */ +-/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */ +-/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */ +-/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */ +-/* */ +-/* The time for incrementally adding PSLG (planar straight line graph) */ +-/* segments to create a constrained Delaunay triangulation is probably */ +-/* O(t^2) per segment in the worst case and O(t) per segment in the */ +-/* common case, where t is the number of triangles that intersect the */ +-/* segment before it is inserted. This doesn't count point location, */ +-/* which can be much more expensive. I could improve this to O(d log d) */ +-/* time, but d is usually quite small, so it's not worth the bother. */ +-/* (This note does not apply when the -s switch is used, invoking a */ +-/* different method is used to insert segments.) */ +-/* */ +-/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */ +-/* in the worst case and O(d) in the common case, where d is the degree */ +-/* of the vertex being deleted. I could improve this to O(d log d) time, */ +-/* but d is usually quite small, so it's not worth the bother. */ +-/* */ +-/* Ruppert's Delaunay refinement algorithm typically generates triangles */ +-/* at a linear rate (constant time per triangle) after the initial */ +-/* triangulation is formed. There may be pathological cases where */ +-/* quadratic time is required, but these never arise in practice. */ +-/* */ +-/* The geometric predicates (circumcenter calculations, segment */ +-/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */ +-/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */ +-/* */ +-/* If you make any improvements to this code, please please please let me */ +-/* know, so that I may obtain the improvements. Even if you don't change */ +-/* the code, I'd still love to hear what it's being used for. */ +-/* */ +-/*****************************************************************************/ +- +-/* For single precision (which will save some memory and reduce paging), */ +-/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */ +-/* writing "#define SINGLE" below. */ +-/* */ +-/* For double precision (which will allow you to refine meshes to a smaller */ +-/* edge length), leave SINGLE undefined. */ +-/* */ +-/* Double precision uses more memory, but improves the resolution of the */ +-/* meshes you can generate with Triangle. It also reduces the likelihood */ +-/* of a floating exception due to overflow. Finally, it is much faster */ +-/* than single precision on 64-bit architectures like the DEC Alpha. I */ +-/* recommend double precision unless you want to generate a mesh for which */ +-/* you do not have enough memory. */ +- +-/* #define SINGLE */ +- +-#ifdef SINGLE +-#define REAL float +-#else /* not SINGLE */ +-#define REAL double +-#endif /* not SINGLE */ +- +-#define TRIANGLE_PTRINT size_t +- +-/* If yours is not a Unix system, define the NO_TIMER compiler switch to */ +-/* remove the Unix-specific timing code. */ +- +-#define NO_TIMER +- +-/* To insert lots of self-checks for internal errors, define the SELF_CHECK */ +-/* symbol. This will slow down the program significantly. It is best to */ +-/* define the symbol using the -DSELF_CHECK compiler switch, but you could */ +-/* write "#define SELF_CHECK" below. If you are modifying this code, I */ +-/* recommend you turn self-checks on until your work is debugged. */ +- +-/* #define SELF_CHECK */ +- +-/* To compile Triangle as a callable object library (triangle.o), define the */ +-/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */ +-/* the procedure triangulate() that results. */ +- +-#define TRILIBRARY +- +-/* It is possible to generate a smaller version of Triangle using one or */ +-/* both of the following symbols. Define the REDUCED symbol to eliminate */ +-/* all features that are primarily of research interest; specifically, the */ +-/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */ +-/* all meshing algorithms above and beyond constrained Delaunay */ +-/* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */ +-/* switches. These reductions are most likely to be useful when */ +-/* generating an object library (triangle.o) by defining the TRILIBRARY */ +-/* symbol. */ +- +-/* #define REDUCED */ +-/* #define CDT_ONLY */ +- +-/* On some machines, my exact arithmetic routines might be defeated by the */ +-/* use of internal extended precision floating-point registers. The best */ +-/* way to solve this problem is to set the floating-point registers to use */ +-/* single or double precision internally. On 80x86 processors, this may */ +-/* be accomplished by setting the CPU86 symbol for the Microsoft C */ +-/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */ +-/* */ +-/* An inferior solution is to declare certain values as `volatile', thus */ +-/* forcing them to be stored to memory and rounded off. Unfortunately, */ +-/* this solution might slow Triangle down quite a bit. To use volatile */ +-/* values, write "#define INEXACT volatile" below. Normally, however, */ +-/* INEXACT should be defined to be nothing. ("#define INEXACT".) */ +-/* */ +-/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */ +-/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */ +-/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */ +-/* available as Section 6.6 of my dissertation). */ +- +-/* #define CPU86 */ +-/* #define LINUX */ +- +-#define INEXACT /* Nothing */ +-/* #define INEXACT volatile */ +- +-/* Maximum number of characters in a file name (including the null). */ +- +-#define FILENAMESIZE 2048 +- +-/* Maximum number of characters in a line read from a file (including the */ +-/* null). */ +- +-#define INPUTLINESIZE 4096 +- +-/* For efficiency, a variety of data structures are allocated in bulk. The */ +-/* following constants determine how many of each structure is allocated */ +-/* at once. */ +- +-#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */ +-#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */ +-#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */ +-#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */ +-/* Number of encroached subsegments allocated at once. */ +-#define BADSUBSEGPERBLOCK 252 +-/* Number of skinny triangles allocated at once. */ +-#define BADTRIPERBLOCK 4092 +-/* Number of flipped triangles allocated at once. */ +-#define FLIPSTACKERPERBLOCK 252 +-/* Number of splay tree nodes allocated at once. */ +-#define SPLAYNODEPERBLOCK 508 +- +-/* The vertex types. A DEADVERTEX has been deleted entirely. An */ +-/* UNDEADVERTEX is not part of the mesh, but is written to the output */ +-/* .node file and affects the node indexing in the other output files. */ +- +-#define INPUTVERTEX 0 +-#define SEGMENTVERTEX 1 +-#define FREEVERTEX 2 +-#define DEADVERTEX -32768 +-#define UNDEADVERTEX -32767 +- +-/* The next line is used to outsmart some very stupid compilers. If your */ +-/* compiler is smarter, feel free to replace the "int" with "void". */ +-/* Not that it matters. */ +- +-/*#define void int */ +- +-/* Two constants for algorithms based on random sampling. Both constants */ +-/* have been chosen empirically to optimize their respective algorithms. */ +- +-/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */ +-/* how large a random sample of triangles to inspect. */ +- +-#define SAMPLEFACTOR 11 +- +-/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */ +-/* of boundary edges should be maintained in the splay tree for point */ +-/* location on the front. */ +- +-#define SAMPLERATE 10 +- +-/* A number that speaks for itself, every kissable digit. */ +- +-#define PI 3.141592653589793238462643383279502884197169399375105820974944592308 +- +-/* Another fave. */ +- +-#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732 +- +-/* And here's one for those of you who are intimidated by math. */ +- +-#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333 +- +-#include +-#include +-#include +-#include +-#ifndef NO_TIMER +-#include +-#endif /* not NO_TIMER */ +-#ifdef CPU86 +-#include +-#endif /* CPU86 */ +-#ifdef LINUX +-#include +-#endif /* LINUX */ +-#ifdef TRILIBRARY +-#include "triangle.h" +-#endif /* TRILIBRARY */ +- +-/* A few forward declarations. */ +- +-#ifndef TRILIBRARY +-char *readline(); +-char *findfield(); +-#endif /* not TRILIBRARY */ +- +-/* Labels that signify the result of point location. The result of a */ +-/* search indicates that the point falls in the interior of a triangle, on */ +-/* an edge, on a vertex, or outside the mesh. */ +- +-enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE}; +- +-/* Labels that signify the result of vertex insertion. The result indicates */ +-/* that the vertex was inserted with complete success, was inserted but */ +-/* encroaches upon a subsegment, was not inserted because it lies on a */ +-/* segment, or was not inserted because another vertex occupies the same */ +-/* location. */ +- +-enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX, +- DUPLICATEVERTEX}; +- +-/* Labels that signify the result of direction finding. The result */ +-/* indicates that a segment connecting the two query points falls within */ +-/* the direction triangle, along the left edge of the direction triangle, */ +-/* or along the right edge of the direction triangle. */ +- +-enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR}; +- +-/* Labels that signify the result of the circumcenter computation routine. */ +-/* The return value indicates which edge of the triangle is shortest. */ +- +-enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX}; +- +-/*****************************************************************************/ +-/* */ +-/* The basic mesh data structures */ +-/* */ +-/* There are three: vertices, triangles, and subsegments (abbreviated */ +-/* `subseg'). These three data structures, linked by pointers, comprise */ +-/* the mesh. A vertex simply represents a mesh vertex and its properties. */ +-/* A triangle is a triangle. A subsegment is a special data structure used */ +-/* to represent an impenetrable edge of the mesh (perhaps on the outer */ +-/* boundary, on the boundary of a hole, or part of an internal boundary */ +-/* separating two triangulated regions). Subsegments represent boundaries, */ +-/* defined by the user, that triangles may not lie across. */ +-/* */ +-/* A triangle consists of a list of three vertices, a list of three */ +-/* adjoining triangles, a list of three adjoining subsegments (when */ +-/* segments exist), an arbitrary number of optional user-defined */ +-/* floating-point attributes, and an optional area constraint. The latter */ +-/* is an upper bound on the permissible area of each triangle in a region, */ +-/* used for mesh refinement. */ +-/* */ +-/* For a triangle on a boundary of the mesh, some or all of the neighboring */ +-/* triangles may not be present. For a triangle in the interior of the */ +-/* mesh, often no neighboring subsegments are present. Such absent */ +-/* triangles and subsegments are never represented by NULL pointers; they */ +-/* are represented by two special records: `dummytri', the triangle that */ +-/* fills "outer space", and `dummysub', the omnipresent subsegment. */ +-/* `dummytri' and `dummysub' are used for several reasons; for instance, */ +-/* they can be dereferenced and their contents examined without violating */ +-/* protected memory. */ +-/* */ +-/* However, it is important to understand that a triangle includes other */ +-/* information as well. The pointers to adjoining vertices, triangles, and */ +-/* subsegments are ordered in a way that indicates their geometric relation */ +-/* to each other. Furthermore, each of these pointers contains orientation */ +-/* information. Each pointer to an adjoining triangle indicates which face */ +-/* of that triangle is contacted. Similarly, each pointer to an adjoining */ +-/* subsegment indicates which side of that subsegment is contacted, and how */ +-/* the subsegment is oriented relative to the triangle. */ +-/* */ +-/* The data structure representing a subsegment may be thought to be */ +-/* abutting the edge of one or two triangle data structures: either */ +-/* sandwiched between two triangles, or resting against one triangle on an */ +-/* exterior boundary or hole boundary. */ +-/* */ +-/* A subsegment consists of a list of four vertices--the vertices of the */ +-/* subsegment, and the vertices of the segment it is a part of--a list of */ +-/* two adjoining subsegments, and a list of two adjoining triangles. One */ +-/* of the two adjoining triangles may not be present (though there should */ +-/* always be one), and neighboring subsegments might not be present. */ +-/* Subsegments also store a user-defined integer "boundary marker". */ +-/* Typically, this integer is used to indicate what boundary conditions are */ +-/* to be applied at that location in a finite element simulation. */ +-/* */ +-/* Like triangles, subsegments maintain information about the relative */ +-/* orientation of neighboring objects. */ +-/* */ +-/* Vertices are relatively simple. A vertex is a list of floating-point */ +-/* numbers, starting with the x, and y coordinates, followed by an */ +-/* arbitrary number of optional user-defined floating-point attributes, */ +-/* followed by an integer boundary marker. During the segment insertion */ +-/* phase, there is also a pointer from each vertex to a triangle that may */ +-/* contain it. Each pointer is not always correct, but when one is, it */ +-/* speeds up segment insertion. These pointers are assigned values once */ +-/* at the beginning of the segment insertion phase, and are not used or */ +-/* updated except during this phase. Edge flipping during segment */ +-/* insertion will render some of them incorrect. Hence, don't rely upon */ +-/* them for anything. */ +-/* */ +-/* Other than the exception mentioned above, vertices have no information */ +-/* about what triangles, subfacets, or subsegments they are linked to. */ +-/* */ +-/*****************************************************************************/ +- +-/*****************************************************************************/ +-/* */ +-/* Handles */ +-/* */ +-/* The oriented triangle (`otri') and oriented subsegment (`osub') data */ +-/* structures defined below do not themselves store any part of the mesh. */ +-/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */ +-/* */ +-/* Oriented triangles and oriented subsegments will usually be referred to */ +-/* as "handles." A handle is essentially a pointer into the mesh; it */ +-/* allows you to "hold" one particular part of the mesh. Handles are used */ +-/* to specify the regions in which one is traversing and modifying the mesh.*/ +-/* A single `triangle' may be held by many handles, or none at all. (The */ +-/* latter case is not a memory leak, because the triangle is still */ +-/* connected to other triangles in the mesh.) */ +-/* */ +-/* An `otri' is a handle that holds a triangle. It holds a specific edge */ +-/* of the triangle. An `osub' is a handle that holds a subsegment. It */ +-/* holds either the left or right side of the subsegment. */ +-/* */ +-/* Navigation about the mesh is accomplished through a set of mesh */ +-/* manipulation primitives, further below. Many of these primitives take */ +-/* a handle and produce a new handle that holds the mesh near the first */ +-/* handle. Other primitives take two handles and glue the corresponding */ +-/* parts of the mesh together. The orientation of the handles is */ +-/* important. For instance, when two triangles are glued together by the */ +-/* bond() primitive, they are glued at the edges on which the handles lie. */ +-/* */ +-/* Because vertices have no information about which triangles they are */ +-/* attached to, I commonly represent a vertex by use of a handle whose */ +-/* origin is the vertex. A single handle can simultaneously represent a */ +-/* triangle, an edge, and a vertex. */ +-/* */ +-/*****************************************************************************/ +- +-/* The triangle data structure. Each triangle contains three pointers to */ +-/* adjoining triangles, plus three pointers to vertices, plus three */ +-/* pointers to subsegments (declared below; these pointers are usually */ +-/* `dummysub'). It may or may not also contain user-defined attributes */ +-/* and/or a floating-point "area constraint." It may also contain extra */ +-/* pointers for nodes, when the user asks for high-order elements. */ +-/* Because the size and structure of a `triangle' is not decided until */ +-/* runtime, I haven't simply declared the type `triangle' as a struct. */ +- +-typedef REAL **triangle; /* Really: typedef triangle *triangle */ +- +-/* An oriented triangle: includes a pointer to a triangle and orientation. */ +-/* The orientation denotes an edge of the triangle. Hence, there are */ +-/* three possible orientations. By convention, each edge always points */ +-/* counterclockwise about the corresponding triangle. */ +- +-struct otri { +- triangle *tri; +- int orient; /* Ranges from 0 to 2. */ +-}; +- +-/* The subsegment data structure. Each subsegment contains two pointers to */ +-/* adjoining subsegments, plus four pointers to vertices, plus two */ +-/* pointers to adjoining triangles, plus one boundary marker, plus one */ +-/* segment number. */ +- +-typedef REAL **subseg; /* Really: typedef subseg *subseg */ +- +-/* An oriented subsegment: includes a pointer to a subsegment and an */ +-/* orientation. The orientation denotes a side of the edge. Hence, there */ +-/* are two possible orientations. By convention, the edge is always */ +-/* directed so that the "side" denoted is the right side of the edge. */ +- +-struct osub { +- subseg *ss; +- int ssorient; /* Ranges from 0 to 1. */ +-}; +- +-/* The vertex data structure. Each vertex is actually an array of REALs. */ +-/* The number of REALs is unknown until runtime. An integer boundary */ +-/* marker, and sometimes a pointer to a triangle, is appended after the */ +-/* REALs. */ +- +-typedef REAL *vertex; +- +-/* A queue used to store encroached subsegments. Each subsegment's vertices */ +-/* are stored so that we can check whether a subsegment is still the same. */ +- +-struct badsubseg { +- subseg encsubseg; /* An encroached subsegment. */ +- vertex subsegorg, subsegdest; /* Its two vertices. */ +-}; +- +-/* A queue used to store bad triangles. The key is the square of the cosine */ +-/* of the smallest angle of the triangle. Each triangle's vertices are */ +-/* stored so that one can check whether a triangle is still the same. */ +- +-struct badtriang { +- triangle poortri; /* A skinny or too-large triangle. */ +- REAL key; /* cos^2 of smallest (apical) angle. */ +- vertex triangorg, triangdest, triangapex; /* Its three vertices. */ +- struct badtriang *nexttriang; /* Pointer to next bad triangle. */ +-}; +- +-/* A stack of triangles flipped during the most recent vertex insertion. */ +-/* The stack is used to undo the vertex insertion if the vertex encroaches */ +-/* upon a subsegment. */ +- +-struct flipstacker { +- triangle flippedtri; /* A recently flipped triangle. */ +- struct flipstacker *prevflip; /* Previous flip in the stack. */ +-}; +- +-/* A node in a heap used to store events for the sweepline Delaunay */ +-/* algorithm. Nodes do not point directly to their parents or children in */ +-/* the heap. Instead, each node knows its position in the heap, and can */ +-/* look up its parent and children in a separate array. The `eventptr' */ +-/* points either to a `vertex' or to a triangle (in encoded format, so */ +-/* that an orientation is included). In the latter case, the origin of */ +-/* the oriented triangle is the apex of a "circle event" of the sweepline */ +-/* algorithm. To distinguish site events from circle events, all circle */ +-/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */ +- +-struct event { +- REAL xkey, ykey; /* Coordinates of the event. */ +- void *eventptr; /* Can be a vertex or the location of a circle event. */ +- int heapposition; /* Marks this event's position in the heap. */ +-}; +- +-/* A node in the splay tree. Each node holds an oriented ghost triangle */ +-/* that represents a boundary edge of the growing triangulation. When a */ +-/* circle event covers two boundary edges with a triangle, so that they */ +-/* are no longer boundary edges, those edges are not immediately deleted */ +-/* from the tree; rather, they are lazily deleted when they are next */ +-/* encountered. (Since only a random sample of boundary edges are kept */ +-/* in the tree, lazy deletion is faster.) `keydest' is used to verify */ +-/* that a triangle is still the same as when it entered the splay tree; if */ +-/* it has been rotated (due to a circle event), it no longer represents a */ +-/* boundary edge and should be deleted. */ +- +-struct splaynode { +- struct otri keyedge; /* Lprev of an edge on the front. */ +- vertex keydest; /* Used to verify that splay node is still live. */ +- struct splaynode *lchild, *rchild; /* Children in splay tree. */ +-}; +- +-/* A type used to allocate memory. firstblock is the first block of items. */ +-/* nowblock is the block from which items are currently being allocated. */ +-/* nextitem points to the next slab of free memory for an item. */ +-/* deaditemstack is the head of a linked list (stack) of deallocated items */ +-/* that can be recycled. unallocateditems is the number of items that */ +-/* remain to be allocated from nowblock. */ +-/* */ +-/* Traversal is the process of walking through the entire list of items, and */ +-/* is separate from allocation. Note that a traversal will visit items on */ +-/* the "deaditemstack" stack as well as live items. pathblock points to */ +-/* the block currently being traversed. pathitem points to the next item */ +-/* to be traversed. pathitemsleft is the number of items that remain to */ +-/* be traversed in pathblock. */ +-/* */ +-/* alignbytes determines how new records should be aligned in memory. */ +-/* itembytes is the length of a record in bytes (after rounding up). */ +-/* itemsperblock is the number of items allocated at once in a single */ +-/* block. itemsfirstblock is the number of items in the first block, */ +-/* which can vary from the others. items is the number of currently */ +-/* allocated items. maxitems is the maximum number of items that have */ +-/* been allocated at once; it is the current number of items plus the */ +-/* number of records kept on deaditemstack. */ +- +-struct memorypool { +- void **firstblock, **nowblock; +- void *nextitem; +- void *deaditemstack; +- void **pathblock; +- void *pathitem; +- int alignbytes; +- int itembytes; +- int itemsperblock; +- int itemsfirstblock; +- long items, maxitems; +- int unallocateditems; +- int pathitemsleft; +-}; +- +- +-/* Global constants. */ +- +-REAL splitter; /* Used to split REAL factors for exact multiplication. */ +-REAL epsilon; /* Floating-point machine epsilon. */ +-REAL resulterrbound; +-REAL ccwerrboundA, ccwerrboundB, ccwerrboundC; +-REAL iccerrboundA, iccerrboundB, iccerrboundC; +-REAL o3derrboundA, o3derrboundB, o3derrboundC; +- +-/* Random number seed is not constant, but I've made it global anyway. */ +- +-TRIANGLE_PTRINT randomseed; /* Current random number seed. */ +- +- +-/* Mesh data structure. Triangle operates on only one mesh, but the mesh */ +-/* structure is used (instead of global variables) to allow reentrancy. */ +- +-struct mesh { +- +-/* Variables used to allocate memory for triangles, subsegments, vertices, */ +-/* viri (triangles being eaten), encroached segments, bad (skinny or too */ +-/* large) triangles, and splay tree nodes. */ +- +- struct memorypool triangles; +- struct memorypool subsegs; +- struct memorypool vertices; +- struct memorypool viri; +- struct memorypool badsubsegs; +- struct memorypool badtriangles; +- struct memorypool flipstackers; +- struct memorypool splaynodes; +- +-/* Variables that maintain the bad triangle queues. The queues are */ +-/* ordered from 4095 (highest priority) to 0 (lowest priority). */ +- +- struct badtriang *queuefront[4096]; +- struct badtriang *queuetail[4096]; +- int nextnonemptyq[4096]; +- int firstnonemptyq; +- +-/* Variable that maintains the stack of recently flipped triangles. */ +- +- struct flipstacker *lastflip; +- +-/* Other variables. */ +- +- REAL xmin, xmax, ymin, ymax; /* x and y bounds. */ +- REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ +- int invertices; /* Number of input vertices. */ +- int inelements; /* Number of input triangles. */ +- int insegments; /* Number of input segments. */ +- int holes; /* Number of input holes. */ +- int regions; /* Number of input regions. */ +- int undeads; /* Number of input vertices that don't appear in the mesh. */ +- long edges; /* Number of output edges. */ +- int mesh_dim; /* Dimension (ought to be 2). */ +- int nextras; /* Number of attributes per vertex. */ +- int eextras; /* Number of attributes per triangle. */ +- long hullsize; /* Number of edges in convex hull. */ +- int steinerleft; /* Number of Steiner points not yet used. */ +- int vertexmarkindex; /* Index to find boundary marker of a vertex. */ +- int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */ +- int highorderindex; /* Index to find extra nodes for high-order elements. */ +- int elemattribindex; /* Index to find attributes of a triangle. */ +- int areaboundindex; /* Index to find area bound of a triangle. */ +- int checksegments; /* Are there segments in the triangulation yet? */ +- int checkquality; /* Has quality triangulation begun yet? */ +- int readnodefile; /* Has a .node file been read? */ +- long samples; /* Number of random samples for point location. */ +- +- long incirclecount; /* Number of incircle tests performed. */ +- long counterclockcount; /* Number of counterclockwise tests performed. */ +- long orient3dcount; /* Number of 3D orientation tests performed. */ +- long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ +- long circumcentercount; /* Number of circumcenter calculations performed. */ +- long circletopcount; /* Number of circle top calculations performed. */ +- +-/* Triangular bounding box vertices. */ +- +- vertex infvertex1, infvertex2, infvertex3; +- +-/* Pointer to the `triangle' that occupies all of "outer space." */ +- +- triangle *dummytri; +- triangle *dummytribase; /* Keep base address so we can free() it later. */ +- +-/* Pointer to the omnipresent subsegment. Referenced by any triangle or */ +-/* subsegment that isn't really connected to a subsegment at that */ +-/* location. */ +- +- subseg *dummysub; +- subseg *dummysubbase; /* Keep base address so we can free() it later. */ +- +-/* Pointer to a recently visited triangle. Improves point location if */ +-/* proximate vertices are inserted sequentially. */ +- +- struct otri recenttri; +- +-}; /* End of `struct mesh'. */ +- +- +-/* Data structure for command line switches and file names. This structure */ +-/* is used (instead of global variables) to allow reentrancy. */ +- +-struct behavior { +- +-/* Switches for the triangulator. */ +-/* poly: -p switch. refine: -r switch. */ +-/* quality: -q switch. */ +-/* minangle: minimum angle bound, specified after -q switch. */ +-/* goodangle: cosine squared of minangle. */ +-/* offconstant: constant used to place off-center Steiner points. */ +-/* vararea: -a switch without number. */ +-/* fixedarea: -a switch with number. */ +-/* maxarea: maximum area bound, specified after -a switch. */ +-/* usertest: -u switch. */ +-/* regionattrib: -A switch. convex: -c switch. */ +-/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */ +-/* firstnumber: inverse of -z switch. All items are numbered starting */ +-/* from `firstnumber'. */ +-/* edgesout: -e switch. voronoi: -v switch. */ +-/* neighbors: -n switch. geomview: -g switch. */ +-/* nobound: -B switch. nopolywritten: -P switch. */ +-/* nonodewritten: -N switch. noelewritten: -E switch. */ +-/* noiterationnum: -I switch. noholes: -O switch. */ +-/* noexact: -X switch. */ +-/* order: element order, specified after -o switch. */ +-/* nobisect: count of how often -Y switch is selected. */ +-/* steiner: maximum number of Steiner points, specified after -S switch. */ +-/* incremental: -i switch. sweepline: -F switch. */ +-/* dwyer: inverse of -l switch. */ +-/* splitseg: -s switch. */ +-/* conformdel: -D switch. docheck: -C switch. */ +-/* quiet: -Q switch. verbose: count of how often -V switch is selected. */ +-/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */ +-/* used at all. */ +-/* */ +-/* Read the instructions to find out the meaning of these switches. */ +- +- int poly, refine, quality, vararea, fixedarea, usertest; +- int regionattrib, convex, weighted, jettison; +- int firstnumber; +- int edgesout, voronoi, neighbors, geomview; +- int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; +- int noholes, noexact, conformdel; +- int incremental, sweepline, dwyer; +- int splitseg; +- int docheck; +- int quiet, verbose; +- int usesegments; +- int order; +- int nobisect; +- int steiner; +- REAL minangle, goodangle, offconstant; +- REAL maxarea; +- +-/* Variables for file names. */ +- +-#ifndef TRILIBRARY +- char innodefilename[FILENAMESIZE]; +- char inelefilename[FILENAMESIZE]; +- char inpolyfilename[FILENAMESIZE]; +- char areafilename[FILENAMESIZE]; +- char outnodefilename[FILENAMESIZE]; +- char outelefilename[FILENAMESIZE]; +- char outpolyfilename[FILENAMESIZE]; +- char edgefilename[FILENAMESIZE]; +- char vnodefilename[FILENAMESIZE]; +- char vedgefilename[FILENAMESIZE]; +- char neighborfilename[FILENAMESIZE]; +- char offfilename[FILENAMESIZE]; +-#endif /* not TRILIBRARY */ +- +-}; /* End of `struct behavior'. */ +- +- +-/*****************************************************************************/ +-/* */ +-/* Mesh manipulation primitives. Each triangle contains three pointers to */ +-/* other triangles, with orientations. Each pointer points not to the */ +-/* first byte of a triangle, but to one of the first three bytes of a */ +-/* triangle. It is necessary to extract both the triangle itself and the */ +-/* orientation. To save memory, I keep both pieces of information in one */ +-/* pointer. To make this possible, I assume that all triangles are aligned */ +-/* to four-byte boundaries. The decode() routine below decodes a pointer, */ +-/* extracting an orientation (in the range 0 to 2) and a pointer to the */ +-/* beginning of a triangle. The encode() routine compresses a pointer to a */ +-/* triangle and an orientation into a single pointer. My assumptions that */ +-/* triangles are four-byte-aligned and that the `TRIANGLE_PTRINT' type is */ +-/* long enough to hold a pointer are two of the few kludges in this program.*/ +-/* */ +-/* Subsegments are manipulated similarly. A pointer to a subsegment */ +-/* carries both an address and an orientation in the range 0 to 1. */ +-/* */ +-/* The other primitives take an oriented triangle or oriented subsegment, */ +-/* and return an oriented triangle or oriented subsegment or vertex; or */ +-/* they change the connections in the data structure. */ +-/* */ +-/* Below, triangles and subsegments are denoted by their vertices. The */ +-/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */ +-/* c. These vertices occur in counterclockwise order about the triangle. */ +-/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */ +-/* abc. */ +-/* */ +-/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */ +-/* b. If ab is thought to be directed upward (with b directly above a), */ +-/* then the handle ab is thought to grasp the right side of ab, and may */ +-/* simultaneously denote vertex a and edge ab. */ +-/* */ +-/* An asterisk (*) denotes a vertex whose identity is unknown. */ +-/* */ +-/* Given this notation, a partial list of mesh manipulation primitives */ +-/* follows. */ +-/* */ +-/* */ +-/* For triangles: */ +-/* */ +-/* sym: Find the abutting triangle; same edge. */ +-/* sym(abc) -> ba* */ +-/* */ +-/* lnext: Find the next edge (counterclockwise) of a triangle. */ +-/* lnext(abc) -> bca */ +-/* */ +-/* lprev: Find the previous edge (clockwise) of a triangle. */ +-/* lprev(abc) -> cab */ +-/* */ +-/* onext: Find the next edge counterclockwise with the same origin. */ +-/* onext(abc) -> ac* */ +-/* */ +-/* oprev: Find the next edge clockwise with the same origin. */ +-/* oprev(abc) -> a*b */ +-/* */ +-/* dnext: Find the next edge counterclockwise with the same destination. */ +-/* dnext(abc) -> *ba */ +-/* */ +-/* dprev: Find the next edge clockwise with the same destination. */ +-/* dprev(abc) -> cb* */ +-/* */ +-/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */ +-/* rnext(abc) -> *a* */ +-/* */ +-/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */ +-/* rprev(abc) -> b** */ +-/* */ +-/* org: Origin dest: Destination apex: Apex */ +-/* org(abc) -> a dest(abc) -> b apex(abc) -> c */ +-/* */ +-/* bond: Bond two triangles together at the resepective handles. */ +-/* bond(abc, bad) */ +-/* */ +-/* */ +-/* For subsegments: */ +-/* */ +-/* ssym: Reverse the orientation of a subsegment. */ +-/* ssym(ab) -> ba */ +-/* */ +-/* spivot: Find adjoining subsegment with the same origin. */ +-/* spivot(ab) -> a* */ +-/* */ +-/* snext: Find next subsegment in sequence. */ +-/* snext(ab) -> b* */ +-/* */ +-/* sorg: Origin sdest: Destination */ +-/* sorg(ab) -> a sdest(ab) -> b */ +-/* */ +-/* sbond: Bond two subsegments together at the respective origins. */ +-/* sbond(ab, ac) */ +-/* */ +-/* */ +-/* For interacting tetrahedra and subfacets: */ +-/* */ +-/* tspivot: Find a subsegment abutting a triangle. */ +-/* tspivot(abc) -> ba */ +-/* */ +-/* stpivot: Find a triangle abutting a subsegment. */ +-/* stpivot(ab) -> ba* */ +-/* */ +-/* tsbond: Bond a triangle to a subsegment. */ +-/* tsbond(abc, ba) */ +-/* */ +-/*****************************************************************************/ +- +-/********* Mesh manipulation primitives begin here *********/ +-/** **/ +-/** **/ +- +-/* Fast lookup arrays to speed some of the mesh manipulation primitives. */ +- +-int plus1mod3[3] = {1, 2, 0}; +-int minus1mod3[3] = {2, 0, 1}; +- +-/********* Primitives for triangles *********/ +-/* */ +-/* */ +- +-/* decode() converts a pointer to an oriented triangle. The orientation is */ +-/* extracted from the two least significant bits of the pointer. */ +- +-#define decode(ptr, otri) \ +- (otri).orient = (int) ((TRIANGLE_PTRINT) (ptr) & (TRIANGLE_PTRINT) 3l); \ +- (otri).tri = (triangle *) \ +- ((TRIANGLE_PTRINT) (ptr) ^ (TRIANGLE_PTRINT) (otri).orient) +- +-/* encode() compresses an oriented triangle into a single pointer. It */ +-/* relies on the assumption that all triangles are aligned to four-byte */ +-/* boundaries, so the two least significant bits of (otri).tri are zero. */ +- +-#define encode(otri) \ +- (triangle) ((TRIANGLE_PTRINT) (otri).tri | (TRIANGLE_PTRINT) (otri).orient) +- +-/* The following handle manipulation primitives are all described by Guibas */ +-/* and Stolfi. However, Guibas and Stolfi use an edge-based data */ +-/* structure, whereas I use a triangle-based data structure. */ +- +-/* sym() finds the abutting triangle, on the same edge. Note that the edge */ +-/* direction is necessarily reversed, because the handle specified by an */ +-/* oriented triangle is directed counterclockwise around the triangle. */ +- +-#define sym(otri1, otri2) \ +- ptr = (otri1).tri[(otri1).orient]; \ +- decode(ptr, otri2); +- +-#define symself(otri) \ +- ptr = (otri).tri[(otri).orient]; \ +- decode(ptr, otri); +- +-/* lnext() finds the next edge (counterclockwise) of a triangle. */ +- +-#define lnext(otri1, otri2) \ +- (otri2).tri = (otri1).tri; \ +- (otri2).orient = plus1mod3[(otri1).orient] +- +-#define lnextself(otri) \ +- (otri).orient = plus1mod3[(otri).orient] +- +-/* lprev() finds the previous edge (clockwise) of a triangle. */ +- +-#define lprev(otri1, otri2) \ +- (otri2).tri = (otri1).tri; \ +- (otri2).orient = minus1mod3[(otri1).orient] +- +-#define lprevself(otri) \ +- (otri).orient = minus1mod3[(otri).orient] +- +-/* onext() spins counterclockwise around a vertex; that is, it finds the */ +-/* next edge with the same origin in the counterclockwise direction. This */ +-/* edge is part of a different triangle. */ +- +-#define onext(otri1, otri2) \ +- lprev(otri1, otri2); \ +- symself(otri2); +- +-#define onextself(otri) \ +- lprevself(otri); \ +- symself(otri); +- +-/* oprev() spins clockwise around a vertex; that is, it finds the next edge */ +-/* with the same origin in the clockwise direction. This edge is part of */ +-/* a different triangle. */ +- +-#define oprev(otri1, otri2) \ +- sym(otri1, otri2); \ +- lnextself(otri2); +- +-#define oprevself(otri) \ +- symself(otri); \ +- lnextself(otri); +- +-/* dnext() spins counterclockwise around a vertex; that is, it finds the */ +-/* next edge with the same destination in the counterclockwise direction. */ +-/* This edge is part of a different triangle. */ +- +-#define dnext(otri1, otri2) \ +- sym(otri1, otri2); \ +- lprevself(otri2); +- +-#define dnextself(otri) \ +- symself(otri); \ +- lprevself(otri); +- +-/* dprev() spins clockwise around a vertex; that is, it finds the next edge */ +-/* with the same destination in the clockwise direction. This edge is */ +-/* part of a different triangle. */ +- +-#define dprev(otri1, otri2) \ +- lnext(otri1, otri2); \ +- symself(otri2); +- +-#define dprevself(otri) \ +- lnextself(otri); \ +- symself(otri); +- +-/* rnext() moves one edge counterclockwise about the adjacent triangle. */ +-/* (It's best understood by reading Guibas and Stolfi. It involves */ +-/* changing triangles twice.) */ +- +-#define rnext(otri1, otri2) \ +- sym(otri1, otri2); \ +- lnextself(otri2); \ +- symself(otri2); +- +-#define rnextself(otri) \ +- symself(otri); \ +- lnextself(otri); \ +- symself(otri); +- +-/* rprev() moves one edge clockwise about the adjacent triangle. */ +-/* (It's best understood by reading Guibas and Stolfi. It involves */ +-/* changing triangles twice.) */ +- +-#define rprev(otri1, otri2) \ +- sym(otri1, otri2); \ +- lprevself(otri2); \ +- symself(otri2); +- +-#define rprevself(otri) \ +- symself(otri); \ +- lprevself(otri); \ +- symself(otri); +- +-/* These primitives determine or set the origin, destination, or apex of a */ +-/* triangle. */ +- +-#define org(otri, vertexptr) \ +- vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3] +- +-#define dest(otri, vertexptr) \ +- vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3] +- +-#define apex(otri, vertexptr) \ +- vertexptr = (vertex) (otri).tri[(otri).orient + 3] +- +-#define setorg(otri, vertexptr) \ +- (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr +- +-#define setdest(otri, vertexptr) \ +- (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr +- +-#define setapex(otri, vertexptr) \ +- (otri).tri[(otri).orient + 3] = (triangle) vertexptr +- +-/* Bond two triangles together. */ +- +-#define bond(otri1, otri2) \ +- (otri1).tri[(otri1).orient] = encode(otri2); \ +- (otri2).tri[(otri2).orient] = encode(otri1) +- +-/* Dissolve a bond (from one side). Note that the other triangle will still */ +-/* think it's connected to this triangle. Usually, however, the other */ +-/* triangle is being deleted entirely, or bonded to another triangle, so */ +-/* it doesn't matter. */ +- +-#define dissolve(otri) \ +- (otri).tri[(otri).orient] = (triangle) m->dummytri +- +-/* Copy an oriented triangle. */ +- +-#define otricopy(otri1, otri2) \ +- (otri2).tri = (otri1).tri; \ +- (otri2).orient = (otri1).orient +- +-/* Test for equality of oriented triangles. */ +- +-#define otriequal(otri1, otri2) \ +- (((otri1).tri == (otri2).tri) && \ +- ((otri1).orient == (otri2).orient)) +- +-/* Primitives to infect or cure a triangle with the virus. These rely on */ +-/* the assumption that all subsegments are aligned to four-byte boundaries.*/ +- +-#define infect(otri) \ +- (otri).tri[6] = (triangle) \ +- ((TRIANGLE_PTRINT) (otri).tri[6] | (TRIANGLE_PTRINT) 2l) +- +-#define uninfect(otri) \ +- (otri).tri[6] = (triangle) \ +- ((TRIANGLE_PTRINT) (otri).tri[6] & ~ (TRIANGLE_PTRINT) 2l) +- +-/* Test a triangle for viral infection. */ +- +-#define infected(otri) \ +- (((TRIANGLE_PTRINT) (otri).tri[6] & (TRIANGLE_PTRINT) 2l) != 0l) +- +-/* Check or set a triangle's attributes. */ +- +-#define elemattribute(otri, attnum) \ +- ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] +- +-#define setelemattribute(otri, attnum, value) \ +- ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value +- +-/* Check or set a triangle's maximum area bound. */ +- +-#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex] +- +-#define setareabound(otri, value) \ +- ((REAL *) (otri).tri)[m->areaboundindex] = value +- +-/* Check or set a triangle's deallocation. Its second pointer is set to */ +-/* NULL to indicate that it is not allocated. (Its first pointer is used */ +-/* for the stack of dead items.) Its fourth pointer (its first vertex) */ +-/* is set to NULL in case a `badtriang' structure points to it. */ +- +-#define deadtri(tria) ((tria)[1] == (triangle) NULL) +- +-#define killtri(tria) \ +- (tria)[1] = (triangle) NULL; \ +- (tria)[3] = (triangle) NULL +- +-/********* Primitives for subsegments *********/ +-/* */ +-/* */ +- +-/* sdecode() converts a pointer to an oriented subsegment. The orientation */ +-/* is extracted from the least significant bit of the pointer. The two */ +-/* least significant bits (one for orientation, one for viral infection) */ +-/* are masked out to produce the real pointer. */ +- +-#define sdecode(sptr, osub) \ +- (osub).ssorient = (int) ((TRIANGLE_PTRINT) (sptr) & (TRIANGLE_PTRINT) 1l); \ +- (osub).ss = (subseg *) \ +- ((TRIANGLE_PTRINT) (sptr) & ~ (TRIANGLE_PTRINT) 3l) +- +-/* sencode() compresses an oriented subsegment into a single pointer. It */ +-/* relies on the assumption that all subsegments are aligned to two-byte */ +-/* boundaries, so the least significant bit of (osub).ss is zero. */ +- +-#define sencode(osub) \ +- (subseg) ((TRIANGLE_PTRINT) (osub).ss | (TRIANGLE_PTRINT) (osub).ssorient) +- +-/* ssym() toggles the orientation of a subsegment. */ +- +-#define ssym(osub1, osub2) \ +- (osub2).ss = (osub1).ss; \ +- (osub2).ssorient = 1 - (osub1).ssorient +- +-#define ssymself(osub) \ +- (osub).ssorient = 1 - (osub).ssorient +- +-/* spivot() finds the other subsegment (from the same segment) that shares */ +-/* the same origin. */ +- +-#define spivot(osub1, osub2) \ +- sptr = (osub1).ss[(osub1).ssorient]; \ +- sdecode(sptr, osub2) +- +-#define spivotself(osub) \ +- sptr = (osub).ss[(osub).ssorient]; \ +- sdecode(sptr, osub) +- +-/* snext() finds the next subsegment (from the same segment) in sequence; */ +-/* one whose origin is the input subsegment's destination. */ +- +-#define snext(osub1, osub2) \ +- sptr = (osub1).ss[1 - (osub1).ssorient]; \ +- sdecode(sptr, osub2) +- +-#define snextself(osub) \ +- sptr = (osub).ss[1 - (osub).ssorient]; \ +- sdecode(sptr, osub) +- +-/* These primitives determine or set the origin or destination of a */ +-/* subsegment or the segment that includes it. */ +- +-#define sorg(osub, vertexptr) \ +- vertexptr = (vertex) (osub).ss[2 + (osub).ssorient] +- +-#define sdest(osub, vertexptr) \ +- vertexptr = (vertex) (osub).ss[3 - (osub).ssorient] +- +-#define setsorg(osub, vertexptr) \ +- (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr +- +-#define setsdest(osub, vertexptr) \ +- (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr +- +-#define segorg(osub, vertexptr) \ +- vertexptr = (vertex) (osub).ss[4 + (osub).ssorient] +- +-#define segdest(osub, vertexptr) \ +- vertexptr = (vertex) (osub).ss[5 - (osub).ssorient] +- +-#define setsegorg(osub, vertexptr) \ +- (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr +- +-#define setsegdest(osub, vertexptr) \ +- (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr +- +-/* These primitives read or set a boundary marker. Boundary markers are */ +-/* used to hold user-defined tags for setting boundary conditions in */ +-/* finite element solvers. */ +- +-#define mark(osub) (* (int *) ((osub).ss + 8)) +- +-#define setmark(osub, value) \ +- * (int *) ((osub).ss + 8) = value +- +-/* Bond two subsegments together. */ +- +-#define sbond(osub1, osub2) \ +- (osub1).ss[(osub1).ssorient] = sencode(osub2); \ +- (osub2).ss[(osub2).ssorient] = sencode(osub1) +- +-/* Dissolve a subsegment bond (from one side). Note that the other */ +-/* subsegment will still think it's connected to this subsegment. */ +- +-#define sdissolve(osub) \ +- (osub).ss[(osub).ssorient] = (subseg) m->dummysub +- +-/* Copy a subsegment. */ +- +-#define subsegcopy(osub1, osub2) \ +- (osub2).ss = (osub1).ss; \ +- (osub2).ssorient = (osub1).ssorient +- +-/* Test for equality of subsegments. */ +- +-#define subsegequal(osub1, osub2) \ +- (((osub1).ss == (osub2).ss) && \ +- ((osub1).ssorient == (osub2).ssorient)) +- +-/* Check or set a subsegment's deallocation. Its second pointer is set to */ +-/* NULL to indicate that it is not allocated. (Its first pointer is used */ +-/* for the stack of dead items.) Its third pointer (its first vertex) */ +-/* is set to NULL in case a `badsubseg' structure points to it. */ +- +-#define deadsubseg(sub) ((sub)[1] == (subseg) NULL) +- +-#define killsubseg(sub) \ +- (sub)[1] = (subseg) NULL; \ +- (sub)[2] = (subseg) NULL +- +-/********* Primitives for interacting triangles and subsegments *********/ +-/* */ +-/* */ +- +-/* tspivot() finds a subsegment abutting a triangle. */ +- +-#define tspivot(otri, osub) \ +- sptr = (subseg) (otri).tri[6 + (otri).orient]; \ +- sdecode(sptr, osub) +- +-/* stpivot() finds a triangle abutting a subsegment. It requires that the */ +-/* variable `ptr' of type `triangle' be defined. */ +- +-#define stpivot(osub, otri) \ +- ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \ +- decode(ptr, otri) +- +-/* Bond a triangle to a subsegment. */ +- +-#define tsbond(otri, osub) \ +- (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \ +- (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri) +- +-/* Dissolve a bond (from the triangle side). */ +- +-#define tsdissolve(otri) \ +- (otri).tri[6 + (otri).orient] = (triangle) m->dummysub +- +-/* Dissolve a bond (from the subsegment side). */ +- +-#define stdissolve(osub) \ +- (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri +- +-/********* Primitives for vertices *********/ +-/* */ +-/* */ +- +-#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex] +- +-#define setvertexmark(vx, value) \ +- ((int *) (vx))[m->vertexmarkindex] = value +- +-#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1] +- +-#define setvertextype(vx, value) \ +- ((int *) (vx))[m->vertexmarkindex + 1] = value +- +-#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex] +- +-#define setvertex2tri(vx, value) \ +- ((triangle *) (vx))[m->vertex2triindex] = value +- +-/** **/ +-/** **/ +-/********* Mesh manipulation primitives end here *********/ +- +-/********* User-defined triangle evaluation routine begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* triunsuitable() Determine if a triangle is unsuitable, and thus must */ +-/* be further refined. */ +-/* */ +-/* You may write your own procedure that decides whether or not a selected */ +-/* triangle is too big (and needs to be refined). There are two ways to do */ +-/* this. */ +-/* */ +-/* (1) Modify the procedure `triunsuitable' below, then recompile */ +-/* Triangle. */ +-/* */ +-/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */ +-/* to this file, or by using the appropriate compiler switch). This way, */ +-/* you can compile triangle.c separately from your test. Write your own */ +-/* `triunsuitable' procedure in a separate C file (using the same prototype */ +-/* as below). Compile it and link the object code with triangle.o. */ +-/* */ +-/* This procedure returns 1 if the triangle is too large and should be */ +-/* refined; 0 otherwise. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef EXTERNAL_TEST +- +-int triunsuitable(); +- +-#else /* not EXTERNAL_TEST */ +- +-#ifdef ANSI_DECLARATORS +-int triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area) +-#else /* not ANSI_DECLARATORS */ +-int triunsuitable(triorg, tridest, triapex, area) +-vertex triorg; /* The triangle's origin vertex. */ +-vertex tridest; /* The triangle's destination vertex. */ +-vertex triapex; /* The triangle's apex vertex. */ +-REAL area; /* The area of the triangle. */ +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL dxoa, dxda, dxod; +- REAL dyoa, dyda, dyod; +- REAL oalen, dalen, odlen; +- REAL maxlen; +- +- dxoa = triorg[0] - triapex[0]; +- dyoa = triorg[1] - triapex[1]; +- dxda = tridest[0] - triapex[0]; +- dyda = tridest[1] - triapex[1]; +- dxod = triorg[0] - tridest[0]; +- dyod = triorg[1] - tridest[1]; +- /* Find the squares of the lengths of the triangle's three edges. */ +- oalen = dxoa * dxoa + dyoa * dyoa; +- dalen = dxda * dxda + dyda * dyda; +- odlen = dxod * dxod + dyod * dyod; +- /* Find the square of the length of the longest edge. */ +- maxlen = (dalen > oalen) ? dalen : oalen; +- maxlen = (odlen > maxlen) ? odlen : maxlen; +- +- if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) { +- return 1; +- } else { +- return 0; +- } +-} +- +-#endif /* not EXTERNAL_TEST */ +- +-/** **/ +-/** **/ +-/********* User-defined triangle evaluation routine ends here *********/ +- +-/********* Memory allocation and program exit wrappers begin here *********/ +-/** **/ +-/** **/ +- +-#ifdef ANSI_DECLARATORS +-void triexit(int status) +-#else /* not ANSI_DECLARATORS */ +-void triexit(status) +-int status; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- exit(status); +-} +- +-#ifdef ANSI_DECLARATORS +-void *trimalloc(int size) +-#else /* not ANSI_DECLARATORS */ +-void *trimalloc(size) +-int size; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- void *memptr; +- +- memptr = (void *) malloc((unsigned int) size); +- if (memptr == (void *) NULL) { +- printf("Error: Out of memory.\n"); +- triexit(1); +- } +- return(memptr); +-} +- +-#ifdef ANSI_DECLARATORS +-void trifree(void *memptr) +-#else /* not ANSI_DECLARATORS */ +-void trifree(memptr) +-void *memptr; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- free(memptr); +-} +- +-/** **/ +-/** **/ +-/********* Memory allocation and program exit wrappers end here *********/ +- +-/********* User interaction routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* syntax() Print list of command line switches. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-void syntax() +-{ +-#ifdef CDT_ONLY +-#ifdef REDUCED +- printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n"); +-#else /* not REDUCED */ +- printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n"); +-#endif /* not REDUCED */ +-#else /* not CDT_ONLY */ +-#ifdef REDUCED +- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n"); +-#else /* not REDUCED */ +- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n"); +-#endif /* not REDUCED */ +-#endif /* not CDT_ONLY */ +- +- printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n"); +-#ifndef CDT_ONLY +- printf(" -r Refines a previously generated mesh.\n"); +- printf( +- " -q Quality mesh generation. A minimum angle may be specified.\n"); +- printf(" -a Applies a maximum triangle area constraint.\n"); +- printf(" -u Applies a user-defined triangle constraint.\n"); +-#endif /* not CDT_ONLY */ +- printf( +- " -A Applies attributes to identify triangles in certain regions.\n"); +- printf(" -c Encloses the convex hull with segments.\n"); +-#ifndef CDT_ONLY +- printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n"); +-#endif /* not CDT_ONLY */ +-/* +- printf(" -w Weighted Delaunay triangulation.\n"); +- printf(" -W Regular triangulation (lower hull of a height field).\n"); +-*/ +- printf(" -j Jettison unused vertices from output .node file.\n"); +- printf(" -e Generates an edge list.\n"); +- printf(" -v Generates a Voronoi diagram.\n"); +- printf(" -n Generates a list of triangle neighbors.\n"); +- printf(" -g Generates an .off file for Geomview.\n"); +- printf(" -B Suppresses output of boundary information.\n"); +- printf(" -P Suppresses output of .poly file.\n"); +- printf(" -N Suppresses output of .node file.\n"); +- printf(" -E Suppresses output of .ele file.\n"); +- printf(" -I Suppresses mesh iteration numbers.\n"); +- printf(" -O Ignores holes in .poly file.\n"); +- printf(" -X Suppresses use of exact arithmetic.\n"); +- printf(" -z Numbers all items starting from zero (rather than one).\n"); +- printf(" -o2 Generates second-order subparametric elements.\n"); +-#ifndef CDT_ONLY +- printf(" -Y Suppresses boundary segment splitting.\n"); +- printf(" -S Specifies maximum number of added Steiner points.\n"); +-#endif /* not CDT_ONLY */ +-#ifndef REDUCED +- printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); +- printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n"); +-#endif /* not REDUCED */ +- printf(" -l Uses vertical cuts only, rather than alternating cuts.\n"); +-#ifndef REDUCED +-#ifndef CDT_ONLY +- printf( +- " -s Force segments into mesh by splitting (instead of using CDT).\n"); +-#endif /* not CDT_ONLY */ +- printf(" -C Check consistency of final mesh.\n"); +-#endif /* not REDUCED */ +- printf(" -Q Quiet: No terminal output except errors.\n"); +- printf(" -V Verbose: Detailed information on what I'm doing.\n"); +- printf(" -h Help: Detailed instructions for Triangle.\n"); +- triexit(0); +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* info() Print out complete instructions. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-void info() +-{ +- printf("Triangle\n"); +- printf( +-"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); +- printf("Version 1.6\n\n"); +- printf( +-"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n"); +- printf("2360 Woolsey #H / Berkeley, California 94705-1927\n"); +- printf("Bugs/comments to jrs@cs.berkeley.edu\n"); +- printf( +-"Created as part of the Quake project (tools for earthquake simulation).\n"); +- printf( +-"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); +- printf("There is no warranty whatsoever. Use at your own risk.\n"); +-#ifdef SINGLE +- printf("This executable is compiled for single precision arithmetic.\n\n\n"); +-#else /* not SINGLE */ +- printf("This executable is compiled for double precision arithmetic.\n\n\n"); +-#endif /* not SINGLE */ +- printf( +-"Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); +- printf( +-"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n"); +- printf( +-"high-quality triangular meshes. The latter can be generated with no small\n" +-); +- printf( +-"or large angles, and are thus suitable for finite element analysis. If no\n" +-); +- printf( +-"command line switch is specified, your .node input file is read, and the\n"); +- printf( +-"Delaunay triangulation is returned in .node and .ele output files. The\n"); +- printf("command syntax is:\n\n"); +- printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n"); +- printf( +-"Underscores indicate that numbers may optionally follow certain switches.\n"); +- printf( +-"Do not leave any space between a switch and its numeric parameter.\n"); +- printf( +-"input_file must be a file with extension .node, or extension .poly if the\n"); +- printf( +-"-p switch is used. If -r is used, you must supply .node and .ele files,\n"); +- printf( +-"and possibly a .poly file and an .area file as well. The formats of these\n" +-); +- printf("files are described below.\n\n"); +- printf("Command Line Switches:\n\n"); +- printf( +-" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n" +-); +- printf( +-" vertices, segments, holes, regional attributes, and regional area\n"); +- printf( +-" constraints. Generates a constrained Delaunay triangulation (CDT)\n" +-); +- printf( +-" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n"); +- printf( +-" constrained Delaunay triangulation (CCDT). If you want a truly\n"); +- printf( +-" Delaunay (not just constrained Delaunay) triangulation, use -D as\n"); +- printf( +-" well. When -p is not used, Triangle reads a .node file by default.\n" +-); +- printf( +-" -r Refines a previously generated mesh. The mesh is read from a .node\n" +-); +- printf( +-" file and an .ele file. If -p is also used, a .poly file is read\n"); +- printf( +-" and used to constrain segments in the mesh. If -a is also used\n"); +- printf( +-" (with no number following), an .area file is read and used to\n"); +- printf( +-" impose area constraints on the mesh. Further details on refinement\n" +-); +- printf(" appear below.\n"); +- printf( +-" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n"); +- printf( +-" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n" +-); +- printf( +-" ensure that all angles are between 20 and 140 degrees. An\n"); +- printf( +-" alternative bound on the minimum angle, replacing 20 degrees, may\n"); +- printf( +-" be specified after the `q'. The specified angle may include a\n"); +- printf( +-" decimal point, but not exponential notation. Note that a bound of\n" +-); +- printf( +-" theta degrees on the smallest angle also implies a bound of\n"); +- printf( +-" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n" +-); +- printf( +-" degrees or smaller, Triangle is mathematically guaranteed to\n"); +- printf( +-" terminate (assuming infinite precision arithmetic--Triangle may\n"); +- printf( +-" fail to terminate if you run out of precision). In practice,\n"); +- printf( +-" Triangle often succeeds for minimum angles up to 34 degrees. For\n"); +- printf( +-" some meshes, however, you might need to reduce the minimum angle to\n" +-); +- printf( +-" avoid problems associated with insufficient floating-point\n"); +- printf(" precision.\n"); +- printf( +-" -a Imposes a maximum triangle area. If a number follows the `a', no\n"); +- printf( +-" triangle is generated whose area is larger than that number. If no\n" +-); +- printf( +-" number is specified, an .area file (if -r is used) or .poly file\n"); +- printf( +-" (if -r is not used) specifies a set of maximum area constraints.\n"); +- printf( +-" An .area file contains a separate area constraint for each\n"); +- printf( +-" triangle, and is useful for refining a finite element mesh based on\n" +-); +- printf( +-" a posteriori error estimates. A .poly file can optionally contain\n" +-); +- printf( +-" an area constraint for each segment-bounded region, thereby\n"); +- printf( +-" controlling triangle densities in a first triangulation of a PSLG.\n" +-); +- printf( +-" You can impose both a fixed area constraint and a varying area\n"); +- printf( +-" constraint by invoking the -a switch twice, once with and once\n"); +- printf( +-" without a number following. Each area specified may include a\n"); +- printf(" decimal point.\n"); +- printf( +-" -u Imposes a user-defined constraint on triangle size. There are two\n" +-); +- printf( +-" ways to use this feature. One is to edit the triunsuitable()\n"); +- printf( +-" procedure in triangle.c to encode any constraint you like, then\n"); +- printf( +-" recompile Triangle. The other is to compile triangle.c with the\n"); +- printf( +-" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n"); +- printf( +-" link Triangle with a separate object file that implements\n"); +- printf( +-" triunsuitable(). In either case, the -u switch causes the user-\n"); +- printf(" defined test to be applied to every triangle.\n"); +- printf( +-" -A Assigns an additional floating-point attribute to each triangle\n"); +- printf( +-" that identifies what segment-bounded region each triangle belongs\n"); +- printf( +-" to. Attributes are assigned to regions by the .poly file. If a\n"); +- printf( +-" region is not explicitly marked by the .poly file, triangles in\n"); +- printf( +-" that region are assigned an attribute of zero. The -A switch has\n"); +- printf( +-" an effect only when the -p switch is used and the -r switch is not.\n" +-); +- printf( +-" -c Creates segments on the convex hull of the triangulation. If you\n"); +- printf( +-" are triangulating a vertex set, this switch causes a .poly file to\n" +-); +- printf( +-" be written, containing all edges of the convex hull. If you are\n"); +- printf( +-" triangulating a PSLG, this switch specifies that the whole convex\n"); +- printf( +-" hull of the PSLG should be triangulated, regardless of what\n"); +- printf( +-" segments the PSLG has. If you do not use this switch when\n"); +- printf( +-" triangulating a PSLG, Triangle assumes that you have identified the\n" +-); +- printf( +-" region to be triangulated by surrounding it with segments of the\n"); +- printf( +-" input PSLG. Beware: if you are not careful, this switch can cause\n" +-); +- printf( +-" the introduction of an extremely thin angle between a PSLG segment\n" +-); +- printf( +-" and a convex hull segment, which can cause overrefinement (and\n"); +- printf( +-" possibly failure if Triangle runs out of precision). If you are\n"); +- printf( +-" refining a mesh, the -c switch works differently: it causes a\n"); +- printf( +-" .poly file to be written containing the boundary edges of the mesh\n" +-); +- printf(" (useful if no .poly file was read).\n"); +- printf( +-" -D Conforming Delaunay triangulation: use this switch if you want to\n" +-); +- printf( +-" ensure that all the triangles in the mesh are Delaunay, and not\n"); +- printf( +-" merely constrained Delaunay; or if you want to ensure that all the\n" +-); +- printf( +-" Voronoi vertices lie within the triangulation. (Some finite volume\n" +-); +- printf( +-" methods have this requirement.) This switch invokes Ruppert's\n"); +- printf( +-" original algorithm, which splits every subsegment whose diametral\n"); +- printf( +-" circle is encroached. It usually increases the number of vertices\n" +-); +- printf(" and triangles.\n"); +- printf( +-" -j Jettisons vertices that are not part of the final triangulation\n"); +- printf( +-" from the output .node file. By default, Triangle copies all\n"); +- printf( +-" vertices in the input .node file to the output .node file, in the\n"); +- printf( +-" same order, so their indices do not change. The -j switch prevents\n" +-); +- printf( +-" duplicated input vertices, or vertices `eaten' by holes, from\n"); +- printf( +-" appearing in the output .node file. Thus, if two input vertices\n"); +- printf( +-" have exactly the same coordinates, only the first appears in the\n"); +- printf( +-" output. If any vertices are jettisoned, the vertex numbering in\n"); +- printf( +-" the output .node file differs from that of the input .node file.\n"); +- printf( +-" -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); +- printf( +-" -v Outputs the Voronoi diagram associated with the triangulation.\n"); +- printf( +-" Does not attempt to detect degeneracies, so some Voronoi vertices\n"); +- printf( +-" may be duplicated. See the discussion of Voronoi diagrams below.\n"); +- printf( +-" -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); +- printf(" triangle.\n"); +- printf( +-" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n" +-); +- printf(" viewing with the Geometry Center's Geomview package.\n"); +- printf( +-" -B No boundary markers in the output .node, .poly, and .edge output\n"); +- printf( +-" files. See the detailed discussion of boundary markers below.\n"); +- printf( +-" -P No output .poly file. Saves disk space, but you lose the ability\n"); +- printf( +-" to maintain constraining segments on later refinements of the mesh.\n" +-); +- printf(" -N No output .node file.\n"); +- printf(" -E No output .ele file.\n"); +- printf( +-" -I No iteration numbers. Suppresses the output of .node and .poly\n"); +- printf( +-" files, so your input files won't be overwritten. (If your input is\n" +-); +- printf( +-" a .poly file only, a .node file is written.) Cannot be used with\n"); +- printf( +-" the -r switch, because that would overwrite your input .ele file.\n"); +- printf( +-" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n"); +- printf( +-" using a .node file for input, because no .node file is written, so\n" +-); +- printf(" there is no record of any added Steiner points.\n"); +- printf(" -O No holes. Ignores the holes in the .poly file.\n"); +- printf( +-" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n" +-); +- printf( +-" arithmetic for certain tests if it thinks the inexact tests are not\n" +-); +- printf( +-" accurate enough. Exact arithmetic ensures the robustness of the\n"); +- printf( +-" triangulation algorithms, despite floating-point roundoff error.\n"); +- printf( +-" Disabling exact arithmetic with the -X switch causes a small\n"); +- printf( +-" improvement in speed and creates the possibility that Triangle will\n" +-); +- printf(" fail to produce a valid mesh. Not recommended.\n"); +- printf( +-" -z Numbers all items starting from zero (rather than one). Note that\n" +-); +- printf( +-" this switch is normally overridden by the value used to number the\n" +-); +- printf( +-" first vertex of the input .node or .poly file. However, this\n"); +- printf( +-" switch is useful when calling Triangle from another program.\n"); +- printf( +-" -o2 Generates second-order subparametric elements with six nodes each.\n" +-); +- printf( +-" -Y No new vertices on the boundary. This switch is useful when the\n"); +- printf( +-" mesh boundary must be preserved so that it conforms to some\n"); +- printf( +-" adjacent mesh. Be forewarned that you will probably sacrifice much\n" +-); +- printf( +-" of the quality of the mesh; Triangle will try, but the resulting\n"); +- printf( +-" mesh may contain poorly shaped triangles. Works well if all the\n"); +- printf( +-" boundary vertices are closely spaced. Specify this switch twice\n"); +- printf( +-" (`-YY') to prevent all segment splitting, including internal\n"); +- printf(" boundaries.\n"); +- printf( +-" -S Specifies the maximum number of Steiner points (vertices that are\n"); +- printf( +-" not in the input, but are added to meet the constraints on minimum\n" +-); +- printf( +-" angle and maximum area). The default is to allow an unlimited\n"); +- printf( +-" number. If you specify this switch with no number after it,\n"); +- printf( +-" the limit is set to zero. Triangle always adds vertices at segment\n" +-); +- printf( +-" intersections, even if it needs to use more vertices than the limit\n" +-); +- printf( +-" you set. When Triangle inserts segments by splitting (-s), it\n"); +- printf( +-" always adds enough vertices to ensure that all the segments of the\n" +-); +- printf(" PLSG are recovered, ignoring the limit if necessary.\n"); +- printf( +-" -i Uses an incremental rather than a divide-and-conquer algorithm to\n"); +- printf( +-" construct a Delaunay triangulation. Try it if the divide-and-\n"); +- printf(" conquer algorithm fails.\n"); +- printf( +-" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n"); +- printf( +-" triangulation. Warning: does not use exact arithmetic for all\n"); +- printf(" calculations. An exact result is not guaranteed.\n"); +- printf( +-" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); +- printf( +-" default, Triangle alternates between vertical and horizontal cuts,\n" +-); +- printf( +-" which usually improve the speed except with vertex sets that are\n"); +- printf( +-" small or short and wide. This switch is primarily of theoretical\n"); +- printf(" interest.\n"); +- printf( +-" -s Specifies that segments should be forced into the triangulation by\n" +-); +- printf( +-" recursively splitting them at their midpoints, rather than by\n"); +- printf( +-" generating a constrained Delaunay triangulation. Segment splitting\n" +-); +- printf( +-" is true to Ruppert's original algorithm, but can create needlessly\n" +-); +- printf( +-" small triangles. This switch is primarily of theoretical interest.\n" +-); +- printf( +-" -C Check the consistency of the final mesh. Uses exact arithmetic for\n" +-); +- printf( +-" checking, even if the -X switch is used. Useful if you suspect\n"); +- printf(" Triangle is buggy.\n"); +- printf( +-" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n"); +- printf(" unless an error occurs.\n"); +- printf( +-" -V Verbose: Gives detailed information about what Triangle is doing.\n" +-); +- printf( +-" Add more `V's for increasing amount of detail. `-V' is most\n"); +- printf( +-" useful; itgives information on algorithmic progress and much more\n"); +- printf( +-" detailed statistics. `-VV' gives vertex-by-vertex details, and\n"); +- printf( +-" prints so much that Triangle runs much more slowly. `-VVVV' gives\n" +-); +- printf(" information only a debugger could love.\n"); +- printf(" -h Help: Displays these instructions.\n"); +- printf("\n"); +- printf("Definitions:\n"); +- printf("\n"); +- printf( +-" A Delaunay triangulation of a vertex set is a triangulation whose\n"); +- printf( +-" vertices are the vertex set, that covers the convex hull of the vertex\n"); +- printf( +-" set. A Delaunay triangulation has the property that no vertex lies\n"); +- printf( +-" inside the circumscribing circle (circle that passes through all three\n"); +- printf(" vertices) of any triangle in the triangulation.\n\n"); +- printf( +-" A Voronoi diagram of a vertex set is a subdivision of the plane into\n"); +- printf( +-" polygonal cells (some of which may be unbounded, meaning infinitely\n"); +- printf( +-" large), where each cell is the set of points in the plane that are closer\n" +-); +- printf( +-" to some input vertex than to any other input vertex. The Voronoi diagram\n" +-); +- printf(" is a geometric dual of the Delaunay triangulation.\n\n"); +- printf( +-" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n"); +- printf( +-" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n" +-); +- printf( +-" Segments may intersect each other only at their endpoints. The file\n"); +- printf(" format for PSLGs (.poly files) is described below.\n\n"); +- printf( +-" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n"); +- printf( +-" Delaunay triangulation, but each PSLG segment is present as a single edge\n" +-); +- printf( +-" of the CDT. (A constrained Delaunay triangulation is not truly a\n"); +- printf( +-" Delaunay triangulation, because some of its triangles might not be\n"); +- printf( +-" Delaunay.) By definition, a CDT does not have any vertices other than\n"); +- printf( +-" those specified in the input PSLG. Depending on context, a CDT might\n"); +- printf( +-" cover the convex hull of the PSLG, or it might cover only a segment-\n"); +- printf(" bounded region (e.g. a polygon).\n\n"); +- printf( +-" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n" +-); +- printf( +-" each triangle is truly Delaunay, and each PSLG segment is represented by\n" +-); +- printf( +-" a linear contiguous sequence of edges of the triangulation. New vertices\n" +-); +- printf( +-" (not part of the PSLG) may appear, and each input segment may have been\n"); +- printf( +-" subdivided into shorter edges (subsegments) by these additional vertices.\n" +-); +- printf( +-" The new vertices are frequently necessary to maintain the Delaunay\n"); +- printf(" property while ensuring that every segment is represented.\n\n"); +- printf( +-" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n"); +- printf( +-" triangulation of a PSLG whose triangles are constrained Delaunay. New\n"); +- printf(" vertices may appear, and input segments may be subdivided into\n"); +- printf( +-" subsegments, but not to guarantee that segments are respected; rather, to\n" +-); +- printf( +-" improve the quality of the triangles. The high-quality meshes produced\n"); +- printf( +-" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n"); +- printf(" with the -D switch.\n\n"); +- printf("File Formats:\n\n"); +- printf( +-" All files may contain comments prefixed by the character '#'. Vertices,\n" +-); +- printf( +-" triangles, edges, holes, and maximum area constraints must be numbered\n"); +- printf( +-" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); +- printf( +-" input files must be consistent; if the vertices are numbered from 1, so\n"); +- printf( +-" must be all other objects. Triangle automatically detects your choice\n"); +- printf( +-" while reading the .node (or .poly) file. (When calling Triangle from\n"); +- printf( +-" another program, use the -z switch if you wish to number objects from\n"); +- printf(" zero.) Examples of these file formats are given below.\n\n"); +- printf(" .node files:\n"); +- printf( +-" First line: <# of vertices> <# of attributes>\n" +-); +- printf( +-" <# of boundary markers (0 or 1)>\n" +-); +- printf( +-" Remaining lines: [attributes] [boundary marker]\n"); +- printf("\n"); +- printf( +-" The attributes, which are typically floating-point values of physical\n"); +- printf( +-" quantities (such as mass or conductivity) associated with the nodes of\n" +-); +- printf( +-" a finite element mesh, are copied unchanged to the output mesh. If -q,\n" +-); +- printf( +-" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n" +-); +- printf(" has attributes assigned to it by linear interpolation.\n\n"); +- printf( +-" If the fourth entry of the first line is `1', the last column of the\n"); +- printf( +-" remainder of the file is assumed to contain boundary markers. Boundary\n" +-); +- printf( +-" markers are used to identify boundary vertices and vertices resting on\n" +-); +- printf( +-" PSLG segments; a complete description appears in a section below. The\n" +-); +- printf( +-" .node file produced by Triangle contains boundary markers in the last\n"); +- printf(" column unless they are suppressed by the -B switch.\n\n"); +- printf(" .ele files:\n"); +- printf( +-" First line: <# of triangles> <# of attributes>\n"); +- printf( +-" Remaining lines: ... [attributes]\n"); +- printf("\n"); +- printf( +-" Nodes are indices into the corresponding .node file. The first three\n"); +- printf( +-" nodes are the corner vertices, and are listed in counterclockwise order\n" +-); +- printf( +-" around each triangle. (The remaining nodes, if any, depend on the type\n" +-); +- printf(" of finite element used.)\n\n"); +- printf( +-" The attributes are just like those of .node files. Because there is no\n" +-); +- printf( +-" simple mapping from input to output triangles, Triangle attempts to\n"); +- printf( +-" interpolate attributes, and may cause a lot of diffusion of attributes\n" +-); +- printf( +-" among nearby triangles as the triangulation is refined. Attributes do\n" +-); +- printf(" not diffuse across segments, so attributes used to identify\n"); +- printf(" segment-bounded regions remain intact.\n\n"); +- printf( +-" In .ele files produced by Triangle, each triangular element has three\n"); +- printf( +-" nodes (vertices) unless the -o2 switch is used, in which case\n"); +- printf( +-" subparametric quadratic elements with six nodes each are generated.\n"); +- printf( +-" The first three nodes are the corners in counterclockwise order, and\n"); +- printf( +-" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n"); +- printf( +-" opposite the first, second, and third vertices, respectively.\n"); +- printf("\n"); +- printf(" .poly files:\n"); +- printf( +-" First line: <# of vertices> <# of attributes>\n" +-); +- printf( +-" <# of boundary markers (0 or 1)>\n" +-); +- printf( +-" Following lines: [attributes] [boundary marker]\n"); +- printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); +- printf( +-" Following lines: [boundary marker]\n"); +- printf(" One line: <# of holes>\n"); +- printf(" Following lines: \n"); +- printf( +-" Optional line: <# of regional attributes and/or area constraints>\n"); +- printf( +-" Optional following lines: \n"); +- printf("\n"); +- printf( +-" A .poly file represents a PSLG, as well as some additional information.\n" +-); +- printf( +-" The first section lists all the vertices, and is identical to the\n"); +- printf( +-" format of .node files. <# of vertices> may be set to zero to indicate\n" +-); +- printf( +-" that the vertices are listed in a separate .node file; .poly files\n"); +- printf( +-" produced by Triangle always have this format. A vertex set represented\n" +-); +- printf( +-" this way has the advantage that it may easily be triangulated with or\n"); +- printf( +-" without segments (depending on whether the -p switch is invoked).\n"); +- printf("\n"); +- printf( +-" The second section lists the segments. Segments are edges whose\n"); +- printf( +-" presence in the triangulation is enforced. (Depending on the choice of\n" +-); +- printf( +-" switches, segment might be subdivided into smaller edges). Each\n"); +- printf( +-" segment is specified by listing the indices of its two endpoints. This\n" +-); +- printf( +-" means that you must include its endpoints in the vertex list. Each\n"); +- printf(" segment, like each point, may have a boundary marker.\n\n"); +- printf( +-" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n" +-); +- printf( +-" Delaunay triangulation (CDT), in which each segment appears as a single\n" +-); +- printf( +-" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n" +-); +- printf( +-" produces a conforming constrained Delaunay triangulation (CCDT), in\n"); +- printf( +-" which segments may be subdivided into smaller edges. If -D is\n"); +- printf( +-" selected, Triangle produces a conforming Delaunay triangulation, so\n"); +- printf( +-" that every triangle is Delaunay, and not just constrained Delaunay.\n"); +- printf("\n"); +- printf( +-" The third section lists holes (and concavities, if -c is selected) in\n"); +- printf( +-" the triangulation. Holes are specified by identifying a point inside\n"); +- printf( +-" each hole. After the triangulation is formed, Triangle creates holes\n"); +- printf( +-" by eating triangles, spreading out from each hole point until its\n"); +- printf( +-" progress is blocked by segments in the PSLG. You must be careful to\n"); +- printf( +-" enclose each hole in segments, or your whole triangulation might be\n"); +- printf( +-" eaten away. If the two triangles abutting a segment are eaten, the\n"); +- printf( +-" segment itself is also eaten. Do not place a hole directly on a\n"); +- printf(" segment; if you do, Triangle chooses one side of the segment\n"); +- printf(" arbitrarily.\n\n"); +- printf( +-" The optional fourth section lists regional attributes (to be assigned\n"); +- printf( +-" to all triangles in a region) and regional constraints on the maximum\n"); +- printf( +-" triangle area. Triangle reads this section only if the -A switch is\n"); +- printf( +-" used or the -a switch is used without a number following it, and the -r\n" +-); +- printf( +-" switch is not used. Regional attributes and area constraints are\n"); +- printf( +-" propagated in the same manner as holes: you specify a point for each\n"); +- printf( +-" attribute and/or constraint, and the attribute and/or constraint\n"); +- printf( +-" affects the whole region (bounded by segments) containing the point.\n"); +- printf( +-" If two values are written on a line after the x and y coordinate, the\n"); +- printf( +-" first such value is assumed to be a regional attribute (but is only\n"); +- printf( +-" applied if the -A switch is selected), and the second value is assumed\n" +-); +- printf( +-" to be a regional area constraint (but is only applied if the -a switch\n" +-); +- printf( +-" is selected). You may specify just one value after the coordinates,\n"); +- printf( +-" which can serve as both an attribute and an area constraint, depending\n" +-); +- printf( +-" on the choice of switches. If you are using the -A and -a switches\n"); +- printf( +-" simultaneously and wish to assign an attribute to some region without\n"); +- printf(" imposing an area constraint, use a negative maximum area.\n\n"); +- printf( +-" When a triangulation is created from a .poly file, you must either\n"); +- printf( +-" enclose the entire region to be triangulated in PSLG segments, or\n"); +- printf( +-" use the -c switch, which automatically creates extra segments that\n"); +- printf( +-" enclose the convex hull of the PSLG. If you do not use the -c switch,\n" +-); +- printf( +-" Triangle eats all triangles that are not enclosed by segments; if you\n"); +- printf( +-" are not careful, your whole triangulation may be eaten away. If you do\n" +-); +- printf( +-" use the -c switch, you can still produce concavities by the appropriate\n" +-); +- printf( +-" placement of holes just inside the boundary of the convex hull.\n"); +- printf("\n"); +- printf( +-" An ideal PSLG has no intersecting segments, nor any vertices that lie\n"); +- printf( +-" upon segments (except, of course, the endpoints of each segment). You\n" +-); +- printf( +-" aren't required to make your .poly files ideal, but you should be aware\n" +-); +- printf( +-" of what can go wrong. Segment intersections are relatively safe--\n"); +- printf( +-" Triangle calculates the intersection points for you and adds them to\n"); +- printf( +-" the triangulation--as long as your machine's floating-point precision\n"); +- printf( +-" doesn't become a problem. You are tempting the fates if you have three\n" +-); +- printf( +-" segments that cross at the same location, and expect Triangle to figure\n" +-); +- printf( +-" out where the intersection point is. Thanks to floating-point roundoff\n" +-); +- printf( +-" error, Triangle will probably decide that the three segments intersect\n" +-); +- printf( +-" at three different points, and you will find a minuscule triangle in\n"); +- printf( +-" your output--unless Triangle tries to refine the tiny triangle, uses\n"); +- printf( +-" up the last bit of machine precision, and fails to terminate at all.\n"); +- printf( +-" You're better off putting the intersection point in the input files,\n"); +- printf( +-" and manually breaking up each segment into two. Similarly, if you\n"); +- printf( +-" place a vertex at the middle of a segment, and hope that Triangle will\n" +-); +- printf( +-" break up the segment at that vertex, you might get lucky. On the other\n" +-); +- printf( +-" hand, Triangle might decide that the vertex doesn't lie precisely on\n"); +- printf( +-" the segment, and you'll have a needle-sharp triangle in your output--or\n" +-); +- printf(" a lot of tiny triangles if you're generating a quality mesh.\n"); +- printf("\n"); +- printf( +-" When Triangle reads a .poly file, it also writes a .poly file, which\n"); +- printf( +-" includes all the subsegments--the edges that are parts of input\n"); +- printf( +-" segments. If the -c switch is used, the output .poly file also\n"); +- printf( +-" includes all of the edges on the convex hull. Hence, the output .poly\n" +-); +- printf( +-" file is useful for finding edges associated with input segments and for\n" +-); +- printf( +-" setting boundary conditions in finite element simulations. Moreover,\n"); +- printf( +-" you will need the output .poly file if you plan to refine the output\n"); +- printf( +-" mesh, and don't want segments to be missing in later triangulations.\n"); +- printf("\n"); +- printf(" .area files:\n"); +- printf(" First line: <# of triangles>\n"); +- printf(" Following lines: \n"); +- printf("\n"); +- printf( +-" An .area file associates with each triangle a maximum area that is used\n" +-); +- printf( +-" for mesh refinement. As with other file formats, every triangle must\n"); +- printf( +-" be represented, and the triangles must be numbered consecutively. A\n"); +- printf( +-" triangle may be left unconstrained by assigning it a negative maximum\n"); +- printf(" area.\n\n"); +- printf(" .edge files:\n"); +- printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); +- printf( +-" Following lines: [boundary marker]\n"); +- printf("\n"); +- printf( +-" Endpoints are indices into the corresponding .node file. Triangle can\n" +-); +- printf( +-" produce .edge files (use the -e switch), but cannot read them. The\n"); +- printf( +-" optional column of boundary markers is suppressed by the -B switch.\n"); +- printf("\n"); +- printf( +-" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); +- printf( +-" infinite ray with only one endpoint. For these edges, a different\n"); +- printf(" format is used:\n\n"); +- printf(" -1 \n\n"); +- printf( +-" The `direction' is a floating-point vector that indicates the direction\n" +-); +- printf(" of the infinite ray.\n\n"); +- printf(" .neigh files:\n"); +- printf( +-" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n" +-); +- printf( +-" Following lines: \n"); +- printf("\n"); +- printf( +-" Neighbors are indices into the corresponding .ele file. An index of -1\n" +-); +- printf( +-" indicates no neighbor (because the triangle is on an exterior\n"); +- printf( +-" boundary). The first neighbor of triangle i is opposite the first\n"); +- printf(" corner of triangle i, and so on.\n\n"); +- printf( +-" Triangle can produce .neigh files (use the -n switch), but cannot read\n" +-); +- printf(" them.\n\n"); +- printf("Boundary Markers:\n\n"); +- printf( +-" Boundary markers are tags used mainly to identify which output vertices\n"); +- printf( +-" and edges are associated with which PSLG segment, and to identify which\n"); +- printf( +-" vertices and edges occur on a boundary of the triangulation. A common\n"); +- printf( +-" use is to determine where boundary conditions should be applied to a\n"); +- printf( +-" finite element mesh. You can prevent boundary markers from being written\n" +-); +- printf(" into files produced by Triangle by using the -B switch.\n\n"); +- printf( +-" The boundary marker associated with each segment in an output .poly file\n" +-); +- printf(" and each edge in an output .edge file is chosen as follows:\n"); +- printf( +-" - If an output edge is part or all of a PSLG segment with a nonzero\n"); +- printf( +-" boundary marker, then the edge is assigned the same marker.\n"); +- printf( +-" - Otherwise, if the edge lies on a boundary of the triangulation\n"); +- printf( +-" (even the boundary of a hole), then the edge is assigned the marker\n"); +- printf(" one (1).\n"); +- printf(" - Otherwise, the edge is assigned the marker zero (0).\n"); +- printf( +-" The boundary marker associated with each vertex in an output .node file\n"); +- printf(" is chosen as follows:\n"); +- printf( +-" - If a vertex is assigned a nonzero boundary marker in the input file,\n" +-); +- printf( +-" then it is assigned the same marker in the output .node file.\n"); +- printf( +-" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n"); +- printf( +-" endpoint of the segment) with a nonzero boundary marker, then the\n"); +- printf( +-" vertex is assigned the same marker. If the vertex lies on several\n"); +- printf(" such segments, one of the markers is chosen arbitrarily.\n"); +- printf( +-" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n"); +- printf(" then the vertex is assigned the marker one (1).\n"); +- printf(" - Otherwise, the vertex is assigned the marker zero (0).\n"); +- printf("\n"); +- printf( +-" If you want Triangle to determine for you which vertices and edges are on\n" +-); +- printf( +-" the boundary, assign them the boundary marker zero (or use no markers at\n" +-); +- printf( +-" all) in your input files. In the output files, all boundary vertices,\n"); +- printf(" edges, and segments will be assigned the value one.\n\n"); +- printf("Triangulation Iteration Numbers:\n\n"); +- printf( +-" Because Triangle can read and refine its own triangulations, input\n"); +- printf( +-" and output files have iteration numbers. For instance, Triangle might\n"); +- printf( +-" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); +- printf( +-" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); +- printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); +- printf( +-" their iteration number is zero; hence, Triangle might read the file\n"); +- printf( +-" points.node, triangulate it, and produce the files points.1.node and\n"); +- printf(" points.1.ele.\n\n"); +- printf( +-" Iteration numbers allow you to create a sequence of successively finer\n"); +- printf( +-" meshes suitable for multigrid methods. They also allow you to produce a\n" +-); +- printf( +-" sequence of meshes using error estimate-driven mesh refinement.\n"); +- printf("\n"); +- printf( +-" If you're not using refinement or quality meshing, and you don't like\n"); +- printf( +-" iteration numbers, use the -I switch to disable them. This switch also\n"); +- printf( +-" disables output of .node and .poly files to prevent your input files from\n" +-); +- printf( +-" being overwritten. (If the input is a .poly file that contains its own\n"); +- printf( +-" points, a .node file is written. This can be quite convenient for\n"); +- printf(" computing CDTs or quality meshes.)\n\n"); +- printf("Examples of How to Use Triangle:\n\n"); +- printf( +-" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n" +-); +- printf( +-" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n"); +- printf( +-" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n"); +- printf( +-" instead. (No additional .node file is needed, so none is written.)\n"); +- printf("\n"); +- printf( +-" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n"); +- printf( +-" object.1.node, if the vertices are omitted from object.1.poly) and writes\n" +-); +- printf( +-" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n" +-); +- printf( +-" The segments are copied to object.2.poly, and all edges are written to\n"); +- printf(" object.2.edge.\n\n"); +- printf( +-" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n" +-); +- printf( +-" object.node), generates a mesh whose angles are all between 31.5 and 117\n" +-); +- printf( +-" degrees and whose triangles all have areas of 0.1 or less, and writes the\n" +-); +- printf( +-" mesh to object.1.node and object.1.ele. Each segment may be broken up\n"); +- printf(" into multiple subsegments; these are written to object.1.poly.\n"); +- printf("\n"); +- printf( +-" Here is a sample file `box.poly' describing a square with a square hole:\n" +-); +- printf("\n"); +- printf( +-" # A box with eight vertices in 2D, no attributes, one boundary marker.\n" +-); +- printf(" 8 2 0 1\n"); +- printf(" # Outer box has these vertices:\n"); +- printf(" 1 0 0 0\n"); +- printf(" 2 0 3 0\n"); +- printf(" 3 3 0 0\n"); +- printf(" 4 3 3 33 # A special marker for this vertex.\n"); +- printf(" # Inner square has these vertices:\n"); +- printf(" 5 1 1 0\n"); +- printf(" 6 1 2 0\n"); +- printf(" 7 2 1 0\n"); +- printf(" 8 2 2 0\n"); +- printf(" # Five segments with boundary markers.\n"); +- printf(" 5 1\n"); +- printf(" 1 1 2 5 # Left side of outer box.\n"); +- printf(" # Square hole has these segments:\n"); +- printf(" 2 5 7 0\n"); +- printf(" 3 7 8 0\n"); +- printf(" 4 8 6 10\n"); +- printf(" 5 6 5 0\n"); +- printf(" # One hole in the middle of the inner square.\n"); +- printf(" 1\n"); +- printf(" 1 1.5 1.5\n"); +- printf("\n"); +- printf( +-" Note that some segments are missing from the outer square, so you must\n"); +- printf( +-" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n" +-); +- printf( +-" file `box.1.node', with twelve vertices. The last four vertices were\n"); +- printf( +-" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n"); +- printf( +-" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n"); +- printf( +-" other vertices but 4 have been marked to indicate that they lie on a\n"); +- printf(" boundary.\n\n"); +- printf(" 12 2 0 1\n"); +- printf(" 1 0 0 5\n"); +- printf(" 2 0 3 5\n"); +- printf(" 3 3 0 1\n"); +- printf(" 4 3 3 33\n"); +- printf(" 5 1 1 1\n"); +- printf(" 6 1 2 10\n"); +- printf(" 7 2 1 1\n"); +- printf(" 8 2 2 10\n"); +- printf(" 9 0 1.5 5\n"); +- printf(" 10 1.5 0 1\n"); +- printf(" 11 3 1.5 1\n"); +- printf(" 12 1.5 3 1\n"); +- printf(" # Generated by triangle -pqc box.poly\n"); +- printf("\n"); +- printf(" Here is the output file `box.1.ele', with twelve triangles.\n"); +- printf("\n"); +- printf(" 12 3 0\n"); +- printf(" 1 5 6 9\n"); +- printf(" 2 10 3 7\n"); +- printf(" 3 6 8 12\n"); +- printf(" 4 9 1 5\n"); +- printf(" 5 6 2 9\n"); +- printf(" 6 7 3 11\n"); +- printf(" 7 11 4 8\n"); +- printf(" 8 7 5 10\n"); +- printf(" 9 12 2 6\n"); +- printf(" 10 8 7 11\n"); +- printf(" 11 5 1 10\n"); +- printf(" 12 8 4 12\n"); +- printf(" # Generated by triangle -pqc box.poly\n\n"); +- printf( +-" Here is the output file `box.1.poly'. Note that segments have been added\n" +-); +- printf( +-" to represent the convex hull, and some segments have been subdivided by\n"); +- printf( +-" newly added vertices. Note also that <# of vertices> is set to zero to\n"); +- printf(" indicate that the vertices should be read from the .node file.\n"); +- printf("\n"); +- printf(" 0 2 0 1\n"); +- printf(" 12 1\n"); +- printf(" 1 1 9 5\n"); +- printf(" 2 5 7 1\n"); +- printf(" 3 8 7 1\n"); +- printf(" 4 6 8 10\n"); +- printf(" 5 5 6 1\n"); +- printf(" 6 3 10 1\n"); +- printf(" 7 4 11 1\n"); +- printf(" 8 2 12 1\n"); +- printf(" 9 9 2 5\n"); +- printf(" 10 10 1 1\n"); +- printf(" 11 11 3 1\n"); +- printf(" 12 12 4 1\n"); +- printf(" 1\n"); +- printf(" 1 1.5 1.5\n"); +- printf(" # Generated by triangle -pqc box.poly\n"); +- printf("\n"); +- printf("Refinement and Area Constraints:\n"); +- printf("\n"); +- printf( +-" The -r switch causes a mesh (.node and .ele files) to be read and\n"); +- printf( +-" refined. If the -p switch is also used, a .poly file is read and used to\n" +-); +- printf( +-" specify edges that are constrained and cannot be eliminated (although\n"); +- printf( +-" they can be subdivided into smaller edges) by the refinement process.\n"); +- printf("\n"); +- printf( +-" When you refine a mesh, you generally want to impose tighter constraints.\n" +-); +- printf( +-" One way to accomplish this is to use -q with a larger angle, or -a\n"); +- printf( +-" followed by a smaller area than you used to generate the mesh you are\n"); +- printf( +-" refining. Another way to do this is to create an .area file, which\n"); +- printf( +-" specifies a maximum area for each triangle, and use the -a switch\n"); +- printf( +-" (without a number following). Each triangle's area constraint is applied\n" +-); +- printf( +-" to that triangle. Area constraints tend to diffuse as the mesh is\n"); +- printf( +-" refined, so if there are large variations in area constraint between\n"); +- printf( +-" adjacent triangles, you may not get the results you want. In that case,\n" +-); +- printf( +-" consider instead using the -u switch and writing a C procedure that\n"); +- printf(" determines which triangles are too large.\n\n"); +- printf( +-" If you are refining a mesh composed of linear (three-node) elements, the\n" +-); +- printf( +-" output mesh contains all the nodes present in the input mesh, in the same\n" +-); +- printf( +-" order, with new nodes added at the end of the .node file. However, the\n"); +- printf( +-" refinement is not hierarchical: there is no guarantee that each output\n"); +- printf( +-" element is contained in a single input element. Often, an output element\n" +-); +- printf( +-" can overlap two or three input elements, and some input edges are not\n"); +- printf( +-" present in the output mesh. Hence, a sequence of refined meshes forms a\n" +-); +- printf( +-" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n"); +- printf( +-" mesh of higher-order elements, the hierarchical property applies only to\n" +-); +- printf( +-" the nodes at the corners of an element; the midpoint nodes on each edge\n"); +- printf(" are discarded before the mesh is refined.\n\n"); +- printf( +-" Maximum area constraints in .poly files operate differently from those in\n" +-); +- printf( +-" .area files. A maximum area in a .poly file applies to the whole\n"); +- printf( +-" (segment-bounded) region in which a point falls, whereas a maximum area\n"); +- printf( +-" in an .area file applies to only one triangle. Area constraints in .poly\n" +-); +- printf( +-" files are used only when a mesh is first generated, whereas area\n"); +- printf( +-" constraints in .area files are used only to refine an existing mesh, and\n" +-); +- printf( +-" are typically based on a posteriori error estimates resulting from a\n"); +- printf(" finite element simulation on that mesh.\n\n"); +- printf( +-" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n"); +- printf( +-" refines the triangulation to enforce a 25 degree minimum angle, and then\n" +-); +- printf( +-" writes the refined triangulation to object.2.node and object.2.ele.\n"); +- printf("\n"); +- printf( +-" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n" +-); +- printf( +-" After reconstructing the mesh and its subsegments, Triangle refines the\n"); +- printf( +-" mesh so that no triangle has area greater than 6.2, and furthermore the\n"); +- printf( +-" triangles satisfy the maximum area constraints in z.3.area. No angle\n"); +- printf( +-" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n" +-); +- printf(" z.4.poly.\n\n"); +- printf( +-" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); +- printf( +-" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n"); +- printf(" suitable for multigrid.\n\n"); +- printf("Convex Hulls and Mesh Boundaries:\n\n"); +- printf( +-" If the input is a vertex set (not a PSLG), Triangle produces its convex\n"); +- printf( +-" hull as a by-product in the output .poly file if you use the -c switch.\n"); +- printf( +-" There are faster algorithms for finding a two-dimensional convex hull\n"); +- printf(" than triangulation, of course, but this one comes for free.\n\n"); +- printf( +-" If the input is an unconstrained mesh (you are using the -r switch but\n"); +- printf( +-" not the -p switch), Triangle produces a list of its boundary edges\n"); +- printf( +-" (including hole boundaries) as a by-product when you use the -c switch.\n"); +- printf( +-" If you also use the -p switch, the output .poly file contains all the\n"); +- printf(" segments from the input .poly file as well.\n\n"); +- printf("Voronoi Diagrams:\n\n"); +- printf( +-" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); +- printf( +-" .v.edge. For example, `triangle -v points' reads points.node, produces\n"); +- printf( +-" its Delaunay triangulation in points.1.node and points.1.ele, and\n"); +- printf( +-" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n" +-); +- printf( +-" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"); +- printf( +-" file contains a list of all Voronoi edges, some of which may be infinite\n" +-); +- printf( +-" rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); +- printf(" vertices through Triangle, if so desired.)\n\n"); +- printf( +-" This implementation does not use exact arithmetic to compute the Voronoi\n" +-); +- printf( +-" vertices, and does not check whether neighboring vertices are identical.\n" +-); +- printf( +-" Be forewarned that if the Delaunay triangulation is degenerate or\n"); +- printf( +-" near-degenerate, the Voronoi diagram may have duplicate vertices or\n"); +- printf(" crossing edges.\n\n"); +- printf( +-" The result is a valid Voronoi diagram only if Triangle's output is a true\n" +-); +- printf( +-" Delaunay triangulation. The Voronoi output is usually meaningless (and\n"); +- printf( +-" may contain crossing edges and other pathology) if the output is a CDT or\n" +-); +- printf( +-" CCDT, or if it has holes or concavities. If the triangulated domain is\n"); +- printf( +-" convex and has no holes, you can use -D switch to force Triangle to\n"); +- printf( +-" construct a conforming Delaunay triangulation instead of a CCDT, so the\n"); +- printf(" Voronoi diagram will be valid.\n\n"); +- printf("Mesh Topology:\n\n"); +- printf( +-" You may wish to know which triangles are adjacent to a certain Delaunay\n"); +- printf( +-" edge in an .edge file, which Voronoi cells are adjacent to a certain\n"); +- printf( +-" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n"); +- printf( +-" each other. All of this information can be found by cross-referencing\n"); +- printf( +-" output files with the recollection that the Delaunay triangulation and\n"); +- printf(" the Voronoi diagram are planar duals.\n\n"); +- printf( +-" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); +- printf( +-" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); +- printf( +-" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); +- printf( +-" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n"); +- printf(" of vertex k of the corresponding .node file.\n\n"); +- printf( +-" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); +- printf( +-" vertices of the corresponding Voronoi edge. If the endpoints of a\n"); +- printf( +-" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n" +-); +- printf( +-" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n" +-); +- printf( +-" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n" +-); +- printf( +-" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n" +-); +- printf( +-" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n" +-); +- printf( +-" adjoin the right and left sides of the corresponding Voronoi edge,\n"); +- printf( +-" respectively. To find which Voronoi cells are adjacent to each other,\n"); +- printf(" just read the list of Delaunay edges.\n\n"); +- printf( +-" Triangle does not write a list of the edges adjoining each Voronoi cell,\n" +-); +- printf( +-" but you can reconstructed it straightforwardly. For instance, to find\n"); +- printf( +-" all the edges of Voronoi cell 1, search the output .edge file for every\n"); +- printf( +-" edge that has input vertex 1 as an endpoint. The corresponding dual\n"); +- printf( +-" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n"); +- printf("\n"); +- printf( +-" For each Voronoi vertex, the .neigh file gives a list of the three\n"); +- printf( +-" Voronoi vertices attached to it. You might find this more convenient\n"); +- printf(" than the .v.edge file.\n\n"); +- printf("Quadratic Elements:\n\n"); +- printf( +-" Triangle generates meshes with subparametric quadratic elements if the\n"); +- printf( +-" -o2 switch is specified. Quadratic elements have six nodes per element,\n" +-); +- printf( +-" rather than three. `Subparametric' means that the edges of the triangles\n" +-); +- printf( +-" are always straight, so that subparametric quadratic elements are\n"); +- printf( +-" geometrically identical to linear elements, even though they can be used\n" +-); +- printf( +-" with quadratic interpolating functions. The three extra nodes of an\n"); +- printf( +-" element fall at the midpoints of the three edges, with the fourth, fifth,\n" +-); +- printf( +-" and sixth nodes appearing opposite the first, second, and third corners\n"); +- printf(" respectively.\n\n"); +- printf("Domains with Small Angles:\n\n"); +- printf( +-" If two input segments adjoin each other at a small angle, clearly the -q\n" +-); +- printf( +-" switch cannot remove the small angle. Moreover, Triangle may have no\n"); +- printf( +-" choice but to generate additional triangles whose smallest angles are\n"); +- printf( +-" smaller than the specified bound. However, these triangles only appear\n"); +- printf( +-" between input segments separated by small angles. Moreover, if you\n"); +- printf( +-" request a minimum angle of theta degrees, Triangle will generally produce\n" +-); +- printf( +-" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n" +-); +- printf(" the minimum angle.\n\n"); +- printf("Statistics:\n\n"); +- printf( +-" After generating a mesh, Triangle prints a count of entities in the\n"); +- printf( +-" output mesh, including the number of vertices, triangles, edges, exterior\n" +-); +- printf( +-" boundary edges (i.e. subsegments on the boundary of the triangulation,\n"); +- printf( +-" including hole boundaries), interior boundary edges (i.e. subsegments of\n" +-); +- printf( +-" input segments not on the boundary), and total subsegments. If you've\n"); +- printf( +-" forgotten the statistics for an existing mesh, run Triangle on that mesh\n" +-); +- printf( +-" with the -rNEP switches to read the mesh and print the statistics without\n" +-); +- printf( +-" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n"); +- printf("\n"); +- printf( +-" The -V switch produces extended statistics, including a rough estimate\n"); +- printf( +-" of memory use, the number of calls to geometric predicates, and\n"); +- printf( +-" histograms of the angles and the aspect ratios of the triangles in the\n"); +- printf(" mesh.\n\n"); +- printf("Exact Arithmetic:\n\n"); +- printf( +-" Triangle uses adaptive exact arithmetic to perform what computational\n"); +- printf( +-" geometers call the `orientation' and `incircle' tests. If the floating-\n" +-); +- printf( +-" point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); +- printf( +-" most workstations do), and does not use extended precision internal\n"); +- printf( +-" floating-point registers, then your output is guaranteed to be an\n"); +- printf( +-" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n" +-); +- printf( +-" error notwithstanding. The word `adaptive' implies that these arithmetic\n" +-); +- printf( +-" routines compute the result only to the precision necessary to guarantee\n" +-); +- printf( +-" correctness, so they are usually nearly as fast as their approximate\n"); +- printf(" counterparts.\n\n"); +- printf( +-" May CPUs, including Intel x86 processors, have extended precision\n"); +- printf( +-" floating-point registers. These must be reconfigured so their precision\n" +-); +- printf( +-" is reduced to memory precision. Triangle does this if it is compiled\n"); +- printf(" correctly. See the makefile for details.\n\n"); +- printf( +-" The exact tests can be disabled with the -X switch. On most inputs, this\n" +-); +- printf( +-" switch reduces the computation time by about eight percent--it's not\n"); +- printf( +-" worth the risk. There are rare difficult inputs (having many collinear\n"); +- printf( +-" and cocircular vertices), however, for which the difference in speed\n"); +- printf( +-" could be a factor of two. Be forewarned that these are precisely the\n"); +- printf( +-" inputs most likely to cause errors if you use the -X switch. Hence, the\n" +-); +- printf(" -X switch is not recommended.\n\n"); +- printf( +-" Unfortunately, the exact tests don't solve every numerical problem.\n"); +- printf( +-" Exact arithmetic is not used to compute the positions of new vertices,\n"); +- printf( +-" because the bit complexity of vertex coordinates would grow without\n"); +- printf( +-" bound. Hence, segment intersections aren't computed exactly; in very\n"); +- printf( +-" unusual cases, roundoff error in computing an intersection point might\n"); +- printf( +-" actually lead to an inverted triangle and an invalid triangulation.\n"); +- printf( +-" (This is one reason to specify your own intersection points in your .poly\n" +-); +- printf( +-" files.) Similarly, exact arithmetic is not used to compute the vertices\n" +-); +- printf(" of the Voronoi diagram.\n\n"); +- printf( +-" Another pair of problems not solved by the exact arithmetic routines is\n"); +- printf( +-" underflow and overflow. If Triangle is compiled for double precision\n"); +- printf( +-" arithmetic, I believe that Triangle's geometric predicates work correctly\n" +-); +- printf( +-" if the exponent of every input coordinate falls in the range [-148, 201].\n" +-); +- printf( +-" Underflow can silently prevent the orientation and incircle tests from\n"); +- printf( +-" being performed exactly, while overflow typically causes a floating\n"); +- printf(" exception.\n\n"); +- printf("Calling Triangle from Another Program:\n\n"); +- printf(" Read the file triangle.h for details.\n\n"); +- printf("Troubleshooting:\n\n"); +- printf(" Please read this section before mailing me bugs.\n\n"); +- printf(" `My output mesh has no triangles!'\n\n"); +- printf( +-" If you're using a PSLG, you've probably failed to specify a proper set\n" +-); +- printf( +-" of bounding segments, or forgotten to use the -c switch. Or you may\n"); +- printf( +-" have placed a hole badly, thereby eating all your triangles. To test\n"); +- printf(" these possibilities, try again with the -c and -O switches.\n"); +- printf( +-" Alternatively, all your input vertices may be collinear, in which case\n" +-); +- printf(" you can hardly expect to triangulate them.\n\n"); +- printf(" `Triangle doesn't terminate, or just crashes.'\n\n"); +- printf( +-" Bad things can happen when triangles get so small that the distance\n"); +- printf( +-" between their vertices isn't much larger than the precision of your\n"); +- printf( +-" machine's arithmetic. If you've compiled Triangle for single-precision\n" +-); +- printf( +-" arithmetic, you might do better by recompiling it for double-precision.\n" +-); +- printf( +-" Then again, you might just have to settle for more lenient constraints\n" +-); +- printf( +-" on the minimum angle and the maximum area than you had planned.\n"); +- printf("\n"); +- printf( +-" You can minimize precision problems by ensuring that the origin lies\n"); +- printf( +-" inside your vertex set, or even inside the densest part of your\n"); +- printf( +-" mesh. If you're triangulating an object whose x-coordinates all fall\n"); +- printf( +-" between 6247133 and 6247134, you're not leaving much floating-point\n"); +- printf(" precision for Triangle to work with.\n\n"); +- printf( +-" Precision problems can occur covertly if the input PSLG contains two\n"); +- printf( +-" segments that meet (or intersect) at an extremely small angle, or if\n"); +- printf( +-" such an angle is introduced by the -c switch. If you don't realize\n"); +- printf( +-" that a tiny angle is being formed, you might never discover why\n"); +- printf( +-" Triangle is crashing. To check for this possibility, use the -S switch\n" +-); +- printf( +-" (with an appropriate limit on the number of Steiner points, found by\n"); +- printf( +-" trial-and-error) to stop Triangle early, and view the output .poly file\n" +-); +- printf( +-" with Show Me (described below). Look carefully for regions where dense\n" +-); +- printf( +-" clusters of vertices are forming and for small angles between segments.\n" +-); +- printf( +-" Zoom in closely, as such segments might look like a single segment from\n" +-); +- printf(" a distance.\n\n"); +- printf( +-" If some of the input values are too large, Triangle may suffer a\n"); +- printf( +-" floating exception due to overflow when attempting to perform an\n"); +- printf( +-" orientation or incircle test. (Read the section on exact arithmetic\n"); +- printf( +-" above.) Again, I recommend compiling Triangle for double (rather\n"); +- printf(" than single) precision arithmetic.\n\n"); +- printf( +-" Unexpected problems can arise if you use quality meshing (-q, -a, or\n"); +- printf( +-" -u) with an input that is not segment-bounded--that is, if your input\n"); +- printf( +-" is a vertex set, or you're using the -c switch. If the convex hull of\n" +-); +- printf( +-" your input vertices has collinear vertices on its boundary, an input\n"); +- printf( +-" vertex that you think lies on the convex hull might actually lie just\n"); +- printf( +-" inside the convex hull. If so, the vertex and the nearby convex hull\n"); +- printf( +-" edge form an extremely thin triangle. When Triangle tries to refine\n"); +- printf( +-" the mesh to enforce angle and area constraints, Triangle might generate\n" +-); +- printf( +-" extremely tiny triangles, or it might fail because of insufficient\n"); +- printf(" floating-point precision.\n\n"); +- printf( +-" `The numbering of the output vertices doesn't match the input vertices.'\n" +-); +- printf("\n"); +- printf( +-" You may have had duplicate input vertices, or you may have eaten some\n"); +- printf( +-" of your input vertices with a hole, or by placing them outside the area\n" +-); +- printf( +-" enclosed by segments. In any case, you can solve the problem by not\n"); +- printf(" using the -j switch.\n\n"); +- printf( +-" `Triangle executes without incident, but when I look at the resulting\n"); +- printf( +-" mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); +- printf("\n"); +- printf( +-" If you select the -X switch, Triangle occasionally makes mistakes due\n"); +- printf( +-" to floating-point roundoff error. Although these errors are rare,\n"); +- printf( +-" don't use the -X switch. If you still have problems, please report the\n" +-); +- printf(" bug.\n\n"); +- printf( +-" `Triangle executes without incident, but when I look at the resulting\n"); +- printf(" Voronoi diagram, it has overlapping edges or other geometric\n"); +- printf(" inconsistencies.'\n"); +- printf("\n"); +- printf( +-" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n" +-); +- printf( +-" diagram if the domain you are triangulating is convex and free of\n"); +- printf( +-" holes, and you use the -D switch to construct a conforming Delaunay\n"); +- printf(" triangulation (instead of a CDT or CCDT).\n\n"); +- printf( +-" Strange things can happen if you've taken liberties with your PSLG. Do\n"); +- printf( +-" you have a vertex lying in the middle of a segment? Triangle sometimes\n"); +- printf( +-" copes poorly with that sort of thing. Do you want to lay out a collinear\n" +-); +- printf( +-" row of evenly spaced, segment-connected vertices? Have you simply\n"); +- printf( +-" defined one long segment connecting the leftmost vertex to the rightmost\n" +-); +- printf( +-" vertex, and a bunch of vertices lying along it? This method occasionally\n" +-); +- printf( +-" works, especially with horizontal and vertical lines, but often it\n"); +- printf( +-" doesn't, and you'll have to connect each adjacent pair of vertices with a\n" +-); +- printf(" separate segment. If you don't like it, tough.\n\n"); +- printf( +-" Furthermore, if you have segments that intersect other than at their\n"); +- printf( +-" endpoints, try not to let the intersections fall extremely close to PSLG\n" +-); +- printf(" vertices or each other.\n\n"); +- printf( +-" If you have problems refining a triangulation not produced by Triangle:\n"); +- printf( +-" Are you sure the triangulation is geometrically valid? Is it formatted\n"); +- printf( +-" correctly for Triangle? Are the triangles all listed so the first three\n" +-); +- printf( +-" vertices are their corners in counterclockwise order? Are all of the\n"); +- printf( +-" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n" +-); +- printf(" assumes that it starts with a CDT.\n\n"); +- printf("Show Me:\n\n"); +- printf( +-" Triangle comes with a separate program named `Show Me', whose primary\n"); +- printf( +-" purpose is to draw meshes on your screen or in PostScript. Its secondary\n" +-); +- printf( +-" purpose is to check the validity of your input files, and do so more\n"); +- printf( +-" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n"); +- printf( +-" you have the X Windows system. Sorry, Microsoft Windows users.\n"); +- printf("\n"); +- printf("Triangle on the Web:\n"); +- printf("\n"); +- printf(" To see an illustrated version of these instructions, check out\n"); +- printf("\n"); +- printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); +- printf("\n"); +- printf("A Brief Plea:\n"); +- printf("\n"); +- printf( +-" If you use Triangle, and especially if you use it to accomplish real\n"); +- printf( +-" work, I would like very much to hear from you. A short letter or email\n"); +- printf( +-" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n" +-); +- printf( +-" to me. The more people I know are using this program, the more easily I\n" +-); +- printf( +-" can justify spending time on improvements, which in turn will benefit\n"); +- printf( +-" you. Also, I can put you on a list to receive email whenever a new\n"); +- printf(" version of Triangle is available.\n\n"); +- printf( +-" If you use a mesh generated by Triangle in a publication, please include\n" +-); +- printf( +-" an acknowledgment as well. And please spell Triangle with a capital `T'!\n" +-); +- printf( +-" If you want to include a citation, use `Jonathan Richard Shewchuk,\n"); +- printf( +-" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n"); +- printf( +-" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n"); +- printf( +-" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n"); +- printf( +-" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n"); +- printf( +-" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n" +-); +- printf(" Geometry.)'\n\n"); +- printf("Research credit:\n\n"); +- printf( +-" Of course, I can take credit for only a fraction of the ideas that made\n"); +- printf( +-" this mesh generator possible. Triangle owes its existence to the efforts\n" +-); +- printf( +-" of many fine computational geometers and other researchers, including\n"); +- printf( +-" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n" +-); +- printf( +-" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n"); +- printf( +-" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n"); +- printf( +-" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n"); +- printf( +-" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n" +-); +- printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n"); +- printf( +-" Walkington, and Binhai Zhu. See the comments at the beginning of the\n"); +- printf(" source code for references.\n\n"); +- triexit(0); +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* internalerror() Ask the user to send me the defective product. Exit. */ +-/* */ +-/*****************************************************************************/ +- +-void internalerror() +-{ +- printf(" Please report this bug to jrs@cs.berkeley.edu\n"); +- printf(" Include the message above, your input data set, and the exact\n"); +- printf(" command line you used to run Triangle.\n"); +- triexit(1); +-} +- +-/*****************************************************************************/ +-/* */ +-/* parsecommandline() Read the command line, identify switches, and set */ +-/* up options and file names. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void parsecommandline(int argc, const char * const * const argv, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void parsecommandline(argc, argv, b) +-int argc; +-const char * const * const argv; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +-#ifdef TRILIBRARY +-#define STARTINDEX 0 +-#else /* not TRILIBRARY */ +-#define STARTINDEX 1 +- int increment; +- int meshnumber; +-#endif /* not TRILIBRARY */ +- int i, j, k; +- char workstring[FILENAMESIZE]; +- +- b->poly = b->refine = b->quality = 0; +- b->vararea = b->fixedarea = b->usertest = 0; +- b->regionattrib = b->convex = b->weighted = b->jettison = 0; +- b->firstnumber = 1; +- b->edgesout = b->voronoi = b->neighbors = b->geomview = 0; +- b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0; +- b->noiterationnum = 0; +- b->noholes = b->noexact = 0; +- b->incremental = b->sweepline = 0; +- b->dwyer = 1; +- b->splitseg = 0; +- b->docheck = 0; +- b->nobisect = 0; +- b->conformdel = 0; +- b->steiner = -1; +- b->order = 1; +- b->minangle = 0.0; +- b->maxarea = -1.0; +- b->quiet = b->verbose = 0; +-#ifndef TRILIBRARY +- b->innodefilename[0] = '\0'; +-#endif /* not TRILIBRARY */ +- +- for (i = STARTINDEX; i < argc; i++) { +-#ifndef TRILIBRARY +- if (argv[i][0] == '-') { +-#endif /* not TRILIBRARY */ +- for (j = STARTINDEX; argv[i][j] != '\0'; j++) { +- if (argv[i][j] == 'p') { +- b->poly = 1; +- } +-#ifndef CDT_ONLY +- if (argv[i][j] == 'r') { +- b->refine = 1; +- } +- if (argv[i][j] == 'q') { +- b->quality = 1; +- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || +- (argv[i][j + 1] == '.')) { +- k = 0; +- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || +- (argv[i][j + 1] == '.')) { +- j++; +- workstring[k] = argv[i][j]; +- k++; +- } +- workstring[k] = '\0'; +- b->minangle = (REAL) strtod(workstring, (char **) NULL); +- } else { +- b->minangle = 20.0; +- } +- } +- if (argv[i][j] == 'a') { +- b->quality = 1; +- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || +- (argv[i][j + 1] == '.')) { +- b->fixedarea = 1; +- k = 0; +- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || +- (argv[i][j + 1] == '.')) { +- j++; +- workstring[k] = argv[i][j]; +- k++; +- } +- workstring[k] = '\0'; +- b->maxarea = (REAL) strtod(workstring, (char **) NULL); +- if (b->maxarea <= 0.0) { +- printf("Error: Maximum area must be greater than zero.\n"); +- triexit(1); +- } +- } else { +- b->vararea = 1; +- } +- } +- if (argv[i][j] == 'u') { +- b->quality = 1; +- b->usertest = 1; +- } +-#endif /* not CDT_ONLY */ +- if (argv[i][j] == 'A') { +- b->regionattrib = 1; +- } +- if (argv[i][j] == 'c') { +- b->convex = 1; +- } +- if (argv[i][j] == 'w') { +- b->weighted = 1; +- } +- if (argv[i][j] == 'W') { +- b->weighted = 2; +- } +- if (argv[i][j] == 'j') { +- b->jettison = 1; +- } +- if (argv[i][j] == 'z') { +- b->firstnumber = 0; +- } +- if (argv[i][j] == 'e') { +- b->edgesout = 1; +- } +- if (argv[i][j] == 'v') { +- b->voronoi = 1; +- } +- if (argv[i][j] == 'n') { +- b->neighbors = 1; +- } +- if (argv[i][j] == 'g') { +- b->geomview = 1; +- } +- if (argv[i][j] == 'B') { +- b->nobound = 1; +- } +- if (argv[i][j] == 'P') { +- b->nopolywritten = 1; +- } +- if (argv[i][j] == 'N') { +- b->nonodewritten = 1; +- } +- if (argv[i][j] == 'E') { +- b->noelewritten = 1; +- } +-#ifndef TRILIBRARY +- if (argv[i][j] == 'I') { +- b->noiterationnum = 1; +- } +-#endif /* not TRILIBRARY */ +- if (argv[i][j] == 'O') { +- b->noholes = 1; +- } +- if (argv[i][j] == 'X') { +- b->noexact = 1; +- } +- if (argv[i][j] == 'o') { +- if (argv[i][j + 1] == '2') { +- j++; +- b->order = 2; +- } +- } +-#ifndef CDT_ONLY +- if (argv[i][j] == 'Y') { +- b->nobisect++; +- } +- if (argv[i][j] == 'S') { +- b->steiner = 0; +- while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { +- j++; +- b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0'); +- } +- } +-#endif /* not CDT_ONLY */ +-#ifndef REDUCED +- if (argv[i][j] == 'i') { +- b->incremental = 1; +- } +- if (argv[i][j] == 'F') { +- b->sweepline = 1; +- } +-#endif /* not REDUCED */ +- if (argv[i][j] == 'l') { +- b->dwyer = 0; +- } +-#ifndef REDUCED +-#ifndef CDT_ONLY +- if (argv[i][j] == 's') { +- b->splitseg = 1; +- } +- if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) { +- b->quality = 1; +- b->conformdel = 1; +- } +-#endif /* not CDT_ONLY */ +- if (argv[i][j] == 'C') { +- b->docheck = 1; +- } +-#endif /* not REDUCED */ +- if (argv[i][j] == 'Q') { +- b->quiet = 1; +- } +- if (argv[i][j] == 'V') { +- b->verbose++; +- } +-#ifndef TRILIBRARY +- if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || +- (argv[i][j] == '?')) { +- info(); +- } +-#endif /* not TRILIBRARY */ +- } +-#ifndef TRILIBRARY +- } else { +- strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1); +- b->innodefilename[FILENAMESIZE - 1] = '\0'; +- } +-#endif /* not TRILIBRARY */ +- } +-#ifndef TRILIBRARY +- if (b->innodefilename[0] == '\0') { +- syntax(); +- } +- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) { +- b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; +- } +- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) { +- b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; +- b->poly = 1; +- } +-#ifndef CDT_ONLY +- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) { +- b->innodefilename[strlen(b->innodefilename) - 4] = '\0'; +- b->refine = 1; +- } +- if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) { +- b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; +- b->refine = 1; +- b->quality = 1; +- b->vararea = 1; +- } +-#endif /* not CDT_ONLY */ +-#endif /* not TRILIBRARY */ +- b->usesegments = b->poly || b->refine || b->quality || b->convex; +- b->goodangle = cos(b->minangle * PI / 180.0); +- if (b->goodangle == 1.0) { +- b->offconstant = 0.0; +- } else { +- b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle)); +- } +- b->goodangle *= b->goodangle; +- if (b->refine && b->noiterationnum) { +- printf( +- "Error: You cannot use the -I switch when refining a triangulation.\n"); +- triexit(1); +- } +- /* Be careful not to allocate space for element area constraints that */ +- /* will never be assigned any value (other than the default -1.0). */ +- if (!b->refine && !b->poly) { +- b->vararea = 0; +- } +- /* Be careful not to add an extra attribute to each element unless the */ +- /* input supports it (PSLG in, but not refining a preexisting mesh). */ +- if (b->refine || !b->poly) { +- b->regionattrib = 0; +- } +- /* Regular/weighted triangulations are incompatible with PSLGs */ +- /* and meshing. */ +- if (b->weighted && (b->poly || b->quality)) { +- b->weighted = 0; +- if (!b->quiet) { +- printf("Warning: weighted triangulations (-w, -W) are incompatible\n"); +- printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n" +- ); +- } +- } +- if (b->jettison && b->nonodewritten && !b->quiet) { +- printf("Warning: -j and -N switches are somewhat incompatible.\n"); +- printf(" If any vertices are jettisoned, you will need the output\n"); +- printf(" .node file to reconstruct the new node indices."); +- } +- +-#ifndef TRILIBRARY +- strcpy(b->inpolyfilename, b->innodefilename); +- strcpy(b->inelefilename, b->innodefilename); +- strcpy(b->areafilename, b->innodefilename); +- increment = 0; +- strcpy(workstring, b->innodefilename); +- j = 1; +- while (workstring[j] != '\0') { +- if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { +- increment = j + 1; +- } +- j++; +- } +- meshnumber = 0; +- if (increment > 0) { +- j = increment; +- do { +- if ((workstring[j] >= '0') && (workstring[j] <= '9')) { +- meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); +- } else { +- increment = 0; +- } +- j++; +- } while (workstring[j] != '\0'); +- } +- if (b->noiterationnum) { +- strcpy(b->outnodefilename, b->innodefilename); +- strcpy(b->outelefilename, b->innodefilename); +- strcpy(b->edgefilename, b->innodefilename); +- strcpy(b->vnodefilename, b->innodefilename); +- strcpy(b->vedgefilename, b->innodefilename); +- strcpy(b->neighborfilename, b->innodefilename); +- strcpy(b->offfilename, b->innodefilename); +- strcat(b->outnodefilename, ".node"); +- strcat(b->outelefilename, ".ele"); +- strcat(b->edgefilename, ".edge"); +- strcat(b->vnodefilename, ".v.node"); +- strcat(b->vedgefilename, ".v.edge"); +- strcat(b->neighborfilename, ".neigh"); +- strcat(b->offfilename, ".off"); +- } else if (increment == 0) { +- strcpy(b->outnodefilename, b->innodefilename); +- strcpy(b->outpolyfilename, b->innodefilename); +- strcpy(b->outelefilename, b->innodefilename); +- strcpy(b->edgefilename, b->innodefilename); +- strcpy(b->vnodefilename, b->innodefilename); +- strcpy(b->vedgefilename, b->innodefilename); +- strcpy(b->neighborfilename, b->innodefilename); +- strcpy(b->offfilename, b->innodefilename); +- strcat(b->outnodefilename, ".1.node"); +- strcat(b->outpolyfilename, ".1.poly"); +- strcat(b->outelefilename, ".1.ele"); +- strcat(b->edgefilename, ".1.edge"); +- strcat(b->vnodefilename, ".1.v.node"); +- strcat(b->vedgefilename, ".1.v.edge"); +- strcat(b->neighborfilename, ".1.neigh"); +- strcat(b->offfilename, ".1.off"); +- } else { +- workstring[increment] = '%'; +- workstring[increment + 1] = 'd'; +- workstring[increment + 2] = '\0'; +- sprintf(b->outnodefilename, workstring, meshnumber + 1); +- strcpy(b->outpolyfilename, b->outnodefilename); +- strcpy(b->outelefilename, b->outnodefilename); +- strcpy(b->edgefilename, b->outnodefilename); +- strcpy(b->vnodefilename, b->outnodefilename); +- strcpy(b->vedgefilename, b->outnodefilename); +- strcpy(b->neighborfilename, b->outnodefilename); +- strcpy(b->offfilename, b->outnodefilename); +- strcat(b->outnodefilename, ".node"); +- strcat(b->outpolyfilename, ".poly"); +- strcat(b->outelefilename, ".ele"); +- strcat(b->edgefilename, ".edge"); +- strcat(b->vnodefilename, ".v.node"); +- strcat(b->vedgefilename, ".v.edge"); +- strcat(b->neighborfilename, ".neigh"); +- strcat(b->offfilename, ".off"); +- } +- strcat(b->innodefilename, ".node"); +- strcat(b->inpolyfilename, ".poly"); +- strcat(b->inelefilename, ".ele"); +- strcat(b->areafilename, ".area"); +-#endif /* not TRILIBRARY */ +-} +- +-/** **/ +-/** **/ +-/********* User interaction routines begin here *********/ +- +-/********* Debugging routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* printtriangle() Print out the details of an oriented triangle. */ +-/* */ +-/* I originally wrote this procedure to simplify debugging; it can be */ +-/* called directly from the debugger, and presents information about an */ +-/* oriented triangle in digestible form. It's also used when the */ +-/* highest level of verbosity (`-VVV') is specified. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void printtriangle(struct mesh *m, struct behavior *b, struct otri *t) +-#else /* not ANSI_DECLARATORS */ +-void printtriangle(m, b, t) +-struct mesh *m; +-struct behavior *b; +-struct otri *t; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri printtri; +- struct osub printsh; +- vertex printvertex; +- +- printf("triangle x%lx with orientation %d:\n", (TRIANGLE_PTRINT) t->tri, +- t->orient); +- decode(t->tri[0], printtri); +- if (printtri.tri == m->dummytri) { +- printf(" [0] = Outer space\n"); +- } else { +- printf(" [0] = x%lx %d\n", (TRIANGLE_PTRINT) printtri.tri, +- printtri.orient); +- } +- decode(t->tri[1], printtri); +- if (printtri.tri == m->dummytri) { +- printf(" [1] = Outer space\n"); +- } else { +- printf(" [1] = x%lx %d\n", (TRIANGLE_PTRINT) printtri.tri, +- printtri.orient); +- } +- decode(t->tri[2], printtri); +- if (printtri.tri == m->dummytri) { +- printf(" [2] = Outer space\n"); +- } else { +- printf(" [2] = x%lx %d\n", (TRIANGLE_PTRINT) printtri.tri, +- printtri.orient); +- } +- +- org(*t, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); +- else +- printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", +- (t->orient + 1) % 3 + 3, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- dest(*t, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); +- else +- printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", +- (t->orient + 2) % 3 + 3, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- apex(*t, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Apex [%d] = NULL\n", t->orient + 3); +- else +- printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", +- t->orient + 3, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- +- if (b->usesegments) { +- sdecode(t->tri[6], printsh); +- if (printsh.ss != m->dummysub) { +- printf(" [6] = x%lx %d\n", (TRIANGLE_PTRINT) printsh.ss, +- printsh.ssorient); +- } +- sdecode(t->tri[7], printsh); +- if (printsh.ss != m->dummysub) { +- printf(" [7] = x%lx %d\n", (TRIANGLE_PTRINT) printsh.ss, +- printsh.ssorient); +- } +- sdecode(t->tri[8], printsh); +- if (printsh.ss != m->dummysub) { +- printf(" [8] = x%lx %d\n", (TRIANGLE_PTRINT) printsh.ss, +- printsh.ssorient); +- } +- } +- +- if (b->vararea) { +- printf(" Area constraint: %.4g\n", areabound(*t)); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* printsubseg() Print out the details of an oriented subsegment. */ +-/* */ +-/* I originally wrote this procedure to simplify debugging; it can be */ +-/* called directly from the debugger, and presents information about an */ +-/* oriented subsegment in digestible form. It's also used when the highest */ +-/* level of verbosity (`-VVV') is specified. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void printsubseg(struct mesh *m, struct behavior *b, struct osub *s) +-#else /* not ANSI_DECLARATORS */ +-void printsubseg(m, b, s) +-struct mesh *m; +-struct behavior *b; +-struct osub *s; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct osub printsh; +- struct otri printtri; +- vertex printvertex; +- +- printf("subsegment x%lx with orientation %d and mark %d:\n", +- (TRIANGLE_PTRINT) s->ss, s->ssorient, mark(*s)); +- sdecode(s->ss[0], printsh); +- if (printsh.ss == m->dummysub) { +- printf(" [0] = No subsegment\n"); +- } else { +- printf(" [0] = x%lx %d\n", (TRIANGLE_PTRINT) printsh.ss, +- printsh.ssorient); +- } +- sdecode(s->ss[1], printsh); +- if (printsh.ss == m->dummysub) { +- printf(" [1] = No subsegment\n"); +- } else { +- printf(" [1] = x%lx %d\n", (TRIANGLE_PTRINT) printsh.ss, +- printsh.ssorient); +- } +- +- sorg(*s, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Origin[%d] = NULL\n", 2 + s->ssorient); +- else +- printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", +- 2 + s->ssorient, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- sdest(*s, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Dest [%d] = NULL\n", 3 - s->ssorient); +- else +- printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", +- 3 - s->ssorient, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- +- decode(s->ss[6], printtri); +- if (printtri.tri == m->dummytri) { +- printf(" [6] = Outer space\n"); +- } else { +- printf(" [6] = x%lx %d\n", (TRIANGLE_PTRINT) printtri.tri, +- printtri.orient); +- } +- decode(s->ss[7], printtri); +- if (printtri.tri == m->dummytri) { +- printf(" [7] = Outer space\n"); +- } else { +- printf(" [7] = x%lx %d\n", (TRIANGLE_PTRINT) printtri.tri, +- printtri.orient); +- } +- +- segorg(*s, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient); +- else +- printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n", +- 4 + s->ssorient, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +- segdest(*s, printvertex); +- if (printvertex == (vertex) NULL) +- printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient); +- else +- printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n", +- 5 - s->ssorient, (TRIANGLE_PTRINT) printvertex, +- printvertex[0], printvertex[1]); +-} +- +-/** **/ +-/** **/ +-/********* Debugging routines end here *********/ +- +-/********* Memory management routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* poolzero() Set all of a pool's fields to zero. */ +-/* */ +-/* This procedure should never be called on a pool that has any memory */ +-/* allocated to it, as that memory would leak. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void poolzero(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void poolzero(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- pool->firstblock = (void **) NULL; +- pool->nowblock = (void **) NULL; +- pool->nextitem = (void *) NULL; +- pool->deaditemstack = (void *) NULL; +- pool->pathblock = (void **) NULL; +- pool->pathitem = (void *) NULL; +- pool->alignbytes = 0; +- pool->itembytes = 0; +- pool->itemsperblock = 0; +- pool->itemsfirstblock = 0; +- pool->items = 0; +- pool->maxitems = 0; +- pool->unallocateditems = 0; +- pool->pathitemsleft = 0; +-} +- +-/*****************************************************************************/ +-/* */ +-/* poolrestart() Deallocate all items in a pool. */ +-/* */ +-/* The pool is returned to its starting state, except that no memory is */ +-/* freed to the operating system. Rather, the previously allocated blocks */ +-/* are ready to be reused. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void poolrestart(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void poolrestart(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- TRIANGLE_PTRINT alignptr; +- +- pool->items = 0; +- pool->maxitems = 0; +- +- /* Set the currently active block. */ +- pool->nowblock = pool->firstblock; +- /* Find the first item in the pool. Increment by the size of (void *). */ +- alignptr = (TRIANGLE_PTRINT) (pool->nowblock + 1); +- /* Align the item on an `alignbytes'-byte boundary. */ +- pool->nextitem = (void *) +- (alignptr + (TRIANGLE_PTRINT) pool->alignbytes - +- (alignptr % (TRIANGLE_PTRINT) pool->alignbytes)); +- /* There are lots of unallocated items left in this block. */ +- pool->unallocateditems = pool->itemsfirstblock; +- /* The stack of deallocated items is empty. */ +- pool->deaditemstack = (void *) NULL; +-} +- +-/*****************************************************************************/ +-/* */ +-/* poolinit() Initialize a pool of memory for allocation of items. */ +-/* */ +-/* This routine initializes the machinery for allocating items. A `pool' */ +-/* is created whose records have size at least `bytecount'. Items will be */ +-/* allocated in `itemcount'-item blocks. Each item is assumed to be a */ +-/* collection of words, and either pointers or floating-point values are */ +-/* assumed to be the "primary" word type. (The "primary" word type is used */ +-/* to determine alignment of items.) If `alignment' isn't zero, all items */ +-/* will be `alignment'-byte aligned in memory. `alignment' must be either */ +-/* a multiple or a factor of the primary word size; powers of two are safe. */ +-/* `alignment' is normally used to create a few unused bits at the bottom */ +-/* of each item's pointer, in which information may be stored. */ +-/* */ +-/* Don't change this routine unless you understand it. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void poolinit(struct memorypool *pool, int bytecount, int itemcount, +- int firstitemcount, int alignment) +-#else /* not ANSI_DECLARATORS */ +-void poolinit(pool, bytecount, itemcount, firstitemcount, alignment) +-struct memorypool *pool; +-int bytecount; +-int itemcount; +-int firstitemcount; +-int alignment; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Find the proper alignment, which must be at least as large as: */ +- /* - The parameter `alignment'. */ +- /* - sizeof(void *), so the stack of dead items can be maintained */ +- /* without unaligned accesses. */ +- if (alignment > sizeof(void *)) { +- pool->alignbytes = alignment; +- } else { +- pool->alignbytes = sizeof(void *); +- } +- pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) * +- pool->alignbytes; +- pool->itemsperblock = itemcount; +- if (firstitemcount == 0) { +- pool->itemsfirstblock = itemcount; +- } else { +- pool->itemsfirstblock = firstitemcount; +- } +- +- /* Allocate a block of items. Space for `itemsfirstblock' items and one */ +- /* pointer (to point to the next block) are allocated, as well as space */ +- /* to ensure alignment of the items. */ +- pool->firstblock = (void **) +- trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(void *) + +- pool->alignbytes); +- /* Set the next block pointer to NULL. */ +- *(pool->firstblock) = (void *) NULL; +- poolrestart(pool); +-} +- +-/*****************************************************************************/ +-/* */ +-/* pooldeinit() Free to the operating system all memory taken by a pool. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void pooldeinit(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void pooldeinit(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- while (pool->firstblock != (void **) NULL) { +- pool->nowblock = (void **) *(pool->firstblock); +- trifree((void *) pool->firstblock); +- pool->firstblock = pool->nowblock; +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* poolalloc() Allocate space for an item. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void *poolalloc(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void *poolalloc(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- void *newitem; +- void **newblock; +- TRIANGLE_PTRINT alignptr; +- +- /* First check the linked list of dead items. If the list is not */ +- /* empty, allocate an item from the list rather than a fresh one. */ +- if (pool->deaditemstack != (void *) NULL) { +- newitem = pool->deaditemstack; /* Take first item in list. */ +- pool->deaditemstack = * (void **) pool->deaditemstack; +- } else { +- /* Check if there are any free items left in the current block. */ +- if (pool->unallocateditems == 0) { +- /* Check if another block must be allocated. */ +- if (*(pool->nowblock) == (void *) NULL) { +- /* Allocate a new block of items, pointed to by the previous block. */ +- newblock = (void **) trimalloc(pool->itemsperblock * pool->itembytes + +- (int) sizeof(void *) + +- pool->alignbytes); +- *(pool->nowblock) = (void *) newblock; +- /* The next block pointer is NULL. */ +- *newblock = (void *) NULL; +- } +- +- /* Move to the new block. */ +- pool->nowblock = (void **) *(pool->nowblock); +- /* Find the first item in the block. */ +- /* Increment by the size of (void *). */ +- alignptr = (TRIANGLE_PTRINT) (pool->nowblock + 1); +- /* Align the item on an `alignbytes'-byte boundary. */ +- pool->nextitem = (void *) +- (alignptr + (TRIANGLE_PTRINT) pool->alignbytes - +- (alignptr % (TRIANGLE_PTRINT) pool->alignbytes)); +- /* There are lots of unallocated items left in this block. */ +- pool->unallocateditems = pool->itemsperblock; +- } +- +- /* Allocate a new item. */ +- newitem = pool->nextitem; +- /* Advance `nextitem' pointer to next free item in block. */ +- pool->nextitem = (void *) ((char *) pool->nextitem + pool->itembytes); +- pool->unallocateditems--; +- pool->maxitems++; +- } +- pool->items++; +- return newitem; +-} +- +-/*****************************************************************************/ +-/* */ +-/* pooldealloc() Deallocate space for an item. */ +-/* */ +-/* The deallocated space is stored in a queue for later reuse. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void pooldealloc(struct memorypool *pool, void *dyingitem) +-#else /* not ANSI_DECLARATORS */ +-void pooldealloc(pool, dyingitem) +-struct memorypool *pool; +-void *dyingitem; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Push freshly killed item onto stack. */ +- *((void **) dyingitem) = pool->deaditemstack; +- pool->deaditemstack = dyingitem; +- pool->items--; +-} +- +-/*****************************************************************************/ +-/* */ +-/* traversalinit() Prepare to traverse the entire list of items. */ +-/* */ +-/* This routine is used in conjunction with traverse(). */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void traversalinit(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void traversalinit(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- TRIANGLE_PTRINT alignptr; +- +- /* Begin the traversal in the first block. */ +- pool->pathblock = pool->firstblock; +- /* Find the first item in the block. Increment by the size of (void *). */ +- alignptr = (TRIANGLE_PTRINT) (pool->pathblock + 1); +- /* Align with item on an `alignbytes'-byte boundary. */ +- pool->pathitem = (void *) +- (alignptr + (TRIANGLE_PTRINT) pool->alignbytes - +- (alignptr % (TRIANGLE_PTRINT) pool->alignbytes)); +- /* Set the number of items left in the current block. */ +- pool->pathitemsleft = pool->itemsfirstblock; +-} +- +-/*****************************************************************************/ +-/* */ +-/* traverse() Find the next item in the list. */ +-/* */ +-/* This routine is used in conjunction with traversalinit(). Be forewarned */ +-/* that this routine successively returns all items in the list, including */ +-/* deallocated ones on the deaditemqueue. It's up to you to figure out */ +-/* which ones are actually dead. Why? I don't want to allocate extra */ +-/* space just to demarcate dead items. It can usually be done more */ +-/* space-efficiently by a routine that knows something about the structure */ +-/* of the item. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void *traverse(struct memorypool *pool) +-#else /* not ANSI_DECLARATORS */ +-void *traverse(pool) +-struct memorypool *pool; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- void *newitem; +- TRIANGLE_PTRINT alignptr; +- +- /* Stop upon exhausting the list of items. */ +- if (pool->pathitem == pool->nextitem) { +- return (void *) NULL; +- } +- +- /* Check whether any untraversed items remain in the current block. */ +- if (pool->pathitemsleft == 0) { +- /* Find the next block. */ +- pool->pathblock = (void **) *(pool->pathblock); +- /* Find the first item in the block. Increment by the size of (void *). */ +- alignptr = (TRIANGLE_PTRINT) (pool->pathblock + 1); +- /* Align with item on an `alignbytes'-byte boundary. */ +- pool->pathitem = (void *) +- (alignptr + (TRIANGLE_PTRINT) pool->alignbytes - +- (alignptr % (TRIANGLE_PTRINT) pool->alignbytes)); +- /* Set the number of items left in the current block. */ +- pool->pathitemsleft = pool->itemsperblock; +- } +- +- newitem = pool->pathitem; +- /* Find the next item in the block. */ +- pool->pathitem = (void *) ((char *) pool->pathitem + pool->itembytes); +- pool->pathitemsleft--; +- return newitem; +-} +- +-/*****************************************************************************/ +-/* */ +-/* dummyinit() Initialize the triangle that fills "outer space" and the */ +-/* omnipresent subsegment. */ +-/* */ +-/* The triangle that fills "outer space," called `dummytri', is pointed to */ +-/* by every triangle and subsegment on a boundary (be it outer or inner) of */ +-/* the triangulation. Also, `dummytri' points to one of the triangles on */ +-/* the convex hull (until the holes and concavities are carved), making it */ +-/* possible to find a starting triangle for point location. */ +-/* */ +-/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */ +-/* or subsegment that doesn't have a full complement of real subsegments */ +-/* to point to. */ +-/* */ +-/* `dummytri' and `dummysub' are generally required to fulfill only a few */ +-/* invariants: their vertices must remain NULL and `dummytri' must always */ +-/* be bonded (at offset zero) to some triangle on the convex hull of the */ +-/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */ +-/* `dummysub' may change willy-nilly. This makes it possible to avoid */ +-/* writing a good deal of special-case code (in the edge flip, for example) */ +-/* for dealing with the boundary of the mesh, places where no subsegment is */ +-/* present, and so forth. Other entities are frequently bonded to */ +-/* `dummytri' and `dummysub' as if they were real mesh entities, with no */ +-/* harm done. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes, +- int subsegbytes) +-#else /* not ANSI_DECLARATORS */ +-void dummyinit(m, b, trianglebytes, subsegbytes) +-struct mesh *m; +-struct behavior *b; +-int trianglebytes; +-int subsegbytes; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- TRIANGLE_PTRINT alignptr; +- +- /* Set up `dummytri', the `triangle' that occupies "outer space." */ +- m->dummytribase = (triangle *) trimalloc(trianglebytes + +- m->triangles.alignbytes); +- /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ +- alignptr = (TRIANGLE_PTRINT) m->dummytribase; +- m->dummytri = (triangle *) +- (alignptr + (TRIANGLE_PTRINT) m->triangles.alignbytes - +- (alignptr % (TRIANGLE_PTRINT) m->triangles.alignbytes)); +- /* Initialize the three adjoining triangles to be "outer space." These */ +- /* will eventually be changed by various bonding operations, but their */ +- /* values don't really matter, as long as they can legally be */ +- /* dereferenced. */ +- m->dummytri[0] = (triangle) m->dummytri; +- m->dummytri[1] = (triangle) m->dummytri; +- m->dummytri[2] = (triangle) m->dummytri; +- /* Three NULL vertices. */ +- m->dummytri[3] = (triangle) NULL; +- m->dummytri[4] = (triangle) NULL; +- m->dummytri[5] = (triangle) NULL; +- +- if (b->usesegments) { +- /* Set up `dummysub', the omnipresent subsegment pointed to by any */ +- /* triangle side or subsegment end that isn't attached to a real */ +- /* subsegment. */ +- m->dummysubbase = (subseg *) trimalloc(subsegbytes + +- m->subsegs.alignbytes); +- /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */ +- alignptr = (TRIANGLE_PTRINT) m->dummysubbase; +- m->dummysub = (subseg *) +- (alignptr + (TRIANGLE_PTRINT) m->subsegs.alignbytes - +- (alignptr % (TRIANGLE_PTRINT) m->subsegs.alignbytes)); +- /* Initialize the two adjoining subsegments to be the omnipresent */ +- /* subsegment. These will eventually be changed by various bonding */ +- /* operations, but their values don't really matter, as long as they */ +- /* can legally be dereferenced. */ +- m->dummysub[0] = (subseg) m->dummysub; +- m->dummysub[1] = (subseg) m->dummysub; +- /* Four NULL vertices. */ +- m->dummysub[2] = (subseg) NULL; +- m->dummysub[3] = (subseg) NULL; +- m->dummysub[4] = (subseg) NULL; +- m->dummysub[5] = (subseg) NULL; +- /* Initialize the two adjoining triangles to be "outer space." */ +- m->dummysub[6] = (subseg) m->dummytri; +- m->dummysub[7] = (subseg) m->dummytri; +- /* Set the boundary marker to zero. */ +- * (int *) (m->dummysub + 8) = 0; +- +- /* Initialize the three adjoining subsegments of `dummytri' to be */ +- /* the omnipresent subsegment. */ +- m->dummytri[6] = (triangle) m->dummysub; +- m->dummytri[7] = (triangle) m->dummysub; +- m->dummytri[8] = (triangle) m->dummysub; +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* initializevertexpool() Calculate the size of the vertex data structure */ +-/* and initialize its memory pool. */ +-/* */ +-/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */ +-/* indices used to find values within each vertex. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void initializevertexpool(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void initializevertexpool(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int vertexsize; +- +- /* The index within each vertex at which the boundary marker is found, */ +- /* followed by the vertex type. Ensure the vertex marker is aligned to */ +- /* a sizeof(int)-byte address. */ +- m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) + +- sizeof(int) - 1) / +- sizeof(int); +- vertexsize = (m->vertexmarkindex + 2) * sizeof(int); +- if (b->poly) { +- /* The index within each vertex at which a triangle pointer is found. */ +- /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ +- m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) / +- sizeof(triangle); +- vertexsize = (m->vertex2triindex + 1) * sizeof(triangle); +- } +- +- /* Initialize the pool of vertices. */ +- poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK, +- m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK, +- sizeof(REAL)); +-} +- +-/*****************************************************************************/ +-/* */ +-/* initializetrisubpools() Calculate the sizes of the triangle and */ +-/* subsegment data structures and initialize */ +-/* their memory pools. */ +-/* */ +-/* This routine also computes the `highorderindex', `elemattribindex', and */ +-/* `areaboundindex' indices used to find values within each triangle. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void initializetrisubpools(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void initializetrisubpools(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int trisize; +- +- /* The index within each triangle at which the extra nodes (above three) */ +- /* associated with high order elements are found. There are three */ +- /* pointers to other triangles, three pointers to corners, and possibly */ +- /* three pointers to subsegments before the extra nodes. */ +- m->highorderindex = 6 + (b->usesegments * 3); +- /* The number of bytes occupied by a triangle. */ +- trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) * +- sizeof(triangle); +- /* The index within each triangle at which its attributes are found, */ +- /* where the index is measured in REALs. */ +- m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL); +- /* The index within each triangle at which the maximum area constraint */ +- /* is found, where the index is measured in REALs. Note that if the */ +- /* `regionattrib' flag is set, an additional attribute will be added. */ +- m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib; +- /* If triangle attributes or an area bound are needed, increase the number */ +- /* of bytes occupied by a triangle. */ +- if (b->vararea) { +- trisize = (m->areaboundindex + 1) * sizeof(REAL); +- } else if (m->eextras + b->regionattrib > 0) { +- trisize = m->areaboundindex * sizeof(REAL); +- } +- /* If a Voronoi diagram or triangle neighbor graph is requested, make */ +- /* sure there's room to store an integer index in each triangle. This */ +- /* integer index can occupy the same space as the subsegment pointers */ +- /* or attributes or area constraint or extra nodes. */ +- if ((b->voronoi || b->neighbors) && +- (trisize < 6 * sizeof(triangle) + sizeof(int))) { +- trisize = 6 * sizeof(triangle) + sizeof(int); +- } +- +- /* Having determined the memory size of a triangle, initialize the pool. */ +- poolinit(&m->triangles, trisize, TRIPERBLOCK, +- (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) : +- TRIPERBLOCK, 4); +- +- if (b->usesegments) { +- /* Initialize the pool of subsegments. Take into account all eight */ +- /* pointers and one boundary marker. */ +- poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int), +- SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4); +- +- /* Initialize the "outer space" triangle and omnipresent subsegment. */ +- dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes); +- } else { +- /* Initialize the "outer space" triangle. */ +- dummyinit(m, b, m->triangles.itembytes, 0); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* triangledealloc() Deallocate space for a triangle, marking it dead. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void triangledealloc(struct mesh *m, triangle *dyingtriangle) +-#else /* not ANSI_DECLARATORS */ +-void triangledealloc(m, dyingtriangle) +-struct mesh *m; +-triangle *dyingtriangle; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Mark the triangle as dead. This makes it possible to detect dead */ +- /* triangles when traversing the list of all triangles. */ +- killtri(dyingtriangle); +- pooldealloc(&m->triangles, (void *) dyingtriangle); +-} +- +-/*****************************************************************************/ +-/* */ +-/* triangletraverse() Traverse the triangles, skipping dead ones. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-triangle *triangletraverse(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-triangle *triangletraverse(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- triangle *newtriangle; +- +- do { +- newtriangle = (triangle *) traverse(&m->triangles); +- if (newtriangle == (triangle *) NULL) { +- return (triangle *) NULL; +- } +- } while (deadtri(newtriangle)); /* Skip dead ones. */ +- return newtriangle; +-} +- +-/*****************************************************************************/ +-/* */ +-/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void subsegdealloc(struct mesh *m, subseg *dyingsubseg) +-#else /* not ANSI_DECLARATORS */ +-void subsegdealloc(m, dyingsubseg) +-struct mesh *m; +-subseg *dyingsubseg; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Mark the subsegment as dead. This makes it possible to detect dead */ +- /* subsegments when traversing the list of all subsegments. */ +- killsubseg(dyingsubseg); +- pooldealloc(&m->subsegs, (void *) dyingsubseg); +-} +- +-/*****************************************************************************/ +-/* */ +-/* subsegtraverse() Traverse the subsegments, skipping dead ones. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-subseg *subsegtraverse(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-subseg *subsegtraverse(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- subseg *newsubseg; +- +- do { +- newsubseg = (subseg *) traverse(&m->subsegs); +- if (newsubseg == (subseg *) NULL) { +- return (subseg *) NULL; +- } +- } while (deadsubseg(newsubseg)); /* Skip dead ones. */ +- return newsubseg; +-} +- +-/*****************************************************************************/ +-/* */ +-/* vertexdealloc() Deallocate space for a vertex, marking it dead. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void vertexdealloc(struct mesh *m, vertex dyingvertex) +-#else /* not ANSI_DECLARATORS */ +-void vertexdealloc(m, dyingvertex) +-struct mesh *m; +-vertex dyingvertex; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Mark the vertex as dead. This makes it possible to detect dead */ +- /* vertices when traversing the list of all vertices. */ +- setvertextype(dyingvertex, DEADVERTEX); +- pooldealloc(&m->vertices, (void *) dyingvertex); +-} +- +-/*****************************************************************************/ +-/* */ +-/* vertextraverse() Traverse the vertices, skipping dead ones. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-vertex vertextraverse(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-vertex vertextraverse(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex newvertex; +- +- do { +- newvertex = (vertex) traverse(&m->vertices); +- if (newvertex == (vertex) NULL) { +- return (vertex) NULL; +- } +- } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */ +- return newvertex; +-} +- +-/*****************************************************************************/ +-/* */ +-/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */ +-/* dead. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg) +-#else /* not ANSI_DECLARATORS */ +-void badsubsegdealloc(m, dyingseg) +-struct mesh *m; +-struct badsubseg *dyingseg; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- /* Set subsegment's origin to NULL. This makes it possible to detect dead */ +- /* badsubsegs when traversing the list of all badsubsegs . */ +- dyingseg->subsegorg = (vertex) NULL; +- pooldealloc(&m->badsubsegs, (void *) dyingseg); +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-struct badsubseg *badsubsegtraverse(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-struct badsubseg *badsubsegtraverse(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct badsubseg *newseg; +- +- do { +- newseg = (struct badsubseg *) traverse(&m->badsubsegs); +- if (newseg == (struct badsubseg *) NULL) { +- return (struct badsubseg *) NULL; +- } +- } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */ +- return newseg; +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* getvertex() Get a specific vertex, by number, from the list. */ +-/* */ +-/* The first vertex is number 'firstnumber'. */ +-/* */ +-/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */ +-/* is large). I don't care to take the trouble to make it work in constant */ +-/* time. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-vertex getvertex(struct mesh *m, struct behavior *b, int number) +-#else /* not ANSI_DECLARATORS */ +-vertex getvertex(m, b, number) +-struct mesh *m; +-struct behavior *b; +-int number; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- void **getblock; +- char *foundvertex; +- TRIANGLE_PTRINT alignptr; +- int current; +- +- getblock = m->vertices.firstblock; +- current = b->firstnumber; +- +- /* Find the right block. */ +- if (current + m->vertices.itemsfirstblock <= number) { +- getblock = (void **) *getblock; +- current += m->vertices.itemsfirstblock; +- while (current + m->vertices.itemsperblock <= number) { +- getblock = (void **) *getblock; +- current += m->vertices.itemsperblock; +- } +- } +- +- /* Now find the right vertex. */ +- alignptr = (TRIANGLE_PTRINT) (getblock + 1); +- foundvertex = (char *) (alignptr + (TRIANGLE_PTRINT) m->vertices.alignbytes - +- (alignptr % (TRIANGLE_PTRINT) m->vertices.alignbytes)); +- return (vertex) (foundvertex + m->vertices.itembytes * (number - current)); +-} +- +-/*****************************************************************************/ +-/* */ +-/* triangledeinit() Free all remaining allocated memory. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void triangledeinit(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void triangledeinit(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- pooldeinit(&m->triangles); +- trifree((void *) m->dummytribase); +- if (b->usesegments) { +- pooldeinit(&m->subsegs); +- trifree((void *) m->dummysubbase); +- } +- pooldeinit(&m->vertices); +-#ifndef CDT_ONLY +- if (b->quality) { +- pooldeinit(&m->badsubsegs); +- if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { +- pooldeinit(&m->badtriangles); +- pooldeinit(&m->flipstackers); +- } +- } +-#endif /* not CDT_ONLY */ +-} +- +-/** **/ +-/** **/ +-/********* Memory management routines end here *********/ +- +-/********* Constructors begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* maketriangle() Create a new triangle with orientation zero. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri) +-#else /* not ANSI_DECLARATORS */ +-void maketriangle(m, b, newotri) +-struct mesh *m; +-struct behavior *b; +-struct otri *newotri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int i; +- +- newotri->tri = (triangle *) poolalloc(&m->triangles); +- /* Initialize the three adjoining triangles to be "outer space". */ +- newotri->tri[0] = (triangle) m->dummytri; +- newotri->tri[1] = (triangle) m->dummytri; +- newotri->tri[2] = (triangle) m->dummytri; +- /* Three NULL vertices. */ +- newotri->tri[3] = (triangle) NULL; +- newotri->tri[4] = (triangle) NULL; +- newotri->tri[5] = (triangle) NULL; +- if (b->usesegments) { +- /* Initialize the three adjoining subsegments to be the omnipresent */ +- /* subsegment. */ +- newotri->tri[6] = (triangle) m->dummysub; +- newotri->tri[7] = (triangle) m->dummysub; +- newotri->tri[8] = (triangle) m->dummysub; +- } +- for (i = 0; i < m->eextras; i++) { +- setelemattribute(*newotri, i, 0.0); +- } +- if (b->vararea) { +- setareabound(*newotri, -1.0); +- } +- +- newotri->orient = 0; +-} +- +-/*****************************************************************************/ +-/* */ +-/* makesubseg() Create a new subsegment with orientation zero. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void makesubseg(struct mesh *m, struct osub *newsubseg) +-#else /* not ANSI_DECLARATORS */ +-void makesubseg(m, newsubseg) +-struct mesh *m; +-struct osub *newsubseg; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- newsubseg->ss = (subseg *) poolalloc(&m->subsegs); +- /* Initialize the two adjoining subsegments to be the omnipresent */ +- /* subsegment. */ +- newsubseg->ss[0] = (subseg) m->dummysub; +- newsubseg->ss[1] = (subseg) m->dummysub; +- /* Four NULL vertices. */ +- newsubseg->ss[2] = (subseg) NULL; +- newsubseg->ss[3] = (subseg) NULL; +- newsubseg->ss[4] = (subseg) NULL; +- newsubseg->ss[5] = (subseg) NULL; +- /* Initialize the two adjoining triangles to be "outer space." */ +- newsubseg->ss[6] = (subseg) m->dummytri; +- newsubseg->ss[7] = (subseg) m->dummytri; +- /* Set the boundary marker to zero. */ +- setmark(*newsubseg, 0); +- +- newsubseg->ssorient = 0; +-} +- +-/** **/ +-/** **/ +-/********* Constructors end here *********/ +- +-/********* Geometric primitives begin here *********/ +-/** **/ +-/** **/ +- +-/* The adaptive exact arithmetic geometric predicates implemented herein are */ +-/* described in detail in my paper, "Adaptive Precision Floating-Point */ +-/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */ +-/* full citation. */ +- +-/* Which of the following two methods of finding the absolute values is */ +-/* fastest is compiler-dependent. A few compilers can inline and optimize */ +-/* the fabs() call; but most will incur the overhead of a function call, */ +-/* which is disastrously slow. A faster way on IEEE machines might be to */ +-/* mask the appropriate bit, but that's difficult to do in C without */ +-/* forcing the value to be stored to memory (rather than be kept in the */ +-/* register to which the optimizer assigned it). */ +- +-#define Absolute(a) ((a) >= 0.0 ? (a) : -(a)) +-/* #define Absolute(a) fabs(a) */ +- +-/* Many of the operations are broken up into two pieces, a main part that */ +-/* performs an approximate operation, and a "tail" that computes the */ +-/* roundoff error of that operation. */ +-/* */ +-/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */ +-/* Split(), and Two_Product() are all implemented as described in the */ +-/* reference. Each of these macros requires certain variables to be */ +-/* defined in the calling routine. The variables `bvirt', `c', `abig', */ +-/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */ +-/* they store the result of an operation that may incur roundoff error. */ +-/* The input parameter `x' (or the highest numbered `x_' parameter) must */ +-/* also be declared `INEXACT'. */ +- +-#define Fast_Two_Sum_Tail(a, b, x, y) \ +- bvirt = x - a; \ +- y = b - bvirt +- +-#define Fast_Two_Sum(a, b, x, y) \ +- x = (REAL) (a + b); \ +- Fast_Two_Sum_Tail(a, b, x, y) +- +-#define Two_Sum_Tail(a, b, x, y) \ +- bvirt = (REAL) (x - a); \ +- avirt = x - bvirt; \ +- bround = b - bvirt; \ +- around = a - avirt; \ +- y = around + bround +- +-#define Two_Sum(a, b, x, y) \ +- x = (REAL) (a + b); \ +- Two_Sum_Tail(a, b, x, y) +- +-#define Two_Diff_Tail(a, b, x, y) \ +- bvirt = (REAL) (a - x); \ +- avirt = x + bvirt; \ +- bround = bvirt - b; \ +- around = a - avirt; \ +- y = around + bround +- +-#define Two_Diff(a, b, x, y) \ +- x = (REAL) (a - b); \ +- Two_Diff_Tail(a, b, x, y) +- +-#define Split(a, ahi, alo) \ +- c = (REAL) (splitter * a); \ +- abig = (REAL) (c - a); \ +- ahi = c - abig; \ +- alo = a - ahi +- +-#define Two_Product_Tail(a, b, x, y) \ +- Split(a, ahi, alo); \ +- Split(b, bhi, blo); \ +- err1 = x - (ahi * bhi); \ +- err2 = err1 - (alo * bhi); \ +- err3 = err2 - (ahi * blo); \ +- y = (alo * blo) - err3 +- +-#define Two_Product(a, b, x, y) \ +- x = (REAL) (a * b); \ +- Two_Product_Tail(a, b, x, y) +- +-/* Two_Product_Presplit() is Two_Product() where one of the inputs has */ +-/* already been split. Avoids redundant splitting. */ +- +-#define Two_Product_Presplit(a, b, bhi, blo, x, y) \ +- x = (REAL) (a * b); \ +- Split(a, ahi, alo); \ +- err1 = x - (ahi * bhi); \ +- err2 = err1 - (alo * bhi); \ +- err3 = err2 - (ahi * blo); \ +- y = (alo * blo) - err3 +- +-/* Square() can be done more quickly than Two_Product(). */ +- +-#define Square_Tail(a, x, y) \ +- Split(a, ahi, alo); \ +- err1 = x - (ahi * ahi); \ +- err3 = err1 - ((ahi + ahi) * alo); \ +- y = (alo * alo) - err3 +- +-#define Square(a, x, y) \ +- x = (REAL) (a * a); \ +- Square_Tail(a, x, y) +- +-/* Macros for summing expansions of various fixed lengths. These are all */ +-/* unrolled versions of Expansion_Sum(). */ +- +-#define Two_One_Sum(a1, a0, b, x2, x1, x0) \ +- Two_Sum(a0, b , _i, x0); \ +- Two_Sum(a1, _i, x2, x1) +- +-#define Two_One_Diff(a1, a0, b, x2, x1, x0) \ +- Two_Diff(a0, b , _i, x0); \ +- Two_Sum( a1, _i, x2, x1) +- +-#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ +- Two_One_Sum(a1, a0, b0, _j, _0, x0); \ +- Two_One_Sum(_j, _0, b1, x3, x2, x1) +- +-#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ +- Two_One_Diff(a1, a0, b0, _j, _0, x0); \ +- Two_One_Diff(_j, _0, b1, x3, x2, x1) +- +-/* Macro for multiplying a two-component expansion by a single component. */ +- +-#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \ +- Split(b, bhi, blo); \ +- Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \ +- Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ +- Two_Sum(_i, _0, _k, x1); \ +- Fast_Two_Sum(_j, _k, x3, x2) +- +-/*****************************************************************************/ +-/* */ +-/* exactinit() Initialize the variables used for exact arithmetic. */ +-/* */ +-/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */ +-/* floating-point arithmetic. `epsilon' bounds the relative roundoff */ +-/* error. It is used for floating-point error analysis. */ +-/* */ +-/* `splitter' is used to split floating-point numbers into two half- */ +-/* length significands for exact multiplication. */ +-/* */ +-/* I imagine that a highly optimizing compiler might be too smart for its */ +-/* own good, and somehow cause this routine to fail, if it pretends that */ +-/* floating-point arithmetic is too much like real arithmetic. */ +-/* */ +-/* Don't change this routine unless you fully understand it. */ +-/* */ +-/*****************************************************************************/ +- +-void exactinit() +-{ +- REAL half; +- REAL check, lastcheck; +- int every_other; +-#ifdef LINUX +- int cword; +-#endif /* LINUX */ +- +-#ifdef CPU86 +-#ifdef SINGLE +- _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */ +-#else /* not SINGLE */ +- _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */ +-#endif /* not SINGLE */ +-#endif /* CPU86 */ +-#ifdef LINUX +-#ifdef SINGLE +- /* cword = 4223; */ +- cword = 4210; /* set FPU control word for single precision */ +-#else /* not SINGLE */ +- /* cword = 4735; */ +- cword = 4722; /* set FPU control word for double precision */ +-#endif /* not SINGLE */ +- _FPU_SETCW(cword); +-#endif /* LINUX */ +- +- every_other = 1; +- half = 0.5; +- epsilon = 1.0; +- splitter = 1.0; +- check = 1.0; +- /* Repeatedly divide `epsilon' by two until it is too small to add to */ +- /* one without causing roundoff. (Also check if the sum is equal to */ +- /* the previous sum, for machines that round up instead of using exact */ +- /* rounding. Not that these routines will work on such machines.) */ +- do { +- lastcheck = check; +- epsilon *= half; +- if (every_other) { +- splitter *= 2.0; +- } +- every_other = !every_other; +- check = 1.0 + epsilon; +- } while ((check != 1.0) && (check != lastcheck)); +- splitter += 1.0; +- /* Error bounds for orientation and incircle tests. */ +- resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; +- ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; +- ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; +- ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; +- iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; +- iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; +- iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; +- o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon; +- o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon; +- o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon; +-} +- +-/*****************************************************************************/ +-/* */ +-/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */ +-/* components from the output expansion. */ +-/* */ +-/* Sets h = e + f. See my Robust Predicates paper for details. */ +-/* */ +-/* If round-to-even is used (as with IEEE 754), maintains the strongly */ +-/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */ +-/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */ +-/* properties. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-static int fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h) +-#else /* not ANSI_DECLARATORS */ +-int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */ +-int elen; +-REAL *e; +-int flen; +-REAL *f; +-REAL *h; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL Q; +- INEXACT REAL Qnew; +- INEXACT REAL hh; +- INEXACT REAL bvirt; +- REAL avirt, bround, around; +- int eindex, findex, hindex; +- REAL enow, fnow; +- +- enow = e[0]; +- fnow = f[0]; +- eindex = findex = 0; +- if ( (fnow > enow) == (fnow > -enow) ) { +- Q = enow; +- enow = e[++eindex]; +- } else { +- Q = fnow; +- fnow = f[++findex]; +- } +- hindex = 0; +- if ((eindex < elen) && (findex < flen)) { +- if ((fnow > enow) == (fnow > -enow)) { +- Fast_Two_Sum(enow, Q, Qnew, hh); +- enow = e[++eindex]; +- } else { +- Fast_Two_Sum(fnow, Q, Qnew, hh); +- fnow = f[++findex]; +- } +- Q = Qnew; +- if (hh != 0.0) { +- h[hindex++] = hh; +- } +- while ((eindex < elen) && (findex < flen)) { +- if ((fnow > enow) == (fnow > -enow)) { +- Two_Sum(Q, enow, Qnew, hh); +- enow = e[++eindex]; +- } else { +- Two_Sum(Q, fnow, Qnew, hh); +- fnow = f[++findex]; +- } +- Q = Qnew; +- if (hh != 0.0) { +- h[hindex++] = hh; +- } +- } +- } +- while (eindex < elen) { +- Two_Sum(Q, enow, Qnew, hh); +- enow = e[++eindex]; +- Q = Qnew; +- if (hh != 0.0) { +- h[hindex++] = hh; +- } +- } +- while (findex < flen) { +- Two_Sum(Q, fnow, Qnew, hh); +- fnow = f[++findex]; +- Q = Qnew; +- if (hh != 0.0) { +- h[hindex++] = hh; +- } +- } +- if ((Q != 0.0) || (hindex == 0)) { +- h[hindex++] = Q; +- } +- return hindex; +-} +- +-/*****************************************************************************/ +-/* */ +-/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */ +-/* eliminating zero components from the */ +-/* output expansion. */ +-/* */ +-/* Sets h = be. See my Robust Predicates paper for details. */ +-/* */ +-/* Maintains the nonoverlapping property. If round-to-even is used (as */ +-/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */ +-/* properties as well. (That is, if e has one of these properties, so */ +-/* will h.) */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h) +-#else /* not ANSI_DECLARATORS */ +-int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */ +-int elen; +-REAL *e; +-REAL b; +-REAL *h; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- INEXACT REAL Q, sum; +- REAL hh; +- INEXACT REAL product1; +- REAL product0; +- int eindex, hindex; +- REAL enow; +- INEXACT REAL bvirt; +- REAL avirt, bround, around; +- INEXACT REAL c; +- INEXACT REAL abig; +- REAL ahi, alo, bhi, blo; +- REAL err1, err2, err3; +- +- Split(b, bhi, blo); +- Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); +- hindex = 0; +- if (hh != 0) { +- h[hindex++] = hh; +- } +- for (eindex = 1; eindex < elen; eindex++) { +- enow = e[eindex]; +- Two_Product_Presplit(enow, b, bhi, blo, product1, product0); +- Two_Sum(Q, product0, sum, hh); +- if (hh != 0) { +- h[hindex++] = hh; +- } +- Fast_Two_Sum(product1, sum, Q, hh); +- if (hh != 0) { +- h[hindex++] = hh; +- } +- } +- if ((Q != 0.0) || (hindex == 0)) { +- h[hindex++] = Q; +- } +- return hindex; +-} +- +-/*****************************************************************************/ +-/* */ +-/* estimate() Produce a one-word estimate of an expansion's value. */ +-/* */ +-/* See my Robust Predicates paper for details. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-REAL estimate(int elen, REAL *e) +-#else /* not ANSI_DECLARATORS */ +-REAL estimate(elen, e) +-int elen; +-REAL *e; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL Q; +- int eindex; +- +- Q = e[0]; +- for (eindex = 1; eindex < elen; eindex++) { +- Q += e[eindex]; +- } +- return Q; +-} +- +-/*****************************************************************************/ +-/* */ +-/* counterclockwise() Return a positive value if the points pa, pb, and */ +-/* pc occur in counterclockwise order; a negative */ +-/* value if they occur in clockwise order; and zero */ +-/* if they are collinear. The result is also a rough */ +-/* approximation of twice the signed area of the */ +-/* triangle defined by the three points. */ +-/* */ +-/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +-/* result returned is the determinant of a matrix. This determinant is */ +-/* computed adaptively, in the sense that exact arithmetic is used only to */ +-/* the degree it is needed to ensure that the returned value has the */ +-/* correct sign. Hence, this function is usually quite fast, but will run */ +-/* more slowly when the input points are collinear or nearly so. */ +-/* */ +-/* See my Robust Predicates paper for details. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-REAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum) +-#else /* not ANSI_DECLARATORS */ +-REAL counterclockwiseadapt(pa, pb, pc, detsum) +-vertex pa; +-vertex pb; +-vertex pc; +-REAL detsum; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- INEXACT REAL acx, acy, bcx, bcy; +- REAL acxtail, acytail, bcxtail, bcytail; +- INEXACT REAL detleft, detright; +- REAL detlefttail, detrighttail; +- REAL det, errbound; +- REAL B[4] = {0.}, C1[8] = {0.}, C2[12] = {0.}, D[16] = {0.}; +- INEXACT REAL B3; +- int C1length, C2length, Dlength; +- REAL u[4] = {0.}; +- INEXACT REAL u3; +- INEXACT REAL s1, t1; +- REAL s0, t0; +- +- INEXACT REAL bvirt; +- REAL avirt, bround, around; +- INEXACT REAL c; +- INEXACT REAL abig; +- REAL ahi, alo, bhi, blo; +- REAL err1, err2, err3; +- INEXACT REAL _i, _j; +- REAL _0; +- +- acx = (REAL) (pa[0] - pc[0]); +- bcx = (REAL) (pb[0] - pc[0]); +- acy = (REAL) (pa[1] - pc[1]); +- bcy = (REAL) (pb[1] - pc[1]); +- +- Two_Product(acx, bcy, detleft, detlefttail); +- Two_Product(acy, bcx, detright, detrighttail); +- +- Two_Two_Diff(detleft, detlefttail, detright, detrighttail, +- B3, B[2], B[1], B[0]); +- B[3] = B3; +- +- det = estimate(4, B); +- errbound = ccwerrboundB * detsum; +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- Two_Diff_Tail(pa[0], pc[0], acx, acxtail); +- Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); +- Two_Diff_Tail(pa[1], pc[1], acy, acytail); +- Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); +- +- if ((acxtail == 0.0) && (acytail == 0.0) +- && (bcxtail == 0.0) && (bcytail == 0.0)) { +- return det; +- } +- +- errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); +- det += (acx * bcytail + bcy * acxtail) +- - (acy * bcxtail + bcx * acytail); +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- Two_Product(acxtail, bcy, s1, s0); +- Two_Product(acytail, bcx, t1, t0); +- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); +- +- Two_Product(acx, bcytail, s1, s0); +- Two_Product(acy, bcxtail, t1, t0); +- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); +- +- Two_Product(acxtail, bcytail, s1, s0); +- Two_Product(acytail, bcxtail, t1, t0); +- Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); +- +- return(D[Dlength - 1]); +-} +- +-#ifdef ANSI_DECLARATORS +-REAL counterclockwise(struct mesh *m, struct behavior *b, +- vertex pa, vertex pb, vertex pc) +-#else /* not ANSI_DECLARATORS */ +-REAL counterclockwise(m, b, pa, pb, pc) +-struct mesh *m; +-struct behavior *b; +-vertex pa; +-vertex pb; +-vertex pc; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL detleft, detright, det; +- REAL detsum, errbound; +- +- m->counterclockcount++; +- +- detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); +- detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); +- det = detleft - detright; +- +- if (b->noexact) { +- return det; +- } +- +- if (detleft > 0.0) { +- if (detright <= 0.0) { +- return det; +- } else { +- detsum = detleft + detright; +- } +- } else if (detleft < 0.0) { +- if (detright >= 0.0) { +- return det; +- } else { +- detsum = -detleft - detright; +- } +- } else { +- return det; +- } +- +- errbound = ccwerrboundA * detsum; +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- return counterclockwiseadapt(pa, pb, pc, detsum); +-} +- +-/*****************************************************************************/ +-/* */ +-/* incircle() Return a positive value if the point pd lies inside the */ +-/* circle passing through pa, pb, and pc; a negative value if */ +-/* it lies outside; and zero if the four points are cocircular.*/ +-/* The points pa, pb, and pc must be in counterclockwise */ +-/* order, or the sign of the result will be reversed. */ +-/* */ +-/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +-/* result returned is the determinant of a matrix. This determinant is */ +-/* computed adaptively, in the sense that exact arithmetic is used only to */ +-/* the degree it is needed to ensure that the returned value has the */ +-/* correct sign. Hence, this function is usually quite fast, but will run */ +-/* more slowly when the input points are cocircular or nearly so. */ +-/* */ +-/* See my Robust Predicates paper for details. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-REAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent) +-#else /* not ANSI_DECLARATORS */ +-REAL incircleadapt(pa, pb, pc, pd, permanent) +-vertex pa; +-vertex pb; +-vertex pc; +-vertex pd; +-REAL permanent; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy; +- REAL det, errbound; +- +- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; +- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; +- REAL bc[4], ca[4], ab[4]; +- INEXACT REAL bc3, ca3, ab3; +- REAL axbc[8], axxbc[16] ={0.}, aybc[8], ayybc[16] = {0.}, adet[32] = {0.}; +- int axbclen, axxbclen, aybclen, ayybclen, alen; +- REAL bxca[8], bxxca[16] = {0.}, byca[8], byyca[16] = {0.}, bdet[32] = {0.}; +- int bxcalen, bxxcalen, bycalen, byycalen, blen; +- REAL cxab[8], cxxab[16] = {0.}, cyab[8], cyyab[16] = {0.}, cdet[32] = {0.}; +- int cxablen, cxxablen, cyablen, cyyablen, clen; +- REAL abdet[64] = {0,}; +- int ablen; +- REAL fin1[1152] = {0.}, fin2[1152] = {0.}; +- REAL *finnow, *finother, *finswap; +- int finlength; +- +- REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; +- INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; +- REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; +- REAL aa[4], bb[4], cc[4]; +- INEXACT REAL aa3, bb3, cc3; +- INEXACT REAL ti1, tj1; +- REAL ti0, tj0; +- REAL u[4] = {0.}, v[4] = {0.}; +- INEXACT REAL u3, v3; +- REAL temp8[8], temp16a[16] = {0.}, temp16b[16] = {0.}, temp16c[16] = {0.}; +- REAL temp32a[32] = {0.}, temp32b[32] = {0.}, temp48[48] = {0.}, temp64[64] = {0.}; +- int temp8len, temp16alen, temp16blen, temp16clen; +- int temp32alen, temp32blen, temp48len, temp64len; +- REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; +- int axtbblen, axtcclen, aytbblen, aytcclen; +- REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; +- int bxtaalen, bxtcclen, bytaalen, bytcclen; +- REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; +- int cxtaalen, cxtbblen, cytaalen, cytbblen; +- REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; +- int axtbclen = 8, aytbclen = 8, bxtcalen = 8, bytcalen = 8, cxtablen = 8, cytablen = 8; +- REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; +- int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; +- REAL axtbctt[8], aytbctt[8], bxtcatt[8]; +- REAL bytcatt[8], cxtabtt[8], cytabtt[8]; +- int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; +- REAL abt[8], bct[8], cat[8]; +- int abtlen, bctlen, catlen; +- REAL abtt[4], bctt[4], catt[4]; +- int abttlen, bcttlen, cattlen; +- INEXACT REAL abtt3, bctt3, catt3; +- REAL negate; +- +- INEXACT REAL bvirt; +- REAL avirt, bround, around; +- INEXACT REAL c; +- INEXACT REAL abig; +- REAL ahi, alo, bhi, blo; +- REAL err1, err2, err3; +- INEXACT REAL _i, _j; +- REAL _0; +- +- adx = (REAL) (pa[0] - pd[0]); +- bdx = (REAL) (pb[0] - pd[0]); +- cdx = (REAL) (pc[0] - pd[0]); +- ady = (REAL) (pa[1] - pd[1]); +- bdy = (REAL) (pb[1] - pd[1]); +- cdy = (REAL) (pc[1] - pd[1]); +- +- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); +- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); +- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); +- bc[3] = bc3; +- axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); +- axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); +- aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); +- ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); +- alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); +- +- Two_Product(cdx, ady, cdxady1, cdxady0); +- Two_Product(adx, cdy, adxcdy1, adxcdy0); +- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); +- ca[3] = ca3; +- bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); +- bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); +- bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); +- byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); +- blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); +- +- Two_Product(adx, bdy, adxbdy1, adxbdy0); +- Two_Product(bdx, ady, bdxady1, bdxady0); +- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); +- ab[3] = ab3; +- cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); +- cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); +- cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); +- cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); +- clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); +- +- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); +- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); +- +- det = estimate(finlength, fin1); +- errbound = iccerrboundB * permanent; +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- Two_Diff_Tail(pa[0], pd[0], adx, adxtail); +- Two_Diff_Tail(pa[1], pd[1], ady, adytail); +- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); +- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); +- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); +- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); +- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) +- && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) { +- return det; +- } +- +- errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); +- det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) +- - (bdy * cdxtail + cdx * bdytail)) +- + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) +- + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) +- - (cdy * adxtail + adx * cdytail)) +- + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) +- + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) +- - (ady * bdxtail + bdx * adytail)) +- + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- finnow = fin1; +- finother = fin2; +- +- if ((bdxtail != 0.0) || (bdytail != 0.0) +- || (cdxtail != 0.0) || (cdytail != 0.0)) { +- Square(adx, adxadx1, adxadx0); +- Square(ady, adyady1, adyady0); +- Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); +- aa[3] = aa3; +- } +- if ((cdxtail != 0.0) || (cdytail != 0.0) +- || (adxtail != 0.0) || (adytail != 0.0)) { +- Square(bdx, bdxbdx1, bdxbdx0); +- Square(bdy, bdybdy1, bdybdy0); +- Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); +- bb[3] = bb3; +- } +- if ((adxtail != 0.0) || (adytail != 0.0) +- || (bdxtail != 0.0) || (bdytail != 0.0)) { +- Square(cdx, cdxcdx1, cdxcdx0); +- Square(cdy, cdycdy1, cdycdy0); +- Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); +- cc[3] = cc3; +- } +- +- if (adxtail != 0.0) { +- axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); +- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, +- temp16a); +- +- axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); +- temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); +- +- axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); +- temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (adytail != 0.0) { +- aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); +- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, +- temp16a); +- +- aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); +- temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); +- +- aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); +- temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdxtail != 0.0) { +- bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); +- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, +- temp16a); +- +- bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); +- temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); +- +- bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); +- temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdytail != 0.0) { +- bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); +- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, +- temp16a); +- +- bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); +- temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); +- +- bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); +- temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdxtail != 0.0) { +- cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); +- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, +- temp16a); +- +- cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); +- temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); +- +- cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); +- temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdytail != 0.0) { +- cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); +- temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, +- temp16a); +- +- cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); +- temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); +- +- cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); +- temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); +- +- temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- +- if ((adxtail != 0.0) || (adytail != 0.0)) { +- if ((bdxtail != 0.0) || (bdytail != 0.0) +- || (cdxtail != 0.0) || (cdytail != 0.0)) { +- Two_Product(bdxtail, cdy, ti1, ti0); +- Two_Product(bdx, cdytail, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- negate = -bdy; +- Two_Product(cdxtail, negate, ti1, ti0); +- negate = -bdytail; +- Two_Product(cdx, negate, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); +- v[3] = v3; +- bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); +- +- Two_Product(bdxtail, cdytail, ti1, ti0); +- Two_Product(cdxtail, bdytail, tj1, tj0); +- Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); +- bctt[3] = bctt3; +- bcttlen = 4; +- } else { +- bct[0] = 0.0; +- bctlen = 1; +- bctt[0] = 0.0; +- bcttlen = 1; +- } +- +- if (adxtail != 0.0) { +- temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); +- axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); +- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (bdytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- +- temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, +- temp32a); +- axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); +- temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, +- temp16a); +- temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (adytail != 0.0) { +- temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); +- aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); +- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- +- temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, +- temp32a); +- aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); +- temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, +- temp16a); +- temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- if ((bdxtail != 0.0) || (bdytail != 0.0)) { +- if ((cdxtail != 0.0) || (cdytail != 0.0) +- || (adxtail != 0.0) || (adytail != 0.0)) { +- Two_Product(cdxtail, ady, ti1, ti0); +- Two_Product(cdx, adytail, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- negate = -cdy; +- Two_Product(adxtail, negate, ti1, ti0); +- negate = -cdytail; +- Two_Product(adx, negate, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); +- v[3] = v3; +- catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); +- +- Two_Product(cdxtail, adytail, ti1, ti0); +- Two_Product(adxtail, cdytail, tj1, tj0); +- Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); +- catt[3] = catt3; +- cattlen = 4; +- } else { +- cat[0] = 0.0; +- catlen = 1; +- catt[0] = 0.0; +- cattlen = 1; +- } +- +- if (bdxtail != 0.0) { +- temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); +- bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); +- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (cdytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (adytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- +- temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, +- temp32a); +- bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); +- temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, +- temp16a); +- temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdytail != 0.0) { +- temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); +- bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); +- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- +- temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, +- temp32a); +- bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); +- temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, +- temp16a); +- temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- if ((cdxtail != 0.0) || (cdytail != 0.0)) { +- if ((adxtail != 0.0) || (adytail != 0.0) +- || (bdxtail != 0.0) || (bdytail != 0.0)) { +- Two_Product(adxtail, bdy, ti1, ti0); +- Two_Product(adx, bdytail, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); +- u[3] = u3; +- negate = -ady; +- Two_Product(bdxtail, negate, ti1, ti0); +- negate = -adytail; +- Two_Product(bdx, negate, tj1, tj0); +- Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); +- v[3] = v3; +- abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); +- +- Two_Product(adxtail, bdytail, ti1, ti0); +- Two_Product(bdxtail, adytail, tj1, tj0); +- Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); +- abtt[3] = abtt3; +- abttlen = 4; +- } else { +- abt[0] = 0.0; +- abtlen = 1; +- abtt[0] = 0.0; +- abttlen = 1; +- } +- +- if (cdxtail != 0.0) { +- temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); +- cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); +- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (adytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdytail != 0.0) { +- temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); +- temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, +- temp16a); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, +- temp16a, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- +- temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, +- temp32a); +- cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); +- temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, +- temp16a); +- temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdytail != 0.0) { +- temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); +- cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); +- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, +- temp32a); +- temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp32alen, temp32a, temp48); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, +- temp48, finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- +- temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, +- temp32a); +- cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); +- temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, +- temp16a); +- temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, +- temp16b); +- temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, +- temp16blen, temp16b, temp32b); +- temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, +- temp32blen, temp32b, temp64); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, +- temp64, finother); +- finnow = finother; +- } +- } +- +- return finnow[finlength - 1]; +-} +- +-#ifdef ANSI_DECLARATORS +-REAL incircle(struct mesh *m, struct behavior *b, +- vertex pa, vertex pb, vertex pc, vertex pd) +-#else /* not ANSI_DECLARATORS */ +-REAL incircle(m, b, pa, pb, pc, pd) +-struct mesh *m; +-struct behavior *b; +-vertex pa; +-vertex pb; +-vertex pc; +-vertex pd; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL adx, bdx, cdx, ady, bdy, cdy; +- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; +- REAL alift, blift, clift; +- REAL det; +- REAL permanent, errbound; +- +- m->incirclecount++; +- +- adx = pa[0] - pd[0]; +- bdx = pb[0] - pd[0]; +- cdx = pc[0] - pd[0]; +- ady = pa[1] - pd[1]; +- bdy = pb[1] - pd[1]; +- cdy = pc[1] - pd[1]; +- +- bdxcdy = bdx * cdy; +- cdxbdy = cdx * bdy; +- alift = adx * adx + ady * ady; +- +- cdxady = cdx * ady; +- adxcdy = adx * cdy; +- blift = bdx * bdx + bdy * bdy; +- +- adxbdy = adx * bdy; +- bdxady = bdx * ady; +- clift = cdx * cdx + cdy * cdy; +- +- det = alift * (bdxcdy - cdxbdy) +- + blift * (cdxady - adxcdy) +- + clift * (adxbdy - bdxady); +- +- if (b->noexact) { +- return det; +- } +- +- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift +- + (Absolute(cdxady) + Absolute(adxcdy)) * blift +- + (Absolute(adxbdy) + Absolute(bdxady)) * clift; +- errbound = iccerrboundA * permanent; +- if ((det > errbound) || (-det > errbound)) { +- return det; +- } +- +- return incircleadapt(pa, pb, pc, pd, permanent); +-} +- +-/*****************************************************************************/ +-/* */ +-/* orient3d() Return a positive value if the point pd lies below the */ +-/* plane passing through pa, pb, and pc; "below" is defined so */ +-/* that pa, pb, and pc appear in counterclockwise order when */ +-/* viewed from above the plane. Returns a negative value if */ +-/* pd lies above the plane. Returns zero if the points are */ +-/* coplanar. The result is also a rough approximation of six */ +-/* times the signed volume of the tetrahedron defined by the */ +-/* four points. */ +-/* */ +-/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +-/* result returned is the determinant of a matrix. This determinant is */ +-/* computed adaptively, in the sense that exact arithmetic is used only to */ +-/* the degree it is needed to ensure that the returned value has the */ +-/* correct sign. Hence, this function is usually quite fast, but will run */ +-/* more slowly when the input points are coplanar or nearly so. */ +-/* */ +-/* See my Robust Predicates paper for details. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-REAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd, +- REAL aheight, REAL bheight, REAL cheight, REAL dheight, +- REAL permanent) +-#else /* not ANSI_DECLARATORS */ +-REAL orient3dadapt(pa, pb, pc, pd, +- aheight, bheight, cheight, dheight, permanent) +-vertex pa; +-vertex pb; +-vertex pc; +-vertex pd; +-REAL aheight; +-REAL bheight; +-REAL cheight; +-REAL dheight; +-REAL permanent; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; +- REAL det, errbound; +- +- INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; +- REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; +- REAL bc[4], ca[4], ab[4]; +- INEXACT REAL bc3, ca3, ab3; +- REAL adet[8]={0.}, bdet[8]={0.}, cdet[8]={0.}; +- int alen, blen, clen; +- REAL abdet[16]={0.}; +- int ablen; +- REAL *finnow, *finother, *finswap; +- REAL fin1[192], fin2[192]; +- int finlength; +- +- REAL adxtail, bdxtail, cdxtail; +- REAL adytail, bdytail, cdytail; +- REAL adheighttail, bdheighttail, cdheighttail; +- INEXACT REAL at_blarge, at_clarge; +- INEXACT REAL bt_clarge, bt_alarge; +- INEXACT REAL ct_alarge, ct_blarge; +- REAL at_b[4]={0.}, at_c[4]={0.}, bt_c[4]={0.}, bt_a[4]={0.}, ct_a[4]={0.}, ct_b[4]={0.}; +- int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen; +- INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1; +- INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1; +- REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0; +- REAL adxt_cdy0, adxt_bdy0, bdxt_ady0; +- INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1; +- INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1; +- REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0; +- REAL adyt_cdx0, adyt_bdx0, bdyt_adx0; +- REAL bct[8], cat[8], abt[8]; +- int bctlen, catlen, abtlen; +- INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1; +- INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1; +- REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0; +- REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0; +- REAL u[4]={0.}, v[12]={0.}, w[16]={0.}; +- INEXACT REAL u3; +- int vlength, wlength; +- REAL negate; +- +- INEXACT REAL bvirt; +- REAL avirt, bround, around; +- INEXACT REAL c; +- INEXACT REAL abig; +- REAL ahi, alo, bhi, blo; +- REAL err1, err2, err3; +- INEXACT REAL _i, _j, _k; +- REAL _0; +- +- adx = (REAL) (pa[0] - pd[0]); +- bdx = (REAL) (pb[0] - pd[0]); +- cdx = (REAL) (pc[0] - pd[0]); +- ady = (REAL) (pa[1] - pd[1]); +- bdy = (REAL) (pb[1] - pd[1]); +- cdy = (REAL) (pc[1] - pd[1]); +- adheight = (REAL) (aheight - dheight); +- bdheight = (REAL) (bheight - dheight); +- cdheight = (REAL) (cheight - dheight); +- +- Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); +- Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); +- Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); +- bc[3] = bc3; +- alen = scale_expansion_zeroelim(4, bc, adheight, adet); +- +- Two_Product(cdx, ady, cdxady1, cdxady0); +- Two_Product(adx, cdy, adxcdy1, adxcdy0); +- Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); +- ca[3] = ca3; +- blen = scale_expansion_zeroelim(4, ca, bdheight, bdet); +- +- Two_Product(adx, bdy, adxbdy1, adxbdy0); +- Two_Product(bdx, ady, bdxady1, bdxady0); +- Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); +- ab[3] = ab3; +- clen = scale_expansion_zeroelim(4, ab, cdheight, cdet); +- +- ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); +- finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); +- +- det = estimate(finlength, fin1); +- errbound = o3derrboundB * permanent; +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- Two_Diff_Tail(pa[0], pd[0], adx, adxtail); +- Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); +- Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); +- Two_Diff_Tail(pa[1], pd[1], ady, adytail); +- Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); +- Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); +- Two_Diff_Tail(aheight, dheight, adheight, adheighttail); +- Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail); +- Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail); +- +- if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && +- (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) && +- (adheighttail == 0.0) && +- (bdheighttail == 0.0) && +- (cdheighttail == 0.0)) { +- return det; +- } +- +- errbound = o3derrboundC * permanent + resulterrbound * Absolute(det); +- det += (adheight * ((bdx * cdytail + cdy * bdxtail) - +- (bdy * cdxtail + cdx * bdytail)) + +- adheighttail * (bdx * cdy - bdy * cdx)) + +- (bdheight * ((cdx * adytail + ady * cdxtail) - +- (cdy * adxtail + adx * cdytail)) + +- bdheighttail * (cdx * ady - cdy * adx)) + +- (cdheight * ((adx * bdytail + bdy * adxtail) - +- (ady * bdxtail + bdx * adytail)) + +- cdheighttail * (adx * bdy - ady * bdx)); +- if ((det >= errbound) || (-det >= errbound)) { +- return det; +- } +- +- finnow = fin1; +- finother = fin2; +- +- if (adxtail == 0.0) { +- if (adytail == 0.0) { +- at_b[0] = 0.0; +- at_blen = 1; +- at_c[0] = 0.0; +- at_clen = 1; +- } else { +- negate = -adytail; +- Two_Product(negate, bdx, at_blarge, at_b[0]); +- at_b[1] = at_blarge; +- at_blen = 2; +- Two_Product(adytail, cdx, at_clarge, at_c[0]); +- at_c[1] = at_clarge; +- at_clen = 2; +- } +- } else { +- if (adytail == 0.0) { +- Two_Product(adxtail, bdy, at_blarge, at_b[0]); +- at_b[1] = at_blarge; +- at_blen = 2; +- negate = -adxtail; +- Two_Product(negate, cdy, at_clarge, at_c[0]); +- at_c[1] = at_clarge; +- at_clen = 2; +- } else { +- Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0); +- Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0); +- Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, +- at_blarge, at_b[2], at_b[1], at_b[0]); +- at_b[3] = at_blarge; +- at_blen = 4; +- Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0); +- Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0); +- Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, +- at_clarge, at_c[2], at_c[1], at_c[0]); +- at_c[3] = at_clarge; +- at_clen = 4; +- } +- } +- if (bdxtail == 0.0) { +- if (bdytail == 0.0) { +- bt_c[0] = 0.0; +- bt_clen = 1; +- bt_a[0] = 0.0; +- bt_alen = 1; +- } else { +- negate = -bdytail; +- Two_Product(negate, cdx, bt_clarge, bt_c[0]); +- bt_c[1] = bt_clarge; +- bt_clen = 2; +- Two_Product(bdytail, adx, bt_alarge, bt_a[0]); +- bt_a[1] = bt_alarge; +- bt_alen = 2; +- } +- } else { +- if (bdytail == 0.0) { +- Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]); +- bt_c[1] = bt_clarge; +- bt_clen = 2; +- negate = -bdxtail; +- Two_Product(negate, ady, bt_alarge, bt_a[0]); +- bt_a[1] = bt_alarge; +- bt_alen = 2; +- } else { +- Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0); +- Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0); +- Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, +- bt_clarge, bt_c[2], bt_c[1], bt_c[0]); +- bt_c[3] = bt_clarge; +- bt_clen = 4; +- Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0); +- Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0); +- Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, +- bt_alarge, bt_a[2], bt_a[1], bt_a[0]); +- bt_a[3] = bt_alarge; +- bt_alen = 4; +- } +- } +- if (cdxtail == 0.0) { +- if (cdytail == 0.0) { +- ct_a[0] = 0.0; +- ct_alen = 1; +- ct_b[0] = 0.0; +- ct_blen = 1; +- } else { +- negate = -cdytail; +- Two_Product(negate, adx, ct_alarge, ct_a[0]); +- ct_a[1] = ct_alarge; +- ct_alen = 2; +- Two_Product(cdytail, bdx, ct_blarge, ct_b[0]); +- ct_b[1] = ct_blarge; +- ct_blen = 2; +- } +- } else { +- if (cdytail == 0.0) { +- Two_Product(cdxtail, ady, ct_alarge, ct_a[0]); +- ct_a[1] = ct_alarge; +- ct_alen = 2; +- negate = -cdxtail; +- Two_Product(negate, bdy, ct_blarge, ct_b[0]); +- ct_b[1] = ct_blarge; +- ct_blen = 2; +- } else { +- Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0); +- Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0); +- Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, +- ct_alarge, ct_a[2], ct_a[1], ct_a[0]); +- ct_a[3] = ct_alarge; +- ct_alen = 4; +- Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0); +- Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0); +- Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, +- ct_blarge, ct_b[2], ct_b[1], ct_b[0]); +- ct_b[3] = ct_blarge; +- ct_blen = 4; +- } +- } +- +- bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct); +- wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat); +- wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt); +- wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- +- if (adheighttail != 0.0) { +- vlength = scale_expansion_zeroelim(4, bc, adheighttail, v); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdheighttail != 0.0) { +- vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdheighttail != 0.0) { +- vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- +- if (adxtail != 0.0) { +- if (bdytail != 0.0) { +- Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0); +- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (cdheighttail != 0.0) { +- Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- if (cdytail != 0.0) { +- negate = -adxtail; +- Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0); +- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (bdheighttail != 0.0) { +- Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- } +- if (bdxtail != 0.0) { +- if (cdytail != 0.0) { +- Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0); +- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (adheighttail != 0.0) { +- Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- if (adytail != 0.0) { +- negate = -bdxtail; +- Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0); +- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (cdheighttail != 0.0) { +- Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- } +- if (cdxtail != 0.0) { +- if (adytail != 0.0) { +- Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0); +- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (bdheighttail != 0.0) { +- Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- if (bdytail != 0.0) { +- negate = -cdxtail; +- Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0); +- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- if (adheighttail != 0.0) { +- Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail, +- u3, u[2], u[1], u[0]); +- u[3] = u3; +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- } +- } +- +- if (adheighttail != 0.0) { +- wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (bdheighttail != 0.0) { +- wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finswap = finnow; finnow = finother; finother = finswap; +- } +- if (cdheighttail != 0.0) { +- wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w); +- finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, +- finother); +- finnow = finother; +- } +- +- return finnow[finlength - 1]; +-} +- +-#ifdef ANSI_DECLARATORS +-REAL orient3d(struct mesh *m, struct behavior *b, +- vertex pa, vertex pb, vertex pc, vertex pd, +- REAL aheight, REAL bheight, REAL cheight, REAL dheight) +-#else /* not ANSI_DECLARATORS */ +-REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight) +-struct mesh *m; +-struct behavior *b; +-vertex pa; +-vertex pb; +-vertex pc; +-vertex pd; +-REAL aheight; +-REAL bheight; +-REAL cheight; +-REAL dheight; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; +- REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; +- REAL det; +- REAL permanent, errbound; +- +- m->orient3dcount++; +- +- adx = pa[0] - pd[0]; +- bdx = pb[0] - pd[0]; +- cdx = pc[0] - pd[0]; +- ady = pa[1] - pd[1]; +- bdy = pb[1] - pd[1]; +- cdy = pc[1] - pd[1]; +- adheight = aheight - dheight; +- bdheight = bheight - dheight; +- cdheight = cheight - dheight; +- +- bdxcdy = bdx * cdy; +- cdxbdy = cdx * bdy; +- +- cdxady = cdx * ady; +- adxcdy = adx * cdy; +- +- adxbdy = adx * bdy; +- bdxady = bdx * ady; +- +- det = adheight * (bdxcdy - cdxbdy) +- + bdheight * (cdxady - adxcdy) +- + cdheight * (adxbdy - bdxady); +- +- if (b->noexact) { +- return det; +- } +- +- permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight) +- + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight) +- + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight); +- errbound = o3derrboundA * permanent; +- if ((det > errbound) || (-det > errbound)) { +- return det; +- } +- +- return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, +- permanent); +-} +- +-/*****************************************************************************/ +-/* */ +-/* nonregular() Return a positive value if the point pd is incompatible */ +-/* with the circle or plane passing through pa, pb, and pc */ +-/* (meaning that pd is inside the circle or below the */ +-/* plane); a negative value if it is compatible; and zero if */ +-/* the four points are cocircular/coplanar. The points pa, */ +-/* pb, and pc must be in counterclockwise order, or the sign */ +-/* of the result will be reversed. */ +-/* */ +-/* If the -w switch is used, the points are lifted onto the parabolic */ +-/* lifting map, then they are dropped according to their weights, then the */ +-/* 3D orientation test is applied. If the -W switch is used, the points' */ +-/* heights are already provided, so the 3D orientation test is applied */ +-/* directly. If neither switch is used, the incircle test is applied. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-REAL nonregular(struct mesh *m, struct behavior *b, +- vertex pa, vertex pb, vertex pc, vertex pd) +-#else /* not ANSI_DECLARATORS */ +-REAL nonregular(m, b, pa, pb, pc, pd) +-struct mesh *m; +-struct behavior *b; +-vertex pa; +-vertex pb; +-vertex pc; +-vertex pd; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- if (b->weighted == 0) { +- return incircle(m, b, pa, pb, pc, pd); +- } else if (b->weighted == 1) { +- return orient3d(m, b, pa, pb, pc, pd, +- pa[0] * pa[0] + pa[1] * pa[1] - pa[2], +- pb[0] * pb[0] + pb[1] * pb[1] - pb[2], +- pc[0] * pc[0] + pc[1] * pc[1] - pc[2], +- pd[0] * pd[0] + pd[1] * pd[1] - pd[2]); +- } else { +- return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* findcircumcenter() Find the circumcenter of a triangle. */ +-/* */ +-/* The result is returned both in terms of x-y coordinates and xi-eta */ +-/* (barycentric) coordinates. The xi-eta coordinate system is defined in */ +-/* terms of the triangle: the origin of the triangle is the origin of the */ +-/* coordinate system; the destination of the triangle is one unit along the */ +-/* xi axis; and the apex of the triangle is one unit along the eta axis. */ +-/* This procedure also returns the square of the length of the triangle's */ +-/* shortest edge. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void findcircumcenter(struct mesh *m, struct behavior *b, +- vertex torg, vertex tdest, vertex tapex, +- vertex circumcenter, REAL *xi, REAL *eta, int offcenter) +-#else /* not ANSI_DECLARATORS */ +-void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta, +- offcenter) +-struct mesh *m; +-struct behavior *b; +-vertex torg; +-vertex tdest; +-vertex tapex; +-vertex circumcenter; +-REAL *xi; +-REAL *eta; +-int offcenter; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL xdo, ydo, xao, yao; +- REAL dodist, aodist, dadist; +- REAL denominator; +- REAL dx, dy, dxoff, dyoff; +- +- m->circumcentercount++; +- +- /* Compute the circumcenter of the triangle. */ +- xdo = tdest[0] - torg[0]; +- ydo = tdest[1] - torg[1]; +- xao = tapex[0] - torg[0]; +- yao = tapex[1] - torg[1]; +- dodist = xdo * xdo + ydo * ydo; +- aodist = xao * xao + yao * yao; +- dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) + +- (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]); +- if (b->noexact) { +- denominator = 0.5 / (xdo * yao - xao * ydo); +- } else { +- /* Use the counterclockwise() routine to ensure a positive (and */ +- /* reasonably accurate) result, avoiding any possibility of */ +- /* division by zero. */ +- denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg); +- /* Don't count the above as an orientation test. */ +- m->counterclockcount--; +- } +- dx = (yao * dodist - ydo * aodist) * denominator; +- dy = (xdo * aodist - xao * dodist) * denominator; +- +- /* Find the (squared) length of the triangle's shortest edge. This */ +- /* serves as a conservative estimate of the insertion radius of the */ +- /* circumcenter's parent. The estimate is used to ensure that */ +- /* the algorithm terminates even if very small angles appear in */ +- /* the input PSLG. */ +- if ((dodist < aodist) && (dodist < dadist)) { +- if (offcenter && (b->offconstant > 0.0)) { +- /* Find the position of the off-center, as described by Alper Ungor. */ +- dxoff = 0.5 * xdo - b->offconstant * ydo; +- dyoff = 0.5 * ydo + b->offconstant * xdo; +- /* If the off-center is closer to the origin than the */ +- /* circumcenter, use the off-center instead. */ +- if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { +- dx = dxoff; +- dy = dyoff; +- } +- } +- } else if (aodist < dadist) { +- if (offcenter && (b->offconstant > 0.0)) { +- dxoff = 0.5 * xao + b->offconstant * yao; +- dyoff = 0.5 * yao - b->offconstant * xao; +- /* If the off-center is closer to the origin than the */ +- /* circumcenter, use the off-center instead. */ +- if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { +- dx = dxoff; +- dy = dyoff; +- } +- } +- } else { +- if (offcenter && (b->offconstant > 0.0)) { +- dxoff = 0.5 * (tapex[0] - tdest[0]) - +- b->offconstant * (tapex[1] - tdest[1]); +- dyoff = 0.5 * (tapex[1] - tdest[1]) + +- b->offconstant * (tapex[0] - tdest[0]); +- /* If the off-center is closer to the destination than the */ +- /* circumcenter, use the off-center instead. */ +- if (dxoff * dxoff + dyoff * dyoff < +- (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) { +- dx = xdo + dxoff; +- dy = ydo + dyoff; +- } +- } +- } +- +- circumcenter[0] = torg[0] + dx; +- circumcenter[1] = torg[1] + dy; +- +- /* To interpolate vertex attributes for the new vertex inserted at */ +- /* the circumcenter, define a coordinate system with a xi-axis, */ +- /* directed from the triangle's origin to its destination, and */ +- /* an eta-axis, directed from its origin to its apex. */ +- /* Calculate the xi and eta coordinates of the circumcenter. */ +- *xi = (yao * dx - xao * dy) * (2.0 * denominator); +- *eta = (xdo * dy - ydo * dx) * (2.0 * denominator); +-} +- +-/** **/ +-/** **/ +-/********* Geometric primitives end here *********/ +- +-/*****************************************************************************/ +-/* */ +-/* triangleinit() Initialize some variables. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void triangleinit(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-void triangleinit(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- poolzero(&m->vertices); +- poolzero(&m->triangles); +- poolzero(&m->subsegs); +- poolzero(&m->viri); +- poolzero(&m->badsubsegs); +- poolzero(&m->badtriangles); +- poolzero(&m->flipstackers); +- poolzero(&m->splaynodes); +- +- m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ +- m->undeads = 0; /* No eliminated input vertices yet. */ +- m->samples = 1; /* Point location should take at least one sample. */ +- m->checksegments = 0; /* There are no segments in the triangulation yet. */ +- m->checkquality = 0; /* The quality triangulation stage has not begun. */ +- m->incirclecount = m->counterclockcount = m->orient3dcount = 0; +- m->hyperbolacount = m->circletopcount = m->circumcentercount = 0; +- randomseed = 1; +- +- exactinit(); /* Initialize exact arithmetic constants. */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* randomnation() Generate a random number between 0 and `choices' - 1. */ +-/* */ +-/* This is a simple linear congruential random number generator. Hence, it */ +-/* is a bad random number generator, but good enough for most randomized */ +-/* geometric algorithms. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-TRIANGLE_PTRINT randomnation(unsigned int choices) +-#else /* not ANSI_DECLARATORS */ +-TRIANGLE_PTRINT randomnation(choices) +-unsigned int choices; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- randomseed = (randomseed * 1366l + 150889l) % 714025l; +- return ( randomseed * (choices + 1 ) )/ 714025l; +-} +- +-/********* Mesh quality testing routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* checkmesh() Test the mesh for topological consistency. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void checkmesh(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void checkmesh(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop; +- struct otri oppotri, oppooppotri; +- vertex triorg, tridest, triapex; +- vertex oppoorg, oppodest; +- int horrors; +- int saveexact; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- /* Temporarily turn on exact arithmetic if it's off. */ +- saveexact = b->noexact; +- b->noexact = 0; +- if (!b->quiet) { +- printf(" Checking consistency of mesh...\n"); +- } +- horrors = 0; +- /* Run through the list of triangles, checking each one. */ +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- while (triangleloop.tri != (triangle *) NULL) { +- /* Check all three edges of the triangle. */ +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- org(triangleloop, triorg); +- dest(triangleloop, tridest); +- if (triangleloop.orient == 0) { /* Only test for inversion once. */ +- /* Test if the triangle is flat or inverted. */ +- apex(triangleloop, triapex); +- if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) { +- printf(" !! !! Inverted "); +- printtriangle(m, b, &triangleloop); +- horrors++; +- } +- } +- /* Find the neighboring triangle on this edge. */ +- sym(triangleloop, oppotri); +- if (oppotri.tri != m->dummytri) { +- /* Check that the triangle's neighbor knows it's a neighbor. */ +- sym(oppotri, oppooppotri); +- if ((triangleloop.tri != oppooppotri.tri) +- || (triangleloop.orient != oppooppotri.orient)) { +- printf(" !! !! Asymmetric triangle-triangle bond:\n"); +- if (triangleloop.tri == oppooppotri.tri) { +- printf(" (Right triangle, wrong orientation)\n"); +- } +- printf(" First "); +- printtriangle(m, b, &triangleloop); +- printf(" Second (nonreciprocating) "); +- printtriangle(m, b, &oppotri); +- horrors++; +- } +- /* Check that both triangles agree on the identities */ +- /* of their shared vertices. */ +- org(oppotri, oppoorg); +- dest(oppotri, oppodest); +- if ((triorg != oppodest) || (tridest != oppoorg)) { +- printf(" !! !! Mismatched edge coordinates between two triangles:\n" +- ); +- printf(" First mismatched "); +- printtriangle(m, b, &triangleloop); +- printf(" Second mismatched "); +- printtriangle(m, b, &oppotri); +- horrors++; +- } +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +- if (horrors == 0) { +- if (!b->quiet) { +- printf(" In my studied opinion, the mesh appears to be consistent.\n"); +- } +- } else if (horrors == 1) { +- printf(" !! !! !! !! Precisely one festering wound discovered.\n"); +- } else { +- printf(" !! !! !! !! %d abominations witnessed.\n", horrors); +- } +- /* Restore the status of exact arithmetic. */ +- b->noexact = saveexact; +-} +- +-#endif /* not REDUCED */ +- +-/*****************************************************************************/ +-/* */ +-/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void checkdelaunay(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void checkdelaunay(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop; +- struct otri oppotri; +- struct osub opposubseg; +- vertex triorg, tridest, triapex; +- vertex oppoapex; +- int shouldbedelaunay; +- int horrors; +- int saveexact; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- /* Temporarily turn on exact arithmetic if it's off. */ +- saveexact = b->noexact; +- b->noexact = 0; +- if (!b->quiet) { +- printf(" Checking Delaunay property of mesh...\n"); +- } +- horrors = 0; +- /* Run through the list of triangles, checking each one. */ +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- while (triangleloop.tri != (triangle *) NULL) { +- /* Check all three edges of the triangle. */ +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- org(triangleloop, triorg); +- dest(triangleloop, tridest); +- apex(triangleloop, triapex); +- sym(triangleloop, oppotri); +- apex(oppotri, oppoapex); +- /* Only test that the edge is locally Delaunay if there is an */ +- /* adjoining triangle whose pointer is larger (to ensure that */ +- /* each pair isn't tested twice). */ +- shouldbedelaunay = (oppotri.tri != m->dummytri) && +- !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) && +- (triorg != m->infvertex1) && (triorg != m->infvertex2) && +- (triorg != m->infvertex3) && +- (tridest != m->infvertex1) && (tridest != m->infvertex2) && +- (tridest != m->infvertex3) && +- (triapex != m->infvertex1) && (triapex != m->infvertex2) && +- (triapex != m->infvertex3) && +- (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) && +- (oppoapex != m->infvertex3); +- if (m->checksegments && shouldbedelaunay) { +- /* If a subsegment separates the triangles, then the edge is */ +- /* constrained, so no local Delaunay test should be done. */ +- tspivot(triangleloop, opposubseg); +- if (opposubseg.ss != m->dummysub){ +- shouldbedelaunay = 0; +- } +- } +- if (shouldbedelaunay) { +- if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) { +- if (!b->weighted) { +- printf(" !! !! Non-Delaunay pair of triangles:\n"); +- printf(" First non-Delaunay "); +- printtriangle(m, b, &triangleloop); +- printf(" Second non-Delaunay "); +- } else { +- printf(" !! !! Non-regular pair of triangles:\n"); +- printf(" First non-regular "); +- printtriangle(m, b, &triangleloop); +- printf(" Second non-regular "); +- } +- printtriangle(m, b, &oppotri); +- horrors++; +- } +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +- if (horrors == 0) { +- if (!b->quiet) { +- printf( +- " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); +- } +- } else if (horrors == 1) { +- printf( +- " !! !! !! !! Precisely one terrifying transgression identified.\n"); +- } else { +- printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); +- } +- /* Restore the status of exact arithmetic. */ +- b->noexact = saveexact; +-} +- +-#endif /* not REDUCED */ +- +-/*****************************************************************************/ +-/* */ +-/* enqueuebadtriang() Add a bad triangle data structure to the end of a */ +-/* queue. */ +-/* */ +-/* The queue is actually a set of 4096 queues. I use multiple queues to */ +-/* give priority to smaller angles. I originally implemented a heap, but */ +-/* the queues are faster by a larger margin than I'd suspected. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void enqueuebadtriang(struct mesh *m, struct behavior *b, +- struct badtriang *badtri) +-#else /* not ANSI_DECLARATORS */ +-void enqueuebadtriang(m, b, badtri) +-struct mesh *m; +-struct behavior *b; +-struct badtriang *badtri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL length, multiplier; +- int exponent, expincrement; +- int queuenumber; +- int posexponent; +- int i; +- +- if (b->verbose > 2) { +- printf(" Queueing bad triangle:\n"); +- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- badtri->triangorg[0], badtri->triangorg[1], +- badtri->triangdest[0], badtri->triangdest[1], +- badtri->triangapex[0], badtri->triangapex[1]); +- } +- +- /* Determine the appropriate queue to put the bad triangle into. */ +- /* Recall that the key is the square of its shortest edge length. */ +- if (badtri->key >= 1.0) { +- length = badtri->key; +- posexponent = 1; +- } else { +- /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */ +- /* fact and use the reciprocal of `badtri->key', which is > 1.0. */ +- length = 1.0 / badtri->key; +- posexponent = 0; +- } +- /* `length' is approximately 2.0 to what exponent? The following code */ +- /* determines the answer in time logarithmic in the exponent. */ +- exponent = 0; +- while (length > 2.0) { +- /* Find an approximation by repeated squaring of two. */ +- expincrement = 1; +- multiplier = 0.5; +- while (length * multiplier * multiplier > 1.0) { +- expincrement *= 2; +- multiplier *= multiplier; +- } +- /* Reduce the value of `length', then iterate if necessary. */ +- exponent += expincrement; +- length *= multiplier; +- } +- /* `length' is approximately squareroot(2.0) to what exponent? */ +- exponent = (int) ( 2.0 * exponent + (length > SQUAREROOTTWO) ); +- /* `exponent' is now in the range 0...2047 for IEEE double precision. */ +- /* Choose a queue in the range 0...4095. The shortest edges have the */ +- /* highest priority (queue 4095). */ +- if (posexponent) { +- queuenumber = 2047 - exponent; +- } else { +- queuenumber = 2048 + exponent; +- } +- +- /* Are we inserting into an empty queue? */ +- if (m->queuefront[queuenumber] == (struct badtriang *) NULL) { +- /* Yes, we are inserting into an empty queue. */ +- /* Will this become the highest-priority queue? */ +- if (queuenumber > m->firstnonemptyq) { +- /* Yes, this is the highest-priority queue. */ +- m->nextnonemptyq[queuenumber] = m->firstnonemptyq; +- m->firstnonemptyq = queuenumber; +- } else { +- /* No, this is not the highest-priority queue. */ +- /* Find the queue with next higher priority. */ +- i = queuenumber + 1; +- while (m->queuefront[i] == (struct badtriang *) NULL) { +- i++; +- } +- /* Mark the newly nonempty queue as following a higher-priority queue. */ +- m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i]; +- m->nextnonemptyq[i] = queuenumber; +- } +- /* Put the bad triangle at the beginning of the (empty) queue. */ +- m->queuefront[queuenumber] = badtri; +- } else { +- /* Add the bad triangle to the end of an already nonempty queue. */ +- m->queuetail[queuenumber]->nexttriang = badtri; +- } +- /* Maintain a pointer to the last triangle of the queue. */ +- m->queuetail[queuenumber] = badtri; +- /* Newly enqueued bad triangle has no successor in the queue. */ +- badtri->nexttriang = (struct badtriang *) NULL; +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* enqueuebadtri() Add a bad triangle to the end of a queue. */ +-/* */ +-/* Allocates a badtriang data structure for the triangle, then passes it to */ +-/* enqueuebadtriang(). */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri, +- REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest) +-#else /* not ANSI_DECLARATORS */ +-void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest) +-struct mesh *m; +-struct behavior *b; +-struct otri *enqtri; +-REAL minedge; +-vertex enqapex; +-vertex enqorg; +-vertex enqdest; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct badtriang *newbad; +- +- /* Allocate space for the bad triangle. */ +- newbad = (struct badtriang *) poolalloc(&m->badtriangles); +- newbad->poortri = encode(*enqtri); +- newbad->key = minedge; +- newbad->triangapex = enqapex; +- newbad->triangorg = enqorg; +- newbad->triangdest = enqdest; +- enqueuebadtriang(m, b, newbad); +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* dequeuebadtriang() Remove a triangle from the front of the queue. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-struct badtriang *dequeuebadtriang(struct mesh *m) +-#else /* not ANSI_DECLARATORS */ +-struct badtriang *dequeuebadtriang(m) +-struct mesh *m; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct badtriang *result; +- +- /* If no queues are nonempty, return NULL. */ +- if (m->firstnonemptyq < 0) { +- return (struct badtriang *) NULL; +- } +- /* Find the first triangle of the highest-priority queue. */ +- result = m->queuefront[m->firstnonemptyq]; +- /* Remove the triangle from the queue. */ +- m->queuefront[m->firstnonemptyq] = result->nexttriang; +- /* If this queue is now empty, note the new highest-priority */ +- /* nonempty queue. */ +- if (result == m->queuetail[m->firstnonemptyq]) { +- m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq]; +- } +- return result; +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* checkseg4encroach() Check a subsegment to see if it is encroached; add */ +-/* it to the list if it is. */ +-/* */ +-/* A subsegment is encroached if there is a vertex in its diametral lens. */ +-/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */ +-/* diametral circle. For Chew's algorithm (default), the diametral lens is */ +-/* just big enough to enclose two isosceles triangles whose bases are the */ +-/* subsegment. Each of the two isosceles triangles has two angles equal */ +-/* to `b->minangle'. */ +-/* */ +-/* Chew's algorithm does not require diametral lenses at all--but they save */ +-/* time. Any vertex inside a subsegment's diametral lens implies that the */ +-/* triangle adjoining the subsegment will be too skinny, so it's only a */ +-/* matter of time before the encroaching vertex is deleted by Chew's */ +-/* algorithm. It's faster to simply not insert the doomed vertex in the */ +-/* first place, which is why I use diametral lenses with Chew's algorithm. */ +-/* */ +-/* Returns a nonzero value if the subsegment is encroached. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-int checkseg4encroach(struct mesh *m, struct behavior *b, +- struct osub *testsubseg) +-#else /* not ANSI_DECLARATORS */ +-int checkseg4encroach(m, b, testsubseg) +-struct mesh *m; +-struct behavior *b; +-struct osub *testsubseg; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri neighbortri; +- struct osub testsym; +- struct badsubseg *encroachedseg; +- REAL dotproduct; +- int encroached; +- int sides; +- vertex eorg, edest, eapex; +- triangle ptr; /* Temporary variable used by stpivot(). */ +- +- encroached = 0; +- sides = 0; +- +- sorg(*testsubseg, eorg); +- sdest(*testsubseg, edest); +- /* Check one neighbor of the subsegment. */ +- stpivot(*testsubseg, neighbortri); +- /* Does the neighbor exist, or is this a boundary edge? */ +- if (neighbortri.tri != m->dummytri) { +- sides++; +- /* Find a vertex opposite this subsegment. */ +- apex(neighbortri, eapex); +- /* Check whether the apex is in the diametral lens of the subsegment */ +- /* (the diametral circle if `conformdel' is set). A dot product */ +- /* of two sides of the triangle is used to check whether the angle */ +- /* at the apex is greater than (180 - 2 `minangle') degrees (for */ +- /* lenses; 90 degrees for diametral circles). */ +- dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); +- if (dotproduct < 0.0) { +- if (b->conformdel || +- (dotproduct * dotproduct >= +- (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * +- ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * +- ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { +- encroached = 1; +- } +- } +- } +- /* Check the other neighbor of the subsegment. */ +- ssym(*testsubseg, testsym); +- stpivot(testsym, neighbortri); +- /* Does the neighbor exist, or is this a boundary edge? */ +- if (neighbortri.tri != m->dummytri) { +- sides++; +- /* Find the other vertex opposite this subsegment. */ +- apex(neighbortri, eapex); +- /* Check whether the apex is in the diametral lens of the subsegment */ +- /* (or the diametral circle, if `conformdel' is set). */ +- dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); +- if (dotproduct < 0.0) { +- if (b->conformdel || +- (dotproduct * dotproduct >= +- (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * +- ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * +- ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { +- encroached += 2; +- } +- } +- } +- +- if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) { +- if (b->verbose > 2) { +- printf( +- " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", +- eorg[0], eorg[1], edest[0], edest[1]); +- } +- /* Add the subsegment to the list of encroached subsegments. */ +- /* Be sure to get the orientation right. */ +- encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs); +- if (encroached == 1) { +- encroachedseg->encsubseg = sencode(*testsubseg); +- encroachedseg->subsegorg = eorg; +- encroachedseg->subsegdest = edest; +- } else { +- encroachedseg->encsubseg = sencode(testsym); +- encroachedseg->subsegorg = edest; +- encroachedseg->subsegdest = eorg; +- } +- } +- +- return encroached; +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* testtriangle() Test a triangle for quality and size. */ +-/* */ +-/* Tests a triangle to see if it satisfies the minimum angle condition and */ +-/* the maximum area condition. Triangles that aren't up to spec are added */ +-/* to the bad triangle queue. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri) +-#else /* not ANSI_DECLARATORS */ +-void testtriangle(m, b, testtri) +-struct mesh *m; +-struct behavior *b; +-struct otri *testtri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri tri1, tri2; +- struct osub testsub; +- vertex torg, tdest, tapex; +- vertex base1, base2; +- vertex org1, dest1, org2, dest2; +- vertex joinvertex; +- REAL dxod, dyod, dxda, dyda, dxao, dyao; +- REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; +- REAL apexlen, orglen, destlen, minedge; +- REAL angle; +- REAL area; +- REAL dist1, dist2; +- subseg sptr; /* Temporary variable used by tspivot(). */ +- triangle ptr; /* Temporary variable used by oprev() and dnext(). */ +- +- org(*testtri, torg); +- dest(*testtri, tdest); +- apex(*testtri, tapex); +- dxod = torg[0] - tdest[0]; +- dyod = torg[1] - tdest[1]; +- dxda = tdest[0] - tapex[0]; +- dyda = tdest[1] - tapex[1]; +- dxao = tapex[0] - torg[0]; +- dyao = tapex[1] - torg[1]; +- dxod2 = dxod * dxod; +- dyod2 = dyod * dyod; +- dxda2 = dxda * dxda; +- dyda2 = dyda * dyda; +- dxao2 = dxao * dxao; +- dyao2 = dyao * dyao; +- /* Find the lengths of the triangle's three edges. */ +- apexlen = dxod2 + dyod2; +- orglen = dxda2 + dyda2; +- destlen = dxao2 + dyao2; +- +- if ((apexlen < orglen) && (apexlen < destlen)) { +- /* The edge opposite the apex is shortest. */ +- minedge = apexlen; +- /* Find the square of the cosine of the angle at the apex. */ +- angle = dxda * dxao + dyda * dyao; +- angle = angle * angle / (orglen * destlen); +- base1 = torg; +- base2 = tdest; +- otricopy(*testtri, tri1); +- } else if (orglen < destlen) { +- /* The edge opposite the origin is shortest. */ +- minedge = orglen; +- /* Find the square of the cosine of the angle at the origin. */ +- angle = dxod * dxao + dyod * dyao; +- angle = angle * angle / (apexlen * destlen); +- base1 = tdest; +- base2 = tapex; +- lnext(*testtri, tri1); +- } else { +- /* The edge opposite the destination is shortest. */ +- minedge = destlen; +- /* Find the square of the cosine of the angle at the destination. */ +- angle = dxod * dxda + dyod * dyda; +- angle = angle * angle / (apexlen * orglen); +- base1 = tapex; +- base2 = torg; +- lprev(*testtri, tri1); +- } +- +- if (b->vararea || b->fixedarea || b->usertest) { +- /* Check whether the area is larger than permitted. */ +- area = 0.5 * (dxod * dyda - dyod * dxda); +- if (b->fixedarea && (area > b->maxarea)) { +- /* Add this triangle to the list of bad triangles. */ +- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); +- return; +- } +- +- /* Nonpositive area constraints are treated as unconstrained. */ +- if ((b->vararea) && (area > areabound(*testtri)) && +- (areabound(*testtri) > 0.0)) { +- /* Add this triangle to the list of bad triangles. */ +- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); +- return; +- } +- +- if (b->usertest) { +- /* Check whether the user thinks this triangle is too large. */ +- if (triunsuitable(torg, tdest, tapex, area)) { +- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); +- return; +- } +- } +- } +- +- /* Check whether the angle is smaller than permitted. */ +- if (angle > b->goodangle) { +- /* Use the rules of Miller, Pav, and Walkington to decide that certain */ +- /* triangles should not be split, even if they have bad angles. */ +- /* A skinny triangle is not split if its shortest edge subtends a */ +- /* small input angle, and both endpoints of the edge lie on a */ +- /* concentric circular shell. For convenience, I make a small */ +- /* adjustment to that rule: I check if the endpoints of the edge */ +- /* both lie in segment interiors, equidistant from the apex where */ +- /* the two segments meet. */ +- /* First, check if both points lie in segment interiors. */ +- if ((vertextype(base1) == SEGMENTVERTEX) && +- (vertextype(base2) == SEGMENTVERTEX)) { +- /* Check if both points lie in a common segment. If they do, the */ +- /* skinny triangle is enqueued to be split as usual. */ +- tspivot(tri1, testsub); +- if (testsub.ss == m->dummysub) { +- /* No common segment. Find a subsegment that contains `torg'. */ +- otricopy(tri1, tri2); +- do { +- oprevself(tri1); +- tspivot(tri1, testsub); +- } while (testsub.ss == m->dummysub); +- /* Find the endpoints of the containing segment. */ +- segorg(testsub, org1); +- segdest(testsub, dest1); +- /* Find a subsegment that contains `tdest'. */ +- do { +- dnextself(tri2); +- tspivot(tri2, testsub); +- } while (testsub.ss == m->dummysub); +- /* Find the endpoints of the containing segment. */ +- segorg(testsub, org2); +- segdest(testsub, dest2); +- /* Check if the two containing segments have an endpoint in common. */ +- joinvertex = (vertex) NULL; +- if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) { +- joinvertex = dest1; +- } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) { +- joinvertex = org1; +- } +- if (joinvertex != (vertex) NULL) { +- /* Compute the distance from the common endpoint (of the two */ +- /* segments) to each of the endpoints of the shortest edge. */ +- dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) + +- (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1])); +- dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) + +- (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1])); +- /* If the two distances are equal, don't split the triangle. */ +- if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) { +- /* Return now to avoid enqueueing the bad triangle. */ +- return; +- } +- } +- } +- } +- +- /* Add this triangle to the list of bad triangles. */ +- enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/** **/ +-/** **/ +-/********* Mesh quality testing routines end here *********/ +- +-/********* Point location routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* makevertexmap() Construct a mapping from vertices to triangles to */ +-/* improve the speed of point location for segment */ +-/* insertion. */ +-/* */ +-/* Traverses all the triangles, and provides each corner of each triangle */ +-/* with a pointer to that triangle. Of course, pointers will be */ +-/* overwritten by other pointers because (almost) each vertex is a corner */ +-/* of several triangles, but in the end every vertex will point to some */ +-/* triangle that contains it. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void makevertexmap(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void makevertexmap(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop; +- vertex triorg; +- +- if (b->verbose) { +- printf(" Constructing mapping from vertices to triangles.\n"); +- } +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- while (triangleloop.tri != (triangle *) NULL) { +- /* Check all three vertices of the triangle. */ +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- org(triangleloop, triorg); +- setvertex2tri(triorg, encode(triangleloop)); +- } +- triangleloop.tri = triangletraverse(m); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* preciselocate() Find a triangle or edge containing a given point. */ +-/* */ +-/* Begins its search from `searchtri'. It is important that `searchtri' */ +-/* be a handle with the property that `searchpoint' is strictly to the left */ +-/* of the edge denoted by `searchtri', or is collinear with that edge and */ +-/* does not intersect that edge. (In particular, `searchpoint' should not */ +-/* be the origin or destination of that edge.) */ +-/* */ +-/* These conditions are imposed because preciselocate() is normally used in */ +-/* one of two situations: */ +-/* */ +-/* (1) To try to find the location to insert a new point. Normally, we */ +-/* know an edge that the point is strictly to the left of. In the */ +-/* incremental Delaunay algorithm, that edge is a bounding box edge. */ +-/* In Ruppert's Delaunay refinement algorithm for quality meshing, */ +-/* that edge is the shortest edge of the triangle whose circumcenter */ +-/* is being inserted. */ +-/* */ +-/* (2) To try to find an existing point. In this case, any edge on the */ +-/* convex hull is a good starting edge. You must screen out the */ +-/* possibility that the vertex sought is an endpoint of the starting */ +-/* edge before you call preciselocate(). */ +-/* */ +-/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +-/* */ +-/* This implementation differs from that given by Guibas and Stolfi. It */ +-/* walks from triangle to triangle, crossing an edge only if `searchpoint' */ +-/* is on the other side of the line containing that edge. After entering */ +-/* a triangle, there are two edges by which one can leave that triangle. */ +-/* If both edges are valid (`searchpoint' is on the other side of both */ +-/* edges), one of the two is chosen by drawing a line perpendicular to */ +-/* the entry edge (whose endpoints are `forg' and `fdest') passing through */ +-/* `fapex'. Depending on which side of this perpendicular `searchpoint' */ +-/* falls on, an exit edge is chosen. */ +-/* */ +-/* This implementation is empirically faster than the Guibas and Stolfi */ +-/* point location routine (which I originally used), which tends to spiral */ +-/* in toward its target. */ +-/* */ +-/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +-/* is a handle whose origin is the existing vertex. */ +-/* */ +-/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +-/* handle whose primary edge is the edge on which the point lies. */ +-/* */ +-/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +-/* `searchtri' is a handle on the triangle that contains the point. */ +-/* */ +-/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +-/* handle whose primary edge the point is to the right of. This might */ +-/* occur when the circumcenter of a triangle falls just slightly outside */ +-/* the mesh due to floating-point roundoff error. It also occurs when */ +-/* seeking a hole or region point that a foolish user has placed outside */ +-/* the mesh. */ +-/* */ +-/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */ +-/* walk through a subsegment, and will return OUTSIDE. */ +-/* */ +-/* WARNING: This routine is designed for convex triangulations, and will */ +-/* not generally work after the holes and concavities have been carved. */ +-/* However, it can still be used to find the circumcenter of a triangle, as */ +-/* long as the search is begun from the triangle in question. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-enum locateresult preciselocate(struct mesh *m, struct behavior *b, +- vertex searchpoint, struct otri *searchtri, +- int stopatsubsegment) +-#else /* not ANSI_DECLARATORS */ +-enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment) +-struct mesh *m; +-struct behavior *b; +-vertex searchpoint; +-struct otri *searchtri; +-int stopatsubsegment; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri backtracktri; +- struct osub checkedge; +- vertex forg, fdest, fapex; +- REAL orgorient, destorient; +- int moveleft; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (b->verbose > 2) { +- printf(" Searching for point (%.12g, %.12g).\n", +- searchpoint[0], searchpoint[1]); +- } +- /* Where are we? */ +- org(*searchtri, forg); +- dest(*searchtri, fdest); +- apex(*searchtri, fapex); +- while (1) { +- if (b->verbose > 2) { +- printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); +- } +- /* Check whether the apex is the point we seek. */ +- if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { +- lprevself(*searchtri); +- return ONVERTEX; +- } +- /* Does the point lie on the other side of the line defined by the */ +- /* triangle edge opposite the triangle's destination? */ +- destorient = counterclockwise(m, b, forg, fapex, searchpoint); +- /* Does the point lie on the other side of the line defined by the */ +- /* triangle edge opposite the triangle's origin? */ +- orgorient = counterclockwise(m, b, fapex, fdest, searchpoint); +- if (destorient > 0.0) { +- if (orgorient > 0.0) { +- /* Move left if the inner product of (fapex - searchpoint) and */ +- /* (fdest - forg) is positive. This is equivalent to drawing */ +- /* a line perpendicular to the line (forg, fdest) and passing */ +- /* through `fapex', and determining which side of this line */ +- /* `searchpoint' falls on. */ +- moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + +- (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0; +- } else { +- moveleft = 1; +- } +- } else { +- if (orgorient > 0.0) { +- moveleft = 0; +- } else { +- /* The point we seek must be on the boundary of or inside this */ +- /* triangle. */ +- if (destorient == 0.0) { +- lprevself(*searchtri); +- return ONEDGE; +- } +- if (orgorient == 0.0) { +- lnextself(*searchtri); +- return ONEDGE; +- } +- return INTRIANGLE; +- } +- } +- +- /* Move to another triangle. Leave a trace `backtracktri' in case */ +- /* floating-point roundoff or some such bogey causes us to walk */ +- /* off a boundary of the triangulation. */ +- if (moveleft) { +- lprev(*searchtri, backtracktri); +- fdest = fapex; +- } else { +- lnext(*searchtri, backtracktri); +- forg = fapex; +- } +- sym(backtracktri, *searchtri); +- +- if (m->checksegments && stopatsubsegment) { +- /* Check for walking through a subsegment. */ +- tspivot(backtracktri, checkedge); +- if (checkedge.ss != m->dummysub) { +- /* Go back to the last triangle. */ +- otricopy(backtracktri, *searchtri); +- return OUTSIDE; +- } +- } +- /* Check for walking right out of the triangulation. */ +- if (searchtri->tri == m->dummytri) { +- /* Go back to the last triangle. */ +- otricopy(backtracktri, *searchtri); +- return OUTSIDE; +- } +- +- apex(*searchtri, fapex); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* locate() Find a triangle or edge containing a given point. */ +-/* */ +-/* Searching begins from one of: the input `searchtri', a recently */ +-/* encountered triangle `recenttri', or from a triangle chosen from a */ +-/* random sample. The choice is made by determining which triangle's */ +-/* origin is closest to the point we are searching for. Normally, */ +-/* `searchtri' should be a handle on the convex hull of the triangulation. */ +-/* */ +-/* Details on the random sampling method can be found in the Mucke, Saias, */ +-/* and Zhu paper cited in the header of this code. */ +-/* */ +-/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +-/* */ +-/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +-/* is a handle whose origin is the existing vertex. */ +-/* */ +-/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +-/* handle whose primary edge is the edge on which the point lies. */ +-/* */ +-/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +-/* `searchtri' is a handle on the triangle that contains the point. */ +-/* */ +-/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +-/* handle whose primary edge the point is to the right of. This might */ +-/* occur when the circumcenter of a triangle falls just slightly outside */ +-/* the mesh due to floating-point roundoff error. It also occurs when */ +-/* seeking a hole or region point that a foolish user has placed outside */ +-/* the mesh. */ +-/* */ +-/* WARNING: This routine is designed for convex triangulations, and will */ +-/* not generally work after the holes and concavities have been carved. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-enum locateresult locate(struct mesh *m, struct behavior *b, +- vertex searchpoint, struct otri *searchtri) +-#else /* not ANSI_DECLARATORS */ +-enum locateresult locate(m, b, searchpoint, searchtri) +-struct mesh *m; +-struct behavior *b; +-vertex searchpoint; +-struct otri *searchtri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- void **sampleblock; +- char *firsttri; +- struct otri sampletri; +- vertex torg, tdest; +- TRIANGLE_PTRINT alignptr; +- REAL searchdist, dist; +- REAL ahead; +- long samplesperblock, totalsamplesleft, samplesleft; +- long population, totalpopulation; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- if (b->verbose > 2) { +- printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", +- searchpoint[0], searchpoint[1]); +- } +- /* Record the distance from the suggested starting triangle to the */ +- /* point we seek. */ +- org(*searchtri, torg); +- searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + +- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); +- if (b->verbose > 2) { +- printf(" Boundary triangle has origin (%.12g, %.12g).\n", +- torg[0], torg[1]); +- } +- +- /* If a recently encountered triangle has been recorded and has not been */ +- /* deallocated, test it as a good starting point. */ +- if (m->recenttri.tri != (triangle *) NULL) { +- if (!deadtri(m->recenttri.tri)) { +- org(m->recenttri, torg); +- if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { +- otricopy(m->recenttri, *searchtri); +- return ONVERTEX; +- } +- dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + +- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); +- if (dist < searchdist) { +- otricopy(m->recenttri, *searchtri); +- searchdist = dist; +- if (b->verbose > 2) { +- printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", +- torg[0], torg[1]); +- } +- } +- } +- } +- +- /* The number of random samples taken is proportional to the cube root of */ +- /* the number of triangles in the mesh. The next bit of code assumes */ +- /* that the number of triangles increases monotonically (or at least */ +- /* doesn't decrease enough to matter). */ +- while (SAMPLEFACTOR * m->samples * m->samples * m->samples < +- m->triangles.items) { +- m->samples++; +- } +- +- /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */ +- /* from each block of triangles (except the first)--until we meet the */ +- /* sample quota. The ceiling means that blocks at the end might be */ +- /* neglected, but I don't care. */ +- samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1; +- /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */ +- /* from the first block of triangles. */ +- samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) / +- m->triangles.maxitems + 1; +- totalsamplesleft = m->samples; +- population = m->triangles.itemsfirstblock; +- totalpopulation = m->triangles.maxitems; +- sampleblock = m->triangles.firstblock; +- sampletri.orient = 0; +- while (totalsamplesleft > 0) { +- /* If we're in the last block, `population' needs to be corrected. */ +- if (population > totalpopulation) { +- population = totalpopulation; +- } +- /* Find a pointer to the first triangle in the block. */ +- alignptr = (TRIANGLE_PTRINT) (sampleblock + 1); +- firsttri = (char *) (alignptr + +- (TRIANGLE_PTRINT) m->triangles.alignbytes - +- (alignptr % +- (TRIANGLE_PTRINT) m->triangles.alignbytes)); +- +- /* Choose `samplesleft' randomly sampled triangles in this block. */ +- do { +- sampletri.tri = (triangle *) (firsttri + +- (randomnation((unsigned int) population) * +- m->triangles.itembytes)); +- if (!deadtri(sampletri.tri)) { +- org(sampletri, torg); +- dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + +- (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); +- if (dist < searchdist) { +- otricopy(sampletri, *searchtri); +- searchdist = dist; +- if (b->verbose > 2) { +- printf(" Choosing triangle with origin (%.12g, %.12g).\n", +- torg[0], torg[1]); +- } +- } +- } +- +- samplesleft--; +- totalsamplesleft--; +- } while ((samplesleft > 0) && (totalsamplesleft > 0)); +- +- if (totalsamplesleft > 0) { +- sampleblock = (void **) *sampleblock; +- samplesleft = samplesperblock; +- totalpopulation -= population; +- population = TRIPERBLOCK; +- } +- } +- +- /* Where are we? */ +- org(*searchtri, torg); +- dest(*searchtri, tdest); +- /* Check the starting triangle's vertices. */ +- if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { +- return ONVERTEX; +- } +- if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { +- lnextself(*searchtri); +- return ONVERTEX; +- } +- /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ +- ahead = counterclockwise(m, b, torg, tdest, searchpoint); +- if (ahead < 0.0) { +- /* Turn around so that `searchpoint' is to the left of the */ +- /* edge specified by `searchtri'. */ +- symself(*searchtri); +- } else if (ahead == 0.0) { +- /* Check if `searchpoint' is between `torg' and `tdest'. */ +- if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) && +- ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { +- return ONEDGE; +- } +- } +- return preciselocate(m, b, searchpoint, searchtri, 0); +-} +- +-/** **/ +-/** **/ +-/********* Point location routines end here *********/ +- +-/********* Mesh transformation routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* insertsubseg() Create a new subsegment and insert it between two */ +-/* triangles. */ +-/* */ +-/* The new subsegment is inserted at the edge described by the handle */ +-/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */ +-/* is applied to the subsegment and, if appropriate, its vertices. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, +- int subsegmark) +-#else /* not ANSI_DECLARATORS */ +-void insertsubseg(m, b, tri, subsegmark) +-struct mesh *m; +-struct behavior *b; +-struct otri *tri; /* Edge at which to insert the new subsegment. */ +-int subsegmark; /* Marker for the new subsegment. */ +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri oppotri; +- struct osub newsubseg; +- vertex triorg, tridest; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- org(*tri, triorg); +- dest(*tri, tridest); +- /* Mark vertices if possible. */ +- if (vertexmark(triorg) == 0) { +- setvertexmark(triorg, subsegmark); +- } +- if (vertexmark(tridest) == 0) { +- setvertexmark(tridest, subsegmark); +- } +- /* Check if there's already a subsegment here. */ +- tspivot(*tri, newsubseg); +- if (newsubseg.ss == m->dummysub) { +- /* Make new subsegment and initialize its vertices. */ +- makesubseg(m, &newsubseg); +- setsorg(newsubseg, tridest); +- setsdest(newsubseg, triorg); +- setsegorg(newsubseg, tridest); +- setsegdest(newsubseg, triorg); +- /* Bond new subsegment to the two triangles it is sandwiched between. */ +- /* Note that the facing triangle `oppotri' might be equal to */ +- /* `dummytri' (outer space), but the new subsegment is bonded to it */ +- /* all the same. */ +- tsbond(*tri, newsubseg); +- sym(*tri, oppotri); +- ssymself(newsubseg); +- tsbond(oppotri, newsubseg); +- setmark(newsubseg, subsegmark); +- if (b->verbose > 2) { +- printf(" Inserting new "); +- printsubseg(m, b, &newsubseg); +- } +- } else { +- if (mark(newsubseg) == 0) { +- setmark(newsubseg, subsegmark); +- } +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* Terminology */ +-/* */ +-/* A "local transformation" replaces a small set of triangles with another */ +-/* set of triangles. This may or may not involve inserting or deleting a */ +-/* vertex. */ +-/* */ +-/* The term "casing" is used to describe the set of triangles that are */ +-/* attached to the triangles being transformed, but are not transformed */ +-/* themselves. Think of the casing as a fixed hollow structure inside */ +-/* which all the action happens. A "casing" is only defined relative to */ +-/* a single transformation; each occurrence of a transformation will */ +-/* involve a different casing. */ +-/* */ +-/*****************************************************************************/ +- +-/*****************************************************************************/ +-/* */ +-/* flip() Transform two triangles to two different triangles by flipping */ +-/* an edge counterclockwise within a quadrilateral. */ +-/* */ +-/* Imagine the original triangles, abc and bad, oriented so that the */ +-/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ +-/* and the vertex a on the right. The vertex c lies below the edge, and */ +-/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ +-/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ +-/* */ +-/* The triangles abc and bad are deleted and replaced by the triangles cdb */ +-/* and dca. The triangles that represent abc and bad are NOT deallocated; */ +-/* they are reused for dca and cdb, respectively. Hence, any handles that */ +-/* may have held the original triangles are still valid, although not */ +-/* directed as they were before. */ +-/* */ +-/* Upon completion of this routine, the `flipedge' handle holds the edge */ +-/* dc of triangle dca, and is directed down, from vertex d to vertex c. */ +-/* (Hence, the two triangles have rotated counterclockwise.) */ +-/* */ +-/* WARNING: This transformation is geometrically valid only if the */ +-/* quadrilateral adbc is convex. Furthermore, this transformation is */ +-/* valid only if there is not a subsegment between the triangles abc and */ +-/* bad. This routine does not check either of these preconditions, and */ +-/* it is the responsibility of the calling routine to ensure that they are */ +-/* met. If they are not, the streets shall be filled with wailing and */ +-/* gnashing of teeth. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void flip(struct mesh *m, struct behavior *b, struct otri *flipedge) +-#else /* not ANSI_DECLARATORS */ +-void flip(m, b, flipedge) +-struct mesh *m; +-struct behavior *b; +-struct otri *flipedge; /* Handle for the triangle abc. */ +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri botleft, botright; +- struct otri topleft, topright; +- struct otri top; +- struct otri botlcasing, botrcasing; +- struct otri toplcasing, toprcasing; +- struct osub botlsubseg, botrsubseg; +- struct osub toplsubseg, toprsubseg; +- vertex leftvertex, rightvertex, botvertex; +- vertex farvertex; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- /* Identify the vertices of the quadrilateral. */ +- org(*flipedge, rightvertex); +- dest(*flipedge, leftvertex); +- apex(*flipedge, botvertex); +- sym(*flipedge, top); +-#ifdef SELF_CHECK +- if (top.tri == m->dummytri) { +- printf("Internal error in flip(): Attempt to flip on boundary.\n"); +- lnextself(*flipedge); +- return; +- } +- if (m->checksegments) { +- tspivot(*flipedge, toplsubseg); +- if (toplsubseg.ss != m->dummysub) { +- printf("Internal error in flip(): Attempt to flip a segment.\n"); +- lnextself(*flipedge); +- return; +- } +- } +-#endif /* SELF_CHECK */ +- apex(top, farvertex); +- +- /* Identify the casing of the quadrilateral. */ +- lprev(top, topleft); +- sym(topleft, toplcasing); +- lnext(top, topright); +- sym(topright, toprcasing); +- lnext(*flipedge, botleft); +- sym(botleft, botlcasing); +- lprev(*flipedge, botright); +- sym(botright, botrcasing); +- /* Rotate the quadrilateral one-quarter turn counterclockwise. */ +- bond(topleft, botlcasing); +- bond(botleft, botrcasing); +- bond(botright, toprcasing); +- bond(topright, toplcasing); +- +- if (m->checksegments) { +- /* Check for subsegments and rebond them to the quadrilateral. */ +- tspivot(topleft, toplsubseg); +- tspivot(botleft, botlsubseg); +- tspivot(botright, botrsubseg); +- tspivot(topright, toprsubseg); +- if (toplsubseg.ss == m->dummysub) { +- tsdissolve(topright); +- } else { +- tsbond(topright, toplsubseg); +- } +- if (botlsubseg.ss == m->dummysub) { +- tsdissolve(topleft); +- } else { +- tsbond(topleft, botlsubseg); +- } +- if (botrsubseg.ss == m->dummysub) { +- tsdissolve(botleft); +- } else { +- tsbond(botleft, botrsubseg); +- } +- if (toprsubseg.ss == m->dummysub) { +- tsdissolve(botright); +- } else { +- tsbond(botright, toprsubseg); +- } +- } +- +- /* New vertex assignments for the rotated quadrilateral. */ +- setorg(*flipedge, farvertex); +- setdest(*flipedge, botvertex); +- setapex(*flipedge, rightvertex); +- setorg(top, botvertex); +- setdest(top, farvertex); +- setapex(top, leftvertex); +- if (b->verbose > 2) { +- printf(" Edge flip results in left "); +- printtriangle(m, b, &top); +- printf(" and right "); +- printtriangle(m, b, flipedge); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* unflip() Transform two triangles to two different triangles by */ +-/* flipping an edge clockwise within a quadrilateral. Reverses */ +-/* the flip() operation so that the data structures representing */ +-/* the triangles are back where they were before the flip(). */ +-/* */ +-/* Imagine the original triangles, abc and bad, oriented so that the */ +-/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ +-/* and the vertex a on the right. The vertex c lies below the edge, and */ +-/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ +-/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ +-/* */ +-/* The triangles abc and bad are deleted and replaced by the triangles cdb */ +-/* and dca. The triangles that represent abc and bad are NOT deallocated; */ +-/* they are reused for cdb and dca, respectively. Hence, any handles that */ +-/* may have held the original triangles are still valid, although not */ +-/* directed as they were before. */ +-/* */ +-/* Upon completion of this routine, the `flipedge' handle holds the edge */ +-/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */ +-/* (Hence, the two triangles have rotated clockwise.) */ +-/* */ +-/* WARNING: This transformation is geometrically valid only if the */ +-/* quadrilateral adbc is convex. Furthermore, this transformation is */ +-/* valid only if there is not a subsegment between the triangles abc and */ +-/* bad. This routine does not check either of these preconditions, and */ +-/* it is the responsibility of the calling routine to ensure that they are */ +-/* met. If they are not, the streets shall be filled with wailing and */ +-/* gnashing of teeth. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge) +-#else /* not ANSI_DECLARATORS */ +-void unflip(m, b, flipedge) +-struct mesh *m; +-struct behavior *b; +-struct otri *flipedge; /* Handle for the triangle abc. */ +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri botleft, botright; +- struct otri topleft, topright; +- struct otri top; +- struct otri botlcasing, botrcasing; +- struct otri toplcasing, toprcasing; +- struct osub botlsubseg, botrsubseg; +- struct osub toplsubseg, toprsubseg; +- vertex leftvertex, rightvertex, botvertex; +- vertex farvertex; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- /* Identify the vertices of the quadrilateral. */ +- org(*flipedge, rightvertex); +- dest(*flipedge, leftvertex); +- apex(*flipedge, botvertex); +- sym(*flipedge, top); +-#ifdef SELF_CHECK +- if (top.tri == m->dummytri) { +- printf("Internal error in unflip(): Attempt to flip on boundary.\n"); +- lnextself(*flipedge); +- return; +- } +- if (m->checksegments) { +- tspivot(*flipedge, toplsubseg); +- if (toplsubseg.ss != m->dummysub) { +- printf("Internal error in unflip(): Attempt to flip a subsegment.\n"); +- lnextself(*flipedge); +- return; +- } +- } +-#endif /* SELF_CHECK */ +- apex(top, farvertex); +- +- /* Identify the casing of the quadrilateral. */ +- lprev(top, topleft); +- sym(topleft, toplcasing); +- lnext(top, topright); +- sym(topright, toprcasing); +- lnext(*flipedge, botleft); +- sym(botleft, botlcasing); +- lprev(*flipedge, botright); +- sym(botright, botrcasing); +- /* Rotate the quadrilateral one-quarter turn clockwise. */ +- bond(topleft, toprcasing); +- bond(botleft, toplcasing); +- bond(botright, botlcasing); +- bond(topright, botrcasing); +- +- if (m->checksegments) { +- /* Check for subsegments and rebond them to the quadrilateral. */ +- tspivot(topleft, toplsubseg); +- tspivot(botleft, botlsubseg); +- tspivot(botright, botrsubseg); +- tspivot(topright, toprsubseg); +- if (toplsubseg.ss == m->dummysub) { +- tsdissolve(botleft); +- } else { +- tsbond(botleft, toplsubseg); +- } +- if (botlsubseg.ss == m->dummysub) { +- tsdissolve(botright); +- } else { +- tsbond(botright, botlsubseg); +- } +- if (botrsubseg.ss == m->dummysub) { +- tsdissolve(topright); +- } else { +- tsbond(topright, botrsubseg); +- } +- if (toprsubseg.ss == m->dummysub) { +- tsdissolve(topleft); +- } else { +- tsbond(topleft, toprsubseg); +- } +- } +- +- /* New vertex assignments for the rotated quadrilateral. */ +- setorg(*flipedge, botvertex); +- setdest(*flipedge, farvertex); +- setapex(*flipedge, leftvertex); +- setorg(top, farvertex); +- setdest(top, botvertex); +- setapex(top, rightvertex); +- if (b->verbose > 2) { +- printf(" Edge unflip results in left "); +- printtriangle(m, b, flipedge); +- printf(" and right "); +- printtriangle(m, b, &top); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* insertvertex() Insert a vertex into a Delaunay triangulation, */ +-/* performing flips as necessary to maintain the Delaunay */ +-/* property. */ +-/* */ +-/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */ +-/* the search for the containing triangle begins from `searchtri'. If */ +-/* `searchtri.tri' is NULL, a full point location procedure is called. */ +-/* If `insertvertex' is found inside a triangle, the triangle is split into */ +-/* three; if `insertvertex' lies on an edge, the edge is split in two, */ +-/* thereby splitting the two adjacent triangles into four. Edge flips are */ +-/* used to restore the Delaunay property. If `insertvertex' lies on an */ +-/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */ +-/* returned. On return, `searchtri' is set to a handle whose origin is the */ +-/* existing vertex. */ +-/* */ +-/* Normally, the parameter `splitseg' is set to NULL, implying that no */ +-/* subsegment should be split. In this case, if `insertvertex' is found to */ +-/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */ +-/* returned. On return, `searchtri' is set to a handle whose primary edge */ +-/* is the violated subsegment. */ +-/* */ +-/* If the calling routine wishes to split a subsegment by inserting a */ +-/* vertex in it, the parameter `splitseg' should be that subsegment. In */ +-/* this case, `searchtri' MUST be the triangle handle reached by pivoting */ +-/* from that subsegment; no point location is done. */ +-/* */ +-/* `segmentflaws' and `triflaws' are flags that indicate whether or not */ +-/* there should be checks for the creation of encroached subsegments or bad */ +-/* quality triangles. If a newly inserted vertex encroaches upon */ +-/* subsegments, these subsegments are added to the list of subsegments to */ +-/* be split if `segmentflaws' is set. If bad triangles are created, these */ +-/* are added to the queue if `triflaws' is set. */ +-/* */ +-/* If a duplicate vertex or violated segment does not prevent the vertex */ +-/* from being inserted, the return value will be ENCROACHINGVERTEX if the */ +-/* vertex encroaches upon a subsegment (and checking is enabled), or */ +-/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */ +-/* handle whose origin is the newly inserted vertex. */ +-/* */ +-/* insertvertex() does not use flip() for reasons of speed; some */ +-/* information can be reused from edge flip to edge flip, like the */ +-/* locations of subsegments. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, +- vertex newvertex, struct otri *searchtri, +- struct osub *splitseg, +- int segmentflaws, int triflaws) +-#else /* not ANSI_DECLARATORS */ +-enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg, +- segmentflaws, triflaws) +-struct mesh *m; +-struct behavior *b; +-vertex newvertex; +-struct otri *searchtri; +-struct osub *splitseg; +-int segmentflaws; +-int triflaws; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri horiz; +- struct otri top; +- struct otri botleft, botright; +- struct otri topleft, topright; +- struct otri newbotleft, newbotright; +- struct otri newtopright; +- struct otri botlcasing, botrcasing; +- struct otri toplcasing, toprcasing; +- struct otri testtri; +- struct osub botlsubseg, botrsubseg; +- struct osub toplsubseg, toprsubseg; +- struct osub brokensubseg; +- struct osub checksubseg; +- struct osub rightsubseg; +- struct osub newsubseg; +- struct badsubseg *encroached; +- struct flipstacker *newflip; +- vertex first; +- vertex leftvertex, rightvertex, botvertex, topvertex, farvertex; +- vertex segmentorg, segmentdest; +- REAL attrib; +- REAL area; +- enum insertvertexresult success; +- enum locateresult intersect; +- int doflip; +- int mirrorflag; +- int enq; +- int i; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by spivot() and tspivot(). */ +- +- if (b->verbose > 1) { +- printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); +- } +- +- if (splitseg == (struct osub *) NULL) { +- /* Find the location of the vertex to be inserted. Check if a good */ +- /* starting triangle has already been provided by the caller. */ +- if (searchtri->tri == m->dummytri) { +- /* Find a boundary triangle. */ +- horiz.tri = m->dummytri; +- horiz.orient = 0; +- symself(horiz); +- /* Search for a triangle containing `newvertex'. */ +- intersect = locate(m, b, newvertex, &horiz); +- } else { +- /* Start searching from the triangle provided by the caller. */ +- otricopy(*searchtri, horiz); +- intersect = preciselocate(m, b, newvertex, &horiz, 1); +- } +- } else { +- /* The calling routine provides the subsegment in which */ +- /* the vertex is inserted. */ +- otricopy(*searchtri, horiz); +- intersect = ONEDGE; +- } +- +- if (intersect == ONVERTEX) { +- /* There's already a vertex there. Return in `searchtri' a triangle */ +- /* whose origin is the existing vertex. */ +- otricopy(horiz, *searchtri); +- otricopy(horiz, m->recenttri); +- return DUPLICATEVERTEX; +- } +- if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { +- /* The vertex falls on an edge or boundary. */ +- if (m->checksegments && (splitseg == (struct osub *) NULL)) { +- /* Check whether the vertex falls on a subsegment. */ +- tspivot(horiz, brokensubseg); +- if (brokensubseg.ss != m->dummysub) { +- /* The vertex falls on a subsegment, and hence will not be inserted. */ +- if (segmentflaws) { +- enq = b->nobisect != 2; +- if (enq && (b->nobisect == 1)) { +- /* This subsegment may be split only if it is an */ +- /* internal boundary. */ +- sym(horiz, testtri); +- enq = testtri.tri != m->dummytri; +- } +- if (enq) { +- /* Add the subsegment to the list of encroached subsegments. */ +- encroached = (struct badsubseg *) poolalloc(&m->badsubsegs); +- encroached->encsubseg = sencode(brokensubseg); +- sorg(brokensubseg, encroached->subsegorg); +- sdest(brokensubseg, encroached->subsegdest); +- if (b->verbose > 2) { +- printf( +- " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", +- encroached->subsegorg[0], encroached->subsegorg[1], +- encroached->subsegdest[0], encroached->subsegdest[1]); +- } +- } +- } +- /* Return a handle whose primary edge contains the vertex, */ +- /* which has not been inserted. */ +- otricopy(horiz, *searchtri); +- otricopy(horiz, m->recenttri); +- return VIOLATINGVERTEX; +- } +- } +- +- /* Insert the vertex on an edge, dividing one triangle into two (if */ +- /* the edge lies on a boundary) or two triangles into four. */ +- lprev(horiz, botright); +- sym(botright, botrcasing); +- sym(horiz, topright); +- /* Is there a second triangle? (Or does this edge lie on a boundary?) */ +- mirrorflag = topright.tri != m->dummytri; +- if (mirrorflag) { +- lnextself(topright); +- sym(topright, toprcasing); +- maketriangle(m, b, &newtopright); +- } else { +- /* Splitting a boundary edge increases the number of boundary edges. */ +- m->hullsize++; +- } +- maketriangle(m, b, &newbotright); +- +- /* Set the vertices of changed and new triangles. */ +- org(horiz, rightvertex); +- dest(horiz, leftvertex); +- apex(horiz, botvertex); +- setorg(newbotright, botvertex); +- setdest(newbotright, rightvertex); +- setapex(newbotright, newvertex); +- setorg(horiz, newvertex); +- for (i = 0; i < m->eextras; i++) { +- /* Set the element attributes of a new triangle. */ +- setelemattribute(newbotright, i, elemattribute(botright, i)); +- } +- if (b->vararea) { +- /* Set the area constraint of a new triangle. */ +- setareabound(newbotright, areabound(botright)); +- } +- if (mirrorflag) { +- dest(topright, topvertex); +- setorg(newtopright, rightvertex); +- setdest(newtopright, topvertex); +- setapex(newtopright, newvertex); +- setorg(topright, newvertex); +- for (i = 0; i < m->eextras; i++) { +- /* Set the element attributes of another new triangle. */ +- setelemattribute(newtopright, i, elemattribute(topright, i)); +- } +- if (b->vararea) { +- /* Set the area constraint of another new triangle. */ +- setareabound(newtopright, areabound(topright)); +- } +- } +- +- /* There may be subsegments that need to be bonded */ +- /* to the new triangle(s). */ +- if (m->checksegments) { +- tspivot(botright, botrsubseg); +- if (botrsubseg.ss != m->dummysub) { +- tsdissolve(botright); +- tsbond(newbotright, botrsubseg); +- } +- if (mirrorflag) { +- tspivot(topright, toprsubseg); +- if (toprsubseg.ss != m->dummysub) { +- tsdissolve(topright); +- tsbond(newtopright, toprsubseg); +- } +- } +- } +- +- /* Bond the new triangle(s) to the surrounding triangles. */ +- bond(newbotright, botrcasing); +- lprevself(newbotright); +- bond(newbotright, botright); +- lprevself(newbotright); +- if (mirrorflag) { +- bond(newtopright, toprcasing); +- lnextself(newtopright); +- bond(newtopright, topright); +- lnextself(newtopright); +- bond(newtopright, newbotright); +- } +- +- if (splitseg != (struct osub *) NULL) { +- /* Split the subsegment into two. */ +- setsdest(*splitseg, newvertex); +- segorg(*splitseg, segmentorg); +- segdest(*splitseg, segmentdest); +- ssymself(*splitseg); +- spivot(*splitseg, rightsubseg); +- insertsubseg(m, b, &newbotright, mark(*splitseg)); +- tspivot(newbotright, newsubseg); +- setsegorg(newsubseg, segmentorg); +- setsegdest(newsubseg, segmentdest); +- sbond(*splitseg, newsubseg); +- ssymself(newsubseg); +- sbond(newsubseg, rightsubseg); +- ssymself(*splitseg); +- /* Transfer the subsegment's boundary marker to the vertex */ +- /* if required. */ +- if (vertexmark(newvertex) == 0) { +- setvertexmark(newvertex, mark(*splitseg)); +- } +- } +- +- if (m->checkquality) { +- poolrestart(&m->flipstackers); +- m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); +- m->lastflip->flippedtri = encode(horiz); +- m->lastflip->prevflip = (struct flipstacker *) &insertvertex; +- } +- +-#ifdef SELF_CHECK +- if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf( +- " Clockwise triangle prior to edge vertex insertion (bottom).\n"); +- } +- if (mirrorflag) { +- if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle prior to edge vertex insertion (top).\n"); +- } +- if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf( +- " Clockwise triangle after edge vertex insertion (top right).\n"); +- } +- if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf( +- " Clockwise triangle after edge vertex insertion (top left).\n"); +- } +- } +- if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf( +- " Clockwise triangle after edge vertex insertion (bottom left).\n"); +- } +- if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf( +- " Clockwise triangle after edge vertex insertion (bottom right).\n"); +- } +-#endif /* SELF_CHECK */ +- if (b->verbose > 2) { +- printf(" Updating bottom left "); +- printtriangle(m, b, &botright); +- if (mirrorflag) { +- printf(" Updating top left "); +- printtriangle(m, b, &topright); +- printf(" Creating top right "); +- printtriangle(m, b, &newtopright); +- } +- printf(" Creating bottom right "); +- printtriangle(m, b, &newbotright); +- } +- +- /* Position `horiz' on the first edge to check for */ +- /* the Delaunay property. */ +- lnextself(horiz); +- } else { +- /* Insert the vertex in a triangle, splitting it into three. */ +- lnext(horiz, botleft); +- lprev(horiz, botright); +- sym(botleft, botlcasing); +- sym(botright, botrcasing); +- maketriangle(m, b, &newbotleft); +- maketriangle(m, b, &newbotright); +- +- /* Set the vertices of changed and new triangles. */ +- org(horiz, rightvertex); +- dest(horiz, leftvertex); +- apex(horiz, botvertex); +- setorg(newbotleft, leftvertex); +- setdest(newbotleft, botvertex); +- setapex(newbotleft, newvertex); +- setorg(newbotright, botvertex); +- setdest(newbotright, rightvertex); +- setapex(newbotright, newvertex); +- setapex(horiz, newvertex); +- for (i = 0; i < m->eextras; i++) { +- /* Set the element attributes of the new triangles. */ +- attrib = elemattribute(horiz, i); +- setelemattribute(newbotleft, i, attrib); +- setelemattribute(newbotright, i, attrib); +- } +- if (b->vararea) { +- /* Set the area constraint of the new triangles. */ +- area = areabound(horiz); +- setareabound(newbotleft, area); +- setareabound(newbotright, area); +- } +- +- /* There may be subsegments that need to be bonded */ +- /* to the new triangles. */ +- if (m->checksegments) { +- tspivot(botleft, botlsubseg); +- if (botlsubseg.ss != m->dummysub) { +- tsdissolve(botleft); +- tsbond(newbotleft, botlsubseg); +- } +- tspivot(botright, botrsubseg); +- if (botrsubseg.ss != m->dummysub) { +- tsdissolve(botright); +- tsbond(newbotright, botrsubseg); +- } +- } +- +- /* Bond the new triangles to the surrounding triangles. */ +- bond(newbotleft, botlcasing); +- bond(newbotright, botrcasing); +- lnextself(newbotleft); +- lprevself(newbotright); +- bond(newbotleft, newbotright); +- lnextself(newbotleft); +- bond(botleft, newbotleft); +- lprevself(newbotright); +- bond(botright, newbotright); +- +- if (m->checkquality) { +- poolrestart(&m->flipstackers); +- m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); +- m->lastflip->flippedtri = encode(horiz); +- m->lastflip->prevflip = (struct flipstacker *) NULL; +- } +- +-#ifdef SELF_CHECK +- if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle prior to vertex insertion.\n"); +- } +- if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle after vertex insertion (top).\n"); +- } +- if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle after vertex insertion (left).\n"); +- } +- if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle after vertex insertion (right).\n"); +- } +-#endif /* SELF_CHECK */ +- if (b->verbose > 2) { +- printf(" Updating top "); +- printtriangle(m, b, &horiz); +- printf(" Creating left "); +- printtriangle(m, b, &newbotleft); +- printf(" Creating right "); +- printtriangle(m, b, &newbotright); +- } +- } +- +- /* The insertion is successful by default, unless an encroached */ +- /* subsegment is found. */ +- success = SUCCESSFULVERTEX; +- /* Circle around the newly inserted vertex, checking each edge opposite */ +- /* it for the Delaunay property. Non-Delaunay edges are flipped. */ +- /* `horiz' is always the edge being checked. `first' marks where to */ +- /* stop circling. */ +- org(horiz, first); +- rightvertex = first; +- dest(horiz, leftvertex); +- /* Circle until finished. */ +- while (1) { +- /* By default, the edge will be flipped. */ +- doflip = 1; +- +- if (m->checksegments) { +- /* Check for a subsegment, which cannot be flipped. */ +- tspivot(horiz, checksubseg); +- if (checksubseg.ss != m->dummysub) { +- /* The edge is a subsegment and cannot be flipped. */ +- doflip = 0; +-#ifndef CDT_ONLY +- if (segmentflaws) { +- /* Does the new vertex encroach upon this subsegment? */ +- if (checkseg4encroach(m, b, &checksubseg)) { +- success = ENCROACHINGVERTEX; +- } +- } +-#endif /* not CDT_ONLY */ +- } +- } +- +- if (doflip) { +- /* Check if the edge is a boundary edge. */ +- sym(horiz, top); +- if (top.tri == m->dummytri) { +- /* The edge is a boundary edge and cannot be flipped. */ +- doflip = 0; +- } else { +- /* Find the vertex on the other side of the edge. */ +- apex(top, farvertex); +- /* In the incremental Delaunay triangulation algorithm, any of */ +- /* `leftvertex', `rightvertex', and `farvertex' could be vertices */ +- /* of the triangular bounding box. These vertices must be */ +- /* treated as if they are infinitely distant, even though their */ +- /* "coordinates" are not. */ +- if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) || +- (leftvertex == m->infvertex3)) { +- /* `leftvertex' is infinitely distant. Check the convexity of */ +- /* the boundary of the triangulation. 'farvertex' might be */ +- /* infinite as well, but trust me, this same condition should */ +- /* be applied. */ +- doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex) +- > 0.0; +- } else if ((rightvertex == m->infvertex1) || +- (rightvertex == m->infvertex2) || +- (rightvertex == m->infvertex3)) { +- /* `rightvertex' is infinitely distant. Check the convexity of */ +- /* the boundary of the triangulation. 'farvertex' might be */ +- /* infinite as well, but trust me, this same condition should */ +- /* be applied. */ +- doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex) +- > 0.0; +- } else if ((farvertex == m->infvertex1) || +- (farvertex == m->infvertex2) || +- (farvertex == m->infvertex3)) { +- /* `farvertex' is infinitely distant and cannot be inside */ +- /* the circumcircle of the triangle `horiz'. */ +- doflip = 0; +- } else { +- /* Test whether the edge is locally Delaunay. */ +- doflip = incircle(m, b, leftvertex, newvertex, rightvertex, +- farvertex) > 0.0; +- } +- if (doflip) { +- /* We made it! Flip the edge `horiz' by rotating its containing */ +- /* quadrilateral (the two triangles adjacent to `horiz'). */ +- /* Identify the casing of the quadrilateral. */ +- lprev(top, topleft); +- sym(topleft, toplcasing); +- lnext(top, topright); +- sym(topright, toprcasing); +- lnext(horiz, botleft); +- sym(botleft, botlcasing); +- lprev(horiz, botright); +- sym(botright, botrcasing); +- /* Rotate the quadrilateral one-quarter turn counterclockwise. */ +- bond(topleft, botlcasing); +- bond(botleft, botrcasing); +- bond(botright, toprcasing); +- bond(topright, toplcasing); +- if (m->checksegments) { +- /* Check for subsegments and rebond them to the quadrilateral. */ +- tspivot(topleft, toplsubseg); +- tspivot(botleft, botlsubseg); +- tspivot(botright, botrsubseg); +- tspivot(topright, toprsubseg); +- if (toplsubseg.ss == m->dummysub) { +- tsdissolve(topright); +- } else { +- tsbond(topright, toplsubseg); +- } +- if (botlsubseg.ss == m->dummysub) { +- tsdissolve(topleft); +- } else { +- tsbond(topleft, botlsubseg); +- } +- if (botrsubseg.ss == m->dummysub) { +- tsdissolve(botleft); +- } else { +- tsbond(botleft, botrsubseg); +- } +- if (toprsubseg.ss == m->dummysub) { +- tsdissolve(botright); +- } else { +- tsbond(botright, toprsubseg); +- } +- } +- /* New vertex assignments for the rotated quadrilateral. */ +- setorg(horiz, farvertex); +- setdest(horiz, newvertex); +- setapex(horiz, rightvertex); +- setorg(top, newvertex); +- setdest(top, farvertex); +- setapex(top, leftvertex); +- for (i = 0; i < m->eextras; i++) { +- /* Take the average of the two triangles' attributes. */ +- attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); +- setelemattribute(top, i, attrib); +- setelemattribute(horiz, i, attrib); +- } +- if (b->vararea) { +- if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) { +- area = -1.0; +- } else { +- /* Take the average of the two triangles' area constraints. */ +- /* This prevents small area constraints from migrating a */ +- /* long, long way from their original location due to flips. */ +- area = 0.5 * (areabound(top) + areabound(horiz)); +- } +- setareabound(top, area); +- setareabound(horiz, area); +- } +- +- if (m->checkquality) { +- newflip = (struct flipstacker *) poolalloc(&m->flipstackers); +- newflip->flippedtri = encode(horiz); +- newflip->prevflip = m->lastflip; +- m->lastflip = newflip; +- } +- +-#ifdef SELF_CHECK +- if (newvertex != (vertex) NULL) { +- if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) < +- 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle prior to edge flip (bottom).\n"); +- } +- /* The following test has been removed because constrainededge() */ +- /* sometimes generates inverted triangles that insertvertex() */ +- /* removes. */ +-/* +- if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) < +- 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle prior to edge flip (top).\n"); +- } +-*/ +- if (counterclockwise(m, b, farvertex, leftvertex, newvertex) < +- 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle after edge flip (left).\n"); +- } +- if (counterclockwise(m, b, newvertex, rightvertex, farvertex) < +- 0.0) { +- printf("Internal error in insertvertex():\n"); +- printf(" Clockwise triangle after edge flip (right).\n"); +- } +- } +-#endif /* SELF_CHECK */ +- if (b->verbose > 2) { +- printf(" Edge flip results in left "); +- lnextself(topleft); +- printtriangle(m, b, &topleft); +- printf(" and right "); +- printtriangle(m, b, &horiz); +- } +- /* On the next iterations, consider the two edges that were */ +- /* exposed (this is, are now visible to the newly inserted */ +- /* vertex) by the edge flip. */ +- lprevself(horiz); +- leftvertex = farvertex; +- } +- } +- } +- if (!doflip) { +- /* The handle `horiz' is accepted as locally Delaunay. */ +-#ifndef CDT_ONLY +- if (triflaws) { +- /* Check the triangle `horiz' for quality. */ +- testtriangle(m, b, &horiz); +- } +-#endif /* not CDT_ONLY */ +- /* Look for the next edge around the newly inserted vertex. */ +- lnextself(horiz); +- sym(horiz, testtri); +- /* Check for finishing a complete revolution about the new vertex, or */ +- /* falling outside of the triangulation. The latter will happen */ +- /* when a vertex is inserted at a boundary. */ +- if ((leftvertex == first) || (testtri.tri == m->dummytri)) { +- /* We're done. Return a triangle whose origin is the new vertex. */ +- lnext(horiz, *searchtri); +- lnext(horiz, m->recenttri); +- return success; +- } +- /* Finish finding the next edge around the newly inserted vertex. */ +- lnext(testtri, horiz); +- rightvertex = leftvertex; +- dest(horiz, leftvertex); +- } +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */ +-/* has a certain "nice" shape. This includes the */ +-/* polygons that result from deletion of a vertex or */ +-/* insertion of a segment. */ +-/* */ +-/* This is a conceptually difficult routine. The starting assumption is */ +-/* that we have a polygon with n sides. n - 1 of these sides are currently */ +-/* represented as edges in the mesh. One side, called the "base", need not */ +-/* be. */ +-/* */ +-/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */ +-/* triangles that share a common origin. For each of these triangles, the */ +-/* edge opposite the origin is one of the sides of the polygon. The */ +-/* primary edge of each triangle is the edge directed from the origin to */ +-/* the destination; note that this is not the same edge that is a side of */ +-/* the polygon. `firstedge' is the primary edge of the first triangle. */ +-/* From there, the triangles follow in counterclockwise order about the */ +-/* polygon, until `lastedge', the primary edge of the last triangle. */ +-/* `firstedge' and `lastedge' are probably connected to other triangles */ +-/* beyond the extremes of the fan, but their identity is not important, as */ +-/* long as the fan remains connected to them. */ +-/* */ +-/* Imagine the polygon oriented so that its base is at the bottom. This */ +-/* puts `firstedge' on the far right, and `lastedge' on the far left. */ +-/* The right vertex of the base is the destination of `firstedge', and the */ +-/* left vertex of the base is the apex of `lastedge'. */ +-/* */ +-/* The challenge now is to find the right sequence of edge flips to */ +-/* transform the fan into a Delaunay triangulation of the polygon. Each */ +-/* edge flip effectively removes one triangle from the fan, committing it */ +-/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */ +-/* is set, the final flip will be performed, resulting in a fan of one */ +-/* (useless?) triangle. If `doflip' is not set, the final flip is not */ +-/* performed, resulting in a fan of two triangles, and an unfinished */ +-/* triangular polygon that is not yet filled out with a single triangle. */ +-/* On completion of the routine, `lastedge' is the last remaining triangle, */ +-/* or the leftmost of the last two. */ +-/* */ +-/* Although the flips are performed in the order described above, the */ +-/* decisions about what flips to perform are made in precisely the reverse */ +-/* order. The recursive triangulatepolygon() procedure makes a decision, */ +-/* uses up to two recursive calls to triangulate the "subproblems" */ +-/* (polygons with fewer edges), and then performs an edge flip. */ +-/* */ +-/* The "decision" it makes is which vertex of the polygon should be */ +-/* connected to the base. This decision is made by testing every possible */ +-/* vertex. Once the best vertex is found, the two edges that connect this */ +-/* vertex to the base become the bases for two smaller polygons. These */ +-/* are triangulated recursively. Unfortunately, this approach can take */ +-/* O(n^2) time not only in the worst case, but in many common cases. It's */ +-/* rarely a big deal for vertex deletion, where n is rarely larger than */ +-/* ten, but it could be a big deal for segment insertion, especially if */ +-/* there's a lot of long segments that each cut many triangles. I ought to */ +-/* code a faster algorithm some day. */ +-/* */ +-/* The `edgecount' parameter is the number of sides of the polygon, */ +-/* including its base. `triflaws' is a flag that determines whether the */ +-/* new triangles should be tested for quality, and enqueued if they are */ +-/* bad. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void triangulatepolygon(struct mesh *m, struct behavior *b, +- struct otri *firstedge, struct otri *lastedge, +- int edgecount, int doflip, int triflaws) +-#else /* not ANSI_DECLARATORS */ +-void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws) +-struct mesh *m; +-struct behavior *b; +-struct otri *firstedge; +-struct otri *lastedge; +-int edgecount; +-int doflip; +-int triflaws; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri testtri; +- struct otri besttri; +- struct otri tempedge; +- vertex leftbasevertex, rightbasevertex; +- vertex testvertex; +- vertex bestvertex; +- int bestnumber; +- int i; +- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ +- +- /* Identify the base vertices. */ +- apex(*lastedge, leftbasevertex); +- dest(*firstedge, rightbasevertex); +- if (b->verbose > 2) { +- printf(" Triangulating interior polygon at edge\n"); +- printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0], +- leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]); +- } +- /* Find the best vertex to connect the base to. */ +- onext(*firstedge, besttri); +- dest(besttri, bestvertex); +- otricopy(besttri, testtri); +- bestnumber = 1; +- for (i = 2; i <= edgecount - 2; i++) { +- onextself(testtri); +- dest(testtri, testvertex); +- /* Is this a better vertex? */ +- if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex, +- testvertex) > 0.0) { +- otricopy(testtri, besttri); +- bestvertex = testvertex; +- bestnumber = i; +- } +- } +- if (b->verbose > 2) { +- printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0], +- bestvertex[1]); +- } +- if (bestnumber > 1) { +- /* Recursively triangulate the smaller polygon on the right. */ +- oprev(besttri, tempedge); +- triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1, +- triflaws); +- } +- if (bestnumber < edgecount - 2) { +- /* Recursively triangulate the smaller polygon on the left. */ +- sym(besttri, tempedge); +- triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1, +- triflaws); +- /* Find `besttri' again; it may have been lost to edge flips. */ +- sym(tempedge, besttri); +- } +- if (doflip) { +- /* Do one final edge flip. */ +- flip(m, b, &besttri); +-#ifndef CDT_ONLY +- if (triflaws) { +- /* Check the quality of the newly committed triangle. */ +- sym(besttri, testtri); +- testtriangle(m, b, &testtri); +- } +-#endif /* not CDT_ONLY */ +- } +- /* Return the base triangle. */ +- otricopy(besttri, *lastedge); +-} +- +-/*****************************************************************************/ +-/* */ +-/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */ +-/* that the triangulation remains Delaunay. */ +-/* */ +-/* The origin of `deltri' is deleted. The union of the triangles adjacent */ +-/* to this vertex is a polygon, for which the Delaunay triangulation is */ +-/* found. Two triangles are removed from the mesh. */ +-/* */ +-/* Only interior vertices that do not lie on segments or boundaries may be */ +-/* deleted. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri) +-#else /* not ANSI_DECLARATORS */ +-void deletevertex(m, b, deltri) +-struct mesh *m; +-struct behavior *b; +-struct otri *deltri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri countingtri; +- struct otri firstedge, lastedge; +- struct otri deltriright; +- struct otri lefttri, righttri; +- struct otri leftcasing, rightcasing; +- struct osub leftsubseg, rightsubseg; +- vertex delvertex; +- vertex neworg; +- int edgecount; +- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- org(*deltri, delvertex); +- if (b->verbose > 1) { +- printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]); +- } +- vertexdealloc(m, delvertex); +- +- /* Count the degree of the vertex being deleted. */ +- onext(*deltri, countingtri); +- edgecount = 1; +- while (!otriequal(*deltri, countingtri)) { +-#ifdef SELF_CHECK +- if (countingtri.tri == m->dummytri) { +- printf("Internal error in deletevertex():\n"); +- printf(" Attempt to delete boundary vertex.\n"); +- internalerror(); +- } +-#endif /* SELF_CHECK */ +- edgecount++; +- onextself(countingtri); +- } +- +-#ifdef SELF_CHECK +- if (edgecount < 3) { +- printf("Internal error in deletevertex():\n Vertex has degree %d.\n", +- edgecount); +- internalerror(); +- } +-#endif /* SELF_CHECK */ +- if (edgecount > 3) { +- /* Triangulate the polygon defined by the union of all triangles */ +- /* adjacent to the vertex being deleted. Check the quality of */ +- /* the resulting triangles. */ +- onext(*deltri, firstedge); +- oprev(*deltri, lastedge); +- triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0, +- !b->nobisect); +- } +- /* Splice out two triangles. */ +- lprev(*deltri, deltriright); +- dnext(*deltri, lefttri); +- sym(lefttri, leftcasing); +- oprev(deltriright, righttri); +- sym(righttri, rightcasing); +- bond(*deltri, leftcasing); +- bond(deltriright, rightcasing); +- tspivot(lefttri, leftsubseg); +- if (leftsubseg.ss != m->dummysub) { +- tsbond(*deltri, leftsubseg); +- } +- tspivot(righttri, rightsubseg); +- if (rightsubseg.ss != m->dummysub) { +- tsbond(deltriright, rightsubseg); +- } +- +- /* Set the new origin of `deltri' and check its quality. */ +- org(lefttri, neworg); +- setorg(*deltri, neworg); +- if (!b->nobisect) { +- testtriangle(m, b, deltri); +- } +- +- /* Delete the two spliced-out triangles. */ +- triangledealloc(m, lefttri.tri); +- triangledealloc(m, righttri.tri); +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* undovertex() Undo the most recent vertex insertion. */ +-/* */ +-/* Walks through the list of transformations (flips and a vertex insertion) */ +-/* in the reverse of the order in which they were done, and undoes them. */ +-/* The inserted vertex is removed from the triangulation and deallocated. */ +-/* Two triangles (possibly just one) are also deallocated. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void undovertex(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void undovertex(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri fliptri; +- struct otri botleft, botright, topright; +- struct otri botlcasing, botrcasing, toprcasing; +- struct otri gluetri; +- struct osub botlsubseg, botrsubseg, toprsubseg; +- vertex botvertex, rightvertex; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- /* Walk through the list of transformations (flips and a vertex insertion) */ +- /* in the reverse of the order in which they were done, and undo them. */ +- while (m->lastflip != (struct flipstacker *) NULL) { +- /* Find a triangle involved in the last unreversed transformation. */ +- decode(m->lastflip->flippedtri, fliptri); +- +- /* We are reversing one of three transformations: a trisection of one */ +- /* triangle into three (by inserting a vertex in the triangle), a */ +- /* bisection of two triangles into four (by inserting a vertex in an */ +- /* edge), or an edge flip. */ +- if (m->lastflip->prevflip == (struct flipstacker *) NULL) { +- /* Restore a triangle that was split into three triangles, */ +- /* so it is again one triangle. */ +- dprev(fliptri, botleft); +- lnextself(botleft); +- onext(fliptri, botright); +- lprevself(botright); +- sym(botleft, botlcasing); +- sym(botright, botrcasing); +- dest(botleft, botvertex); +- +- setapex(fliptri, botvertex); +- lnextself(fliptri); +- bond(fliptri, botlcasing); +- tspivot(botleft, botlsubseg); +- tsbond(fliptri, botlsubseg); +- lnextself(fliptri); +- bond(fliptri, botrcasing); +- tspivot(botright, botrsubseg); +- tsbond(fliptri, botrsubseg); +- +- /* Delete the two spliced-out triangles. */ +- triangledealloc(m, botleft.tri); +- triangledealloc(m, botright.tri); +- } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) { +- /* Restore two triangles that were split into four triangles, */ +- /* so they are again two triangles. */ +- lprev(fliptri, gluetri); +- sym(gluetri, botright); +- lnextself(botright); +- sym(botright, botrcasing); +- dest(botright, rightvertex); +- +- setorg(fliptri, rightvertex); +- bond(gluetri, botrcasing); +- tspivot(botright, botrsubseg); +- tsbond(gluetri, botrsubseg); +- +- /* Delete the spliced-out triangle. */ +- triangledealloc(m, botright.tri); +- +- sym(fliptri, gluetri); +- if (gluetri.tri != m->dummytri) { +- lnextself(gluetri); +- dnext(gluetri, topright); +- sym(topright, toprcasing); +- +- setorg(gluetri, rightvertex); +- bond(gluetri, toprcasing); +- tspivot(topright, toprsubseg); +- tsbond(gluetri, toprsubseg); +- +- /* Delete the spliced-out triangle. */ +- triangledealloc(m, topright.tri); +- } +- +- /* This is the end of the list, sneakily encoded. */ +- m->lastflip->prevflip = (struct flipstacker *) NULL; +- } else { +- /* Undo an edge flip. */ +- unflip(m, b, &fliptri); +- } +- +- /* Go on and process the next transformation. */ +- m->lastflip = m->lastflip->prevflip; +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/** **/ +-/** **/ +-/********* Mesh transformation routines end here *********/ +- +-/********* Divide-and-conquer Delaunay triangulation begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* The divide-and-conquer bounding box */ +-/* */ +-/* I originally implemented the divide-and-conquer and incremental Delaunay */ +-/* triangulations using the edge-based data structure presented by Guibas */ +-/* and Stolfi. Switching to a triangle-based data structure doubled the */ +-/* speed. However, I had to think of a few extra tricks to maintain the */ +-/* elegance of the original algorithms. */ +-/* */ +-/* The "bounding box" used by my variant of the divide-and-conquer */ +-/* algorithm uses one triangle for each edge of the convex hull of the */ +-/* triangulation. These bounding triangles all share a common apical */ +-/* vertex, which is represented by NULL and which represents nothing. */ +-/* The bounding triangles are linked in a circular fan about this NULL */ +-/* vertex, and the edges on the convex hull of the triangulation appear */ +-/* opposite the NULL vertex. You might find it easiest to imagine that */ +-/* the NULL vertex is a point in 3D space behind the center of the */ +-/* triangulation, and that the bounding triangles form a sort of cone. */ +-/* */ +-/* This bounding box makes it easy to represent degenerate cases. For */ +-/* instance, the triangulation of two vertices is a single edge. This edge */ +-/* is represented by two bounding box triangles, one on each "side" of the */ +-/* edge. These triangles are also linked together in a fan about the NULL */ +-/* vertex. */ +-/* */ +-/* The bounding box also makes it easy to traverse the convex hull, as the */ +-/* divide-and-conquer algorithm needs to do. */ +-/* */ +-/*****************************************************************************/ +- +-/*****************************************************************************/ +-/* */ +-/* vertexsort() Sort an array of vertices by x-coordinate, using the */ +-/* y-coordinate as a secondary key. */ +-/* */ +-/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */ +-/* the usual quicksort mistakes. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void vertexsort(vertex *sortarray, int arraysize) +-#else /* not ANSI_DECLARATORS */ +-void vertexsort(sortarray, arraysize) +-vertex *sortarray; +-int arraysize; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int left, right; +- int pivot; +- REAL pivotx, pivoty; +- vertex temp; +- +- if (arraysize == 2) { +- /* Recursive base case. */ +- if ((sortarray[0][0] > sortarray[1][0]) || +- ((sortarray[0][0] == sortarray[1][0]) && +- (sortarray[0][1] > sortarray[1][1]))) { +- temp = sortarray[1]; +- sortarray[1] = sortarray[0]; +- sortarray[0] = temp; +- } +- return; +- } +- /* Choose a random pivot to split the array. */ +- pivot = (int) randomnation((unsigned int) arraysize); +- if (pivot == arraysize)//JLM without this test, pivot can equal arraysize and segfault +- pivot--; +- pivotx = sortarray[pivot][0]; +- pivoty = sortarray[pivot][1]; +- /* Split the array. */ +- left = -1; +- right = arraysize; +- while (left < right) { +- /* Search for a vertex whose x-coordinate is too large for the left. */ +- do { +- left++; +- } while ((left <= right) && ((sortarray[left][0] < pivotx) || +- ((sortarray[left][0] == pivotx) && +- (sortarray[left][1] < pivoty)))); +- /* Search for a vertex whose x-coordinate is too small for the right. */ +- do { +- right--; +- } while ((left <= right) && ((sortarray[right][0] > pivotx) || +- ((sortarray[right][0] == pivotx) && +- (sortarray[right][1] > pivoty)))); +- if (left < right) { +- /* Swap the left and right vertices. */ +- temp = sortarray[left]; +- sortarray[left] = sortarray[right]; +- sortarray[right] = temp; +- } +- } +- if (left > 1) { +- /* Recursively sort the left subset. */ +- vertexsort(sortarray, left); +- } +- if (right < arraysize - 2) { +- /* Recursively sort the right subset. */ +- vertexsort(&sortarray[right + 1], arraysize - right - 1); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* vertexmedian() An order statistic algorithm, almost. Shuffles an */ +-/* array of vertices so that the first `median' vertices */ +-/* occur lexicographically before the remaining vertices. */ +-/* */ +-/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */ +-/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */ +-/* randomized linear time. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void vertexmedian(vertex *sortarray, int arraysize, int median, int axis) +-#else /* not ANSI_DECLARATORS */ +-void vertexmedian(sortarray, arraysize, median, axis) +-vertex *sortarray; +-int arraysize; +-int median; +-int axis; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int left, right; +- int pivot; +- REAL pivot1, pivot2; +- vertex temp; +- +- if (arraysize == 2) { +- /* Recursive base case. */ +- if ((sortarray[0][axis] > sortarray[1][axis]) || +- ((sortarray[0][axis] == sortarray[1][axis]) && +- (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { +- temp = sortarray[1]; +- sortarray[1] = sortarray[0]; +- sortarray[0] = temp; +- } +- return; +- } +- /* Choose a random pivot to split the array. */ +- pivot = (int) randomnation((unsigned int) arraysize); +- if (pivot == arraysize)//JLM/SES without this test, pivot can equal arraysize and segfault +- pivot--; +- pivot1 = sortarray[pivot][axis]; +- pivot2 = sortarray[pivot][1 - axis]; +- /* Split the array. */ +- left = -1; +- right = arraysize; +- while (left < right) { +- /* Search for a vertex whose x-coordinate is too large for the left. */ +- do { +- left++; +- } while ((left <= right) && ((sortarray[left][axis] < pivot1) || +- ((sortarray[left][axis] == pivot1) && +- (sortarray[left][1 - axis] < pivot2)))); +- /* Search for a vertex whose x-coordinate is too small for the right. */ +- do { +- right--; +- } while ((left <= right) && ((sortarray[right][axis] > pivot1) || +- ((sortarray[right][axis] == pivot1) && +- (sortarray[right][1 - axis] > pivot2)))); +- if (left < right) { +- /* Swap the left and right vertices. */ +- temp = sortarray[left]; +- sortarray[left] = sortarray[right]; +- sortarray[right] = temp; +- } +- } +- /* Unlike in vertexsort(), at most one of the following */ +- /* conditionals is true. */ +- if (left > median) { +- /* Recursively shuffle the left subset. */ +- vertexmedian(sortarray, left, median, axis); +- } +- if (right < median - 1) { +- /* Recursively shuffle the right subset. */ +- vertexmedian(&sortarray[right + 1], arraysize - right - 1, +- median - right - 1, axis); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */ +-/* conquer algorithm with alternating cuts. */ +-/* */ +-/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */ +-/* For the base case, subsets containing only two or three vertices are */ +-/* always sorted by x-coordinate. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void alternateaxes(vertex *sortarray, int arraysize, int axis) +-#else /* not ANSI_DECLARATORS */ +-void alternateaxes(sortarray, arraysize, axis) +-vertex *sortarray; +-int arraysize; +-int axis; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int divider; +- +- divider = arraysize >> 1; +- if (arraysize <= 3) { +- /* Recursive base case: subsets of two or three vertices will be */ +- /* handled specially, and should always be sorted by x-coordinate. */ +- axis = 0; +- } +- /* Partition with a horizontal or vertical cut. */ +- vertexmedian(sortarray, arraysize, divider, axis); +- /* Recursively partition the subsets with a cross cut. */ +- if (arraysize - divider >= 2) { +- if (divider >= 2) { +- alternateaxes(sortarray, divider, 1 - axis); +- } +- alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* mergehulls() Merge two adjacent Delaunay triangulations into a */ +-/* single Delaunay triangulation. */ +-/* */ +-/* This is similar to the algorithm given by Guibas and Stolfi, but uses */ +-/* a triangle-based, rather than edge-based, data structure. */ +-/* */ +-/* The algorithm walks up the gap between the two triangulations, knitting */ +-/* them together. As they are merged, some of their bounding triangles */ +-/* are converted into real triangles of the triangulation. The procedure */ +-/* pulls each hull's bounding triangles apart, then knits them together */ +-/* like the teeth of two gears. The Delaunay property determines, at each */ +-/* step, whether the next "tooth" is a bounding triangle of the left hull */ +-/* or the right. When a bounding triangle becomes real, its apex is */ +-/* changed from NULL to a real vertex. */ +-/* */ +-/* Only two new triangles need to be allocated. These become new bounding */ +-/* triangles at the top and bottom of the seam. They are used to connect */ +-/* the remaining bounding triangles (those that have not been converted */ +-/* into real triangles) into a single fan. */ +-/* */ +-/* On entry, `farleft' and `innerleft' are bounding triangles of the left */ +-/* triangulation. The origin of `farleft' is the leftmost vertex, and */ +-/* the destination of `innerleft' is the rightmost vertex of the */ +-/* triangulation. Similarly, `innerright' and `farright' are bounding */ +-/* triangles of the right triangulation. The origin of `innerright' and */ +-/* destination of `farright' are the leftmost and rightmost vertices. */ +-/* */ +-/* On completion, the origin of `farleft' is the leftmost vertex of the */ +-/* merged triangulation, and the destination of `farright' is the rightmost */ +-/* vertex. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, +- struct otri *innerleft, struct otri *innerright, +- struct otri *farright, int axis) +-#else /* not ANSI_DECLARATORS */ +-void mergehulls(m, b, farleft, innerleft, innerright, farright, axis) +-struct mesh *m; +-struct behavior *b; +-struct otri *farleft; +-struct otri *innerleft; +-struct otri *innerright; +-struct otri *farright; +-int axis; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri leftcand, rightcand; +- struct otri baseedge; +- struct otri nextedge; +- struct otri sidecasing, topcasing, outercasing; +- struct otri checkedge; +- vertex innerleftdest; +- vertex innerrightorg; +- vertex innerleftapex, innerrightapex; +- vertex farleftpt, farrightpt; +- vertex farleftapex, farrightapex; +- vertex lowerleft, lowerright; +- vertex upperleft, upperright; +- vertex nextapex; +- vertex checkvertex; +- int changemade; +- int badedge; +- int leftfinished, rightfinished; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- dest(*innerleft, innerleftdest); +- apex(*innerleft, innerleftapex); +- org(*innerright, innerrightorg); +- apex(*innerright, innerrightapex); +- /* Special treatment for horizontal cuts. */ +- if (b->dwyer && (axis == 1)) { +- org(*farleft, farleftpt); +- apex(*farleft, farleftapex); +- dest(*farright, farrightpt); +- apex(*farright, farrightapex); +- /* The pointers to the extremal vertices are shifted to point to the */ +- /* topmost and bottommost vertex of each hull, rather than the */ +- /* leftmost and rightmost vertices. */ +- while (farleftapex[1] < farleftpt[1]) { +- lnextself(*farleft); +- symself(*farleft); +- farleftpt = farleftapex; +- apex(*farleft, farleftapex); +- } +- sym(*innerleft, checkedge); +- apex(checkedge, checkvertex); +- while (checkvertex[1] > innerleftdest[1]) { +- lnext(checkedge, *innerleft); +- innerleftapex = innerleftdest; +- innerleftdest = checkvertex; +- sym(*innerleft, checkedge); +- apex(checkedge, checkvertex); +- } +- while (innerrightapex[1] < innerrightorg[1]) { +- lnextself(*innerright); +- symself(*innerright); +- innerrightorg = innerrightapex; +- apex(*innerright, innerrightapex); +- } +- sym(*farright, checkedge); +- apex(checkedge, checkvertex); +- while (checkvertex[1] > farrightpt[1]) { +- lnext(checkedge, *farright); +- farrightpt = checkvertex; +- sym(*farright, checkedge); +- apex(checkedge, checkvertex); +- } +- } +- /* Find a line tangent to and below both hulls. */ +- do { +- changemade = 0; +- /* Make innerleftdest the "bottommost" vertex of the left hull. */ +- if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) > +- 0.0) { +- lprevself(*innerleft); +- symself(*innerleft); +- innerleftdest = innerleftapex; +- apex(*innerleft, innerleftapex); +- changemade = 1; +- } +- /* Make innerrightorg the "bottommost" vertex of the right hull. */ +- if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) > +- 0.0) { +- lnextself(*innerright); +- symself(*innerright); +- innerrightorg = innerrightapex; +- apex(*innerright, innerrightapex); +- changemade = 1; +- } +- } while (changemade); +- /* Find the two candidates to be the next "gear tooth." */ +- sym(*innerleft, leftcand); +- sym(*innerright, rightcand); +- /* Create the bottom new bounding triangle. */ +- maketriangle(m, b, &baseedge); +- /* Connect it to the bounding boxes of the left and right triangulations. */ +- bond(baseedge, *innerleft); +- lnextself(baseedge); +- bond(baseedge, *innerright); +- lnextself(baseedge); +- setorg(baseedge, innerrightorg); +- setdest(baseedge, innerleftdest); +- /* Apex is intentionally left NULL. */ +- if (b->verbose > 2) { +- printf(" Creating base bounding "); +- printtriangle(m, b, &baseedge); +- } +- /* Fix the extreme triangles if necessary. */ +- org(*farleft, farleftpt); +- if (innerleftdest == farleftpt) { +- lnext(baseedge, *farleft); +- } +- dest(*farright, farrightpt); +- if (innerrightorg == farrightpt) { +- lprev(baseedge, *farright); +- } +- /* The vertices of the current knitting edge. */ +- lowerleft = innerleftdest; +- lowerright = innerrightorg; +- /* The candidate vertices for knitting. */ +- apex(leftcand, upperleft); +- apex(rightcand, upperright); +- /* Walk up the gap between the two triangulations, knitting them together. */ +- while (1) { +- /* Have we reached the top? (This isn't quite the right question, */ +- /* because even though the left triangulation might seem finished now, */ +- /* moving up on the right triangulation might reveal a new vertex of */ +- /* the left triangulation. And vice-versa.) */ +- leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <= +- 0.0; +- rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright) +- <= 0.0; +- if (leftfinished && rightfinished) { +- /* Create the top new bounding triangle. */ +- maketriangle(m, b, &nextedge); +- setorg(nextedge, lowerleft); +- setdest(nextedge, lowerright); +- /* Apex is intentionally left NULL. */ +- /* Connect it to the bounding boxes of the two triangulations. */ +- bond(nextedge, baseedge); +- lnextself(nextedge); +- bond(nextedge, rightcand); +- lnextself(nextedge); +- bond(nextedge, leftcand); +- if (b->verbose > 2) { +- printf(" Creating top bounding "); +- printtriangle(m, b, &nextedge); +- } +- /* Special treatment for horizontal cuts. */ +- if (b->dwyer && (axis == 1)) { +- org(*farleft, farleftpt); +- apex(*farleft, farleftapex); +- dest(*farright, farrightpt); +- apex(*farright, farrightapex); +- sym(*farleft, checkedge); +- apex(checkedge, checkvertex); +- /* The pointers to the extremal vertices are restored to the */ +- /* leftmost and rightmost vertices (rather than topmost and */ +- /* bottommost). */ +- while (checkvertex[0] < farleftpt[0]) { +- lprev(checkedge, *farleft); +- farleftpt = checkvertex; +- sym(*farleft, checkedge); +- apex(checkedge, checkvertex); +- } +- while (farrightapex[0] > farrightpt[0]) { +- lprevself(*farright); +- symself(*farright); +- farrightpt = farrightapex; +- apex(*farright, farrightapex); +- } +- } +- return; +- } +- /* Consider eliminating edges from the left triangulation. */ +- if (!leftfinished) { +- /* What vertex would be exposed if an edge were deleted? */ +- lprev(leftcand, nextedge); +- symself(nextedge); +- apex(nextedge, nextapex); +- /* If nextapex is NULL, then no vertex would be exposed; the */ +- /* triangulation would have been eaten right through. */ +- if (nextapex != (vertex) NULL) { +- /* Check whether the edge is Delaunay. */ +- badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > +- 0.0; +- while (badedge) { +- /* Eliminate the edge with an edge flip. As a result, the */ +- /* left triangulation will have one more boundary triangle. */ +- lnextself(nextedge); +- sym(nextedge, topcasing); +- lnextself(nextedge); +- sym(nextedge, sidecasing); +- bond(nextedge, topcasing); +- bond(leftcand, sidecasing); +- lnextself(leftcand); +- sym(leftcand, outercasing); +- lprevself(nextedge); +- bond(nextedge, outercasing); +- /* Correct the vertices to reflect the edge flip. */ +- setorg(leftcand, lowerleft); +- setdest(leftcand, NULL); +- setapex(leftcand, nextapex); +- setorg(nextedge, NULL); +- setdest(nextedge, upperleft); +- setapex(nextedge, nextapex); +- /* Consider the newly exposed vertex. */ +- upperleft = nextapex; +- /* What vertex would be exposed if another edge were deleted? */ +- otricopy(sidecasing, nextedge); +- apex(nextedge, nextapex); +- if (nextapex != (vertex) NULL) { +- /* Check whether the edge is Delaunay. */ +- badedge = incircle(m, b, lowerleft, lowerright, upperleft, +- nextapex) > 0.0; +- } else { +- /* Avoid eating right through the triangulation. */ +- badedge = 0; +- } +- } +- } +- } +- /* Consider eliminating edges from the right triangulation. */ +- if (!rightfinished) { +- /* What vertex would be exposed if an edge were deleted? */ +- lnext(rightcand, nextedge); +- symself(nextedge); +- apex(nextedge, nextapex); +- /* If nextapex is NULL, then no vertex would be exposed; the */ +- /* triangulation would have been eaten right through. */ +- if (nextapex != (vertex) NULL) { +- /* Check whether the edge is Delaunay. */ +- badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > +- 0.0; +- while (badedge) { +- /* Eliminate the edge with an edge flip. As a result, the */ +- /* right triangulation will have one more boundary triangle. */ +- lprevself(nextedge); +- sym(nextedge, topcasing); +- lprevself(nextedge); +- sym(nextedge, sidecasing); +- bond(nextedge, topcasing); +- bond(rightcand, sidecasing); +- lprevself(rightcand); +- sym(rightcand, outercasing); +- lnextself(nextedge); +- bond(nextedge, outercasing); +- /* Correct the vertices to reflect the edge flip. */ +- setorg(rightcand, NULL); +- setdest(rightcand, lowerright); +- setapex(rightcand, nextapex); +- setorg(nextedge, upperright); +- setdest(nextedge, NULL); +- setapex(nextedge, nextapex); +- /* Consider the newly exposed vertex. */ +- upperright = nextapex; +- /* What vertex would be exposed if another edge were deleted? */ +- otricopy(sidecasing, nextedge); +- apex(nextedge, nextapex); +- if (nextapex != (vertex) NULL) { +- /* Check whether the edge is Delaunay. */ +- badedge = incircle(m, b, lowerleft, lowerright, upperright, +- nextapex) > 0.0; +- } else { +- /* Avoid eating right through the triangulation. */ +- badedge = 0; +- } +- } +- } +- } +- if (leftfinished || (!rightfinished && +- (incircle(m, b, upperleft, lowerleft, lowerright, upperright) > +- 0.0))) { +- /* Knit the triangulations, adding an edge from `lowerleft' */ +- /* to `upperright'. */ +- bond(baseedge, rightcand); +- lprev(rightcand, baseedge); +- setdest(baseedge, lowerleft); +- lowerright = upperright; +- sym(baseedge, rightcand); +- apex(rightcand, upperright); +- } else { +- /* Knit the triangulations, adding an edge from `upperleft' */ +- /* to `lowerright'. */ +- bond(baseedge, leftcand); +- lnext(leftcand, baseedge); +- setorg(baseedge, lowerright); +- lowerleft = upperleft; +- sym(baseedge, leftcand); +- apex(leftcand, upperleft); +- } +- if (b->verbose > 2) { +- printf(" Connecting "); +- printtriangle(m, b, &baseedge); +- } +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* divconqrecurse() Recursively form a Delaunay triangulation by the */ +-/* divide-and-conquer method. */ +-/* */ +-/* Recursively breaks down the problem into smaller pieces, which are */ +-/* knitted together by mergehulls(). The base cases (problems of two or */ +-/* three vertices) are handled specially here. */ +-/* */ +-/* On completion, `farleft' and `farright' are bounding triangles such that */ +-/* the origin of `farleft' is the leftmost vertex (breaking ties by */ +-/* choosing the highest leftmost vertex), and the destination of */ +-/* `farright' is the rightmost vertex (breaking ties by choosing the */ +-/* lowest rightmost vertex). */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, +- int vertices, int axis, +- struct otri *farleft, struct otri *farright) +-#else /* not ANSI_DECLARATORS */ +-void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright) +-struct mesh *m; +-struct behavior *b; +-vertex *sortarray; +-int vertices; +-int axis; +-struct otri *farleft; +-struct otri *farright; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri midtri, tri1, tri2, tri3; +- struct otri innerleft, innerright; +- REAL area; +- int divider; +- +- if (b->verbose > 2) { +- printf(" Triangulating %d vertices.\n", vertices); +- } +- if (vertices == 2) { +- /* The triangulation of two vertices is an edge. An edge is */ +- /* represented by two bounding triangles. */ +- maketriangle(m, b, farleft); +- setorg(*farleft, sortarray[0]); +- setdest(*farleft, sortarray[1]); +- /* The apex is intentionally left NULL. */ +- maketriangle(m, b, farright); +- setorg(*farright, sortarray[1]); +- setdest(*farright, sortarray[0]); +- /* The apex is intentionally left NULL. */ +- bond(*farleft, *farright); +- lprevself(*farleft); +- lnextself(*farright); +- bond(*farleft, *farright); +- lprevself(*farleft); +- lnextself(*farright); +- bond(*farleft, *farright); +- if (b->verbose > 2) { +- printf(" Creating "); +- printtriangle(m, b, farleft); +- printf(" Creating "); +- printtriangle(m, b, farright); +- } +- /* Ensure that the origin of `farleft' is sortarray[0]. */ +- lprev(*farright, *farleft); +- return; +- } else if (vertices == 3) { +- /* The triangulation of three vertices is either a triangle (with */ +- /* three bounding triangles) or two edges (with four bounding */ +- /* triangles). In either case, four triangles are created. */ +- maketriangle(m, b, &midtri); +- maketriangle(m, b, &tri1); +- maketriangle(m, b, &tri2); +- maketriangle(m, b, &tri3); +- area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]); +- if (area == 0.0) { +- /* Three collinear vertices; the triangulation is two edges. */ +- setorg(midtri, sortarray[0]); +- setdest(midtri, sortarray[1]); +- setorg(tri1, sortarray[1]); +- setdest(tri1, sortarray[0]); +- setorg(tri2, sortarray[2]); +- setdest(tri2, sortarray[1]); +- setorg(tri3, sortarray[1]); +- setdest(tri3, sortarray[2]); +- /* All apices are intentionally left NULL. */ +- bond(midtri, tri1); +- bond(tri2, tri3); +- lnextself(midtri); +- lprevself(tri1); +- lnextself(tri2); +- lprevself(tri3); +- bond(midtri, tri3); +- bond(tri1, tri2); +- lnextself(midtri); +- lprevself(tri1); +- lnextself(tri2); +- lprevself(tri3); +- bond(midtri, tri1); +- bond(tri2, tri3); +- /* Ensure that the origin of `farleft' is sortarray[0]. */ +- otricopy(tri1, *farleft); +- /* Ensure that the destination of `farright' is sortarray[2]. */ +- otricopy(tri2, *farright); +- } else { +- /* The three vertices are not collinear; the triangulation is one */ +- /* triangle, namely `midtri'. */ +- setorg(midtri, sortarray[0]); +- setdest(tri1, sortarray[0]); +- setorg(tri3, sortarray[0]); +- /* Apices of tri1, tri2, and tri3 are left NULL. */ +- if (area > 0.0) { +- /* The vertices are in counterclockwise order. */ +- setdest(midtri, sortarray[1]); +- setorg(tri1, sortarray[1]); +- setdest(tri2, sortarray[1]); +- setapex(midtri, sortarray[2]); +- setorg(tri2, sortarray[2]); +- setdest(tri3, sortarray[2]); +- } else { +- /* The vertices are in clockwise order. */ +- setdest(midtri, sortarray[2]); +- setorg(tri1, sortarray[2]); +- setdest(tri2, sortarray[2]); +- setapex(midtri, sortarray[1]); +- setorg(tri2, sortarray[1]); +- setdest(tri3, sortarray[1]); +- } +- /* The topology does not depend on how the vertices are ordered. */ +- bond(midtri, tri1); +- lnextself(midtri); +- bond(midtri, tri2); +- lnextself(midtri); +- bond(midtri, tri3); +- lprevself(tri1); +- lnextself(tri2); +- bond(tri1, tri2); +- lprevself(tri1); +- lprevself(tri3); +- bond(tri1, tri3); +- lnextself(tri2); +- lprevself(tri3); +- bond(tri2, tri3); +- /* Ensure that the origin of `farleft' is sortarray[0]. */ +- otricopy(tri1, *farleft); +- /* Ensure that the destination of `farright' is sortarray[2]. */ +- if (area > 0.0) { +- otricopy(tri2, *farright); +- } else { +- lnext(*farleft, *farright); +- } +- } +- if (b->verbose > 2) { +- printf(" Creating "); +- printtriangle(m, b, &midtri); +- printf(" Creating "); +- printtriangle(m, b, &tri1); +- printf(" Creating "); +- printtriangle(m, b, &tri2); +- printf(" Creating "); +- printtriangle(m, b, &tri3); +- } +- return; +- } else { +- /* Split the vertices in half. */ +- divider = vertices >> 1; +- /* Recursively triangulate each half. */ +- divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft); +- divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis, +- &innerright, farright); +- if (b->verbose > 1) { +- printf(" Joining triangulations with %d and %d vertices.\n", divider, +- vertices - divider); +- } +- /* Merge the two triangulations into one. */ +- mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis); +- } +-} +- +-#ifdef ANSI_DECLARATORS +-long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost) +-#else /* not ANSI_DECLARATORS */ +-long removeghosts(m, b, startghost) +-struct mesh *m; +-struct behavior *b; +-struct otri *startghost; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri searchedge; +- struct otri dissolveedge; +- struct otri deadtriangle; +- vertex markorg; +- long hullsize; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- if (b->verbose) { +- printf(" Removing ghost triangles.\n"); +- } +- /* Find an edge on the convex hull to start point location from. */ +- lprev(*startghost, searchedge); +- symself(searchedge); +- m->dummytri[0] = encode(searchedge); +- /* Remove the bounding box and count the convex hull edges. */ +- otricopy(*startghost, dissolveedge); +- hullsize = 0; +- do { +- hullsize++; +- lnext(dissolveedge, deadtriangle); +- lprevself(dissolveedge); +- symself(dissolveedge); +- /* If no PSLG is involved, set the boundary markers of all the vertices */ +- /* on the convex hull. If a PSLG is used, this step is done later. */ +- if (!b->poly) { +- /* Watch out for the case where all the input vertices are collinear. */ +- if (dissolveedge.tri != m->dummytri) { +- org(dissolveedge, markorg); +- if (vertexmark(markorg) == 0) { +- setvertexmark(markorg, 1); +- } +- } +- } +- /* Remove a bounding triangle from a convex hull triangle. */ +- dissolve(dissolveedge); +- /* Find the next bounding triangle. */ +- sym(deadtriangle, dissolveedge); +- /* Delete the bounding triangle. */ +- triangledealloc(m, deadtriangle.tri); +- } while (!otriequal(dissolveedge, *startghost)); +- return hullsize; +-} +- +-/*****************************************************************************/ +-/* */ +-/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */ +-/* conquer method. */ +-/* */ +-/* Sorts the vertices, calls a recursive procedure to triangulate them, and */ +-/* removes the bounding box, setting boundary markers as appropriate. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-long divconqdelaunay(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-long divconqdelaunay(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex *sortarray; +- struct otri hullleft, hullright; +- int divider; +- int i, j; +- +- if (b->verbose) { +- printf(" Sorting vertices.\n"); +- } +- +- /* Allocate an array of pointers to vertices for sorting. */ +- sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex)); +- traversalinit(&m->vertices); +- for (i = 0; i < m->invertices; i++) { +- sortarray[i] = vertextraverse(m); +- } +- /* Sort the vertices. */ +- vertexsort(sortarray, m->invertices); +- /* Discard duplicate vertices, which can really mess up the algorithm. */ +- i = 0; +- for (j = 1; j < m->invertices; j++) { +- if ((sortarray[i][0] == sortarray[j][0]) +- && (sortarray[i][1] == sortarray[j][1])) { +- if (!b->quiet) { +- printf( +-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", +- sortarray[j][0], sortarray[j][1]); +- } +- setvertextype(sortarray[j], UNDEADVERTEX); +- m->undeads++; +- } else { +- i++; +- sortarray[i] = sortarray[j]; +- } +- } +- i++; +- if (b->dwyer) { +- /* Re-sort the array of vertices to accommodate alternating cuts. */ +- divider = i >> 1; +- if (i - divider >= 2) { +- if (divider >= 2) { +- alternateaxes(sortarray, divider, 1); +- } +- alternateaxes(&sortarray[divider], i - divider, 1); +- } +- } +- +- if (b->verbose) { +- printf(" Forming triangulation.\n"); +- } +- +- /* Form the Delaunay triangulation. */ +- divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright); +- trifree((void *) sortarray); +- +- return removeghosts(m, b, &hullleft); +-} +- +-/** **/ +-/** **/ +-/********* Divide-and-conquer Delaunay triangulation ends here *********/ +- +-/********* Incremental Delaunay triangulation begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* boundingbox() Form an "infinite" bounding triangle to insert vertices */ +-/* into. */ +-/* */ +-/* The vertices at "infinity" are assigned finite coordinates, which are */ +-/* used by the point location routines, but (mostly) ignored by the */ +-/* Delaunay edge flip routines. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void boundingbox(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void boundingbox(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri inftri; /* Handle for the triangular bounding box. */ +- REAL width; +- +- if (b->verbose) { +- printf(" Creating triangular bounding box.\n"); +- } +- /* Find the width (or height, whichever is larger) of the triangulation. */ +- width = m->xmax - m->xmin; +- if (m->ymax - m->ymin > width) { +- width = m->ymax - m->ymin; +- } +- if (width == 0.0) { +- width = 1.0; +- } +- /* Create the vertices of the bounding box. */ +- m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes); +- m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes); +- m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes); +- m->infvertex1[0] = m->xmin - 50.0 * width; +- m->infvertex1[1] = m->ymin - 40.0 * width; +- m->infvertex2[0] = m->xmax + 50.0 * width; +- m->infvertex2[1] = m->ymin - 40.0 * width; +- m->infvertex3[0] = 0.5 * (m->xmin + m->xmax); +- m->infvertex3[1] = m->ymax + 60.0 * width; +- +- /* Create the bounding box. */ +- maketriangle(m, b, &inftri); +- setorg(inftri, m->infvertex1); +- setdest(inftri, m->infvertex2); +- setapex(inftri, m->infvertex3); +- /* Link dummytri to the bounding box so we can always find an */ +- /* edge to begin searching (point location) from. */ +- m->dummytri[0] = (triangle) inftri.tri; +- if (b->verbose > 2) { +- printf(" Creating "); +- printtriangle(m, b, &inftri); +- } +-} +- +-#endif /* not REDUCED */ +- +-/*****************************************************************************/ +-/* */ +-/* removebox() Remove the "infinite" bounding triangle, setting boundary */ +-/* markers as appropriate. */ +-/* */ +-/* The triangular bounding box has three boundary triangles (one for each */ +-/* side of the bounding box), and a bunch of triangles fanning out from */ +-/* the three bounding box vertices (one triangle for each edge of the */ +-/* convex hull of the inner mesh). This routine removes these triangles. */ +-/* */ +-/* Returns the number of edges on the convex hull of the triangulation. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-long removebox(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-long removebox(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri deadtriangle; +- struct otri searchedge; +- struct otri checkedge; +- struct otri nextedge, finaledge, dissolveedge; +- vertex markorg; +- long hullsize; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- if (b->verbose) { +- printf(" Removing triangular bounding box.\n"); +- } +- /* Find a boundary triangle. */ +- nextedge.tri = m->dummytri; +- nextedge.orient = 0; +- symself(nextedge); +- /* Mark a place to stop. */ +- lprev(nextedge, finaledge); +- lnextself(nextedge); +- symself(nextedge); +- /* Find a triangle (on the boundary of the vertex set) that isn't */ +- /* a bounding box triangle. */ +- lprev(nextedge, searchedge); +- symself(searchedge); +- /* Check whether nextedge is another boundary triangle */ +- /* adjacent to the first one. */ +- lnext(nextedge, checkedge); +- symself(checkedge); +- if (checkedge.tri == m->dummytri) { +- /* Go on to the next triangle. There are only three boundary */ +- /* triangles, and this next triangle cannot be the third one, */ +- /* so it's safe to stop here. */ +- lprevself(searchedge); +- symself(searchedge); +- } +- /* Find a new boundary edge to search from, as the current search */ +- /* edge lies on a bounding box triangle and will be deleted. */ +- m->dummytri[0] = encode(searchedge); +- hullsize = -2l; +- while (!otriequal(nextedge, finaledge)) { +- hullsize++; +- lprev(nextedge, dissolveedge); +- symself(dissolveedge); +- /* If not using a PSLG, the vertices should be marked now. */ +- /* (If using a PSLG, markhull() will do the job.) */ +- if (!b->poly) { +- /* Be careful! One must check for the case where all the input */ +- /* vertices are collinear, and thus all the triangles are part of */ +- /* the bounding box. Otherwise, the setvertexmark() call below */ +- /* will cause a bad pointer reference. */ +- if (dissolveedge.tri != m->dummytri) { +- org(dissolveedge, markorg); +- if (vertexmark(markorg) == 0) { +- setvertexmark(markorg, 1); +- } +- } +- } +- /* Disconnect the bounding box triangle from the mesh triangle. */ +- dissolve(dissolveedge); +- lnext(nextedge, deadtriangle); +- sym(deadtriangle, nextedge); +- /* Get rid of the bounding box triangle. */ +- triangledealloc(m, deadtriangle.tri); +- /* Do we need to turn the corner? */ +- if (nextedge.tri == m->dummytri) { +- /* Turn the corner. */ +- otricopy(dissolveedge, nextedge); +- } +- } +- triangledealloc(m, finaledge.tri); +- +- trifree((void *) m->infvertex1); /* Deallocate the bounding box vertices. */ +- trifree((void *) m->infvertex2); +- trifree((void *) m->infvertex3); +- +- return hullsize; +-} +- +-#endif /* not REDUCED */ +- +-/*****************************************************************************/ +-/* */ +-/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */ +-/* inserting vertices. */ +-/* */ +-/* Returns the number of edges on the convex hull of the triangulation. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-long incrementaldelaunay(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-long incrementaldelaunay(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri starttri; +- vertex vertexloop; +- +- /* Create a triangular bounding box. */ +- boundingbox(m, b); +- if (b->verbose) { +- printf(" Incrementally inserting vertices.\n"); +- } +- traversalinit(&m->vertices); +- vertexloop = vertextraverse(m); +- while (vertexloop != (vertex) NULL) { +- starttri.tri = m->dummytri; +- if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0) +- == DUPLICATEVERTEX) { +- if (!b->quiet) { +- printf( +-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", +- vertexloop[0], vertexloop[1]); +- } +- setvertextype(vertexloop, UNDEADVERTEX); +- m->undeads++; +- } +- vertexloop = vertextraverse(m); +- } +- /* Remove the bounding box. */ +- return removebox(m, b); +-} +- +-#endif /* not REDUCED */ +- +-/** **/ +-/** **/ +-/********* Incremental Delaunay triangulation ends here *********/ +- +-/********* Sweepline Delaunay triangulation begins here *********/ +-/** **/ +-/** **/ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void eventheapinsert(struct event **heap, int heapsize, struct event *newevent) +-#else /* not ANSI_DECLARATORS */ +-void eventheapinsert(heap, heapsize, newevent) +-struct event **heap; +-int heapsize; +-struct event *newevent; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL eventx, eventy; +- int eventnum; +- int parent; +- int notdone; +- +- eventx = newevent->xkey; +- eventy = newevent->ykey; +- eventnum = heapsize; +- notdone = eventnum > 0; +- while (notdone) { +- parent = (eventnum - 1) >> 1; +- if ((heap[parent]->ykey < eventy) || +- ((heap[parent]->ykey == eventy) +- && (heap[parent]->xkey <= eventx))) { +- notdone = 0; +- } else { +- heap[eventnum] = heap[parent]; +- heap[eventnum]->heapposition = eventnum; +- +- eventnum = parent; +- notdone = eventnum > 0; +- } +- } +- heap[eventnum] = newevent; +- newevent->heapposition = eventnum; +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void eventheapify(struct event **heap, int heapsize, int eventnum) +-#else /* not ANSI_DECLARATORS */ +-void eventheapify(heap, heapsize, eventnum) +-struct event **heap; +-int heapsize; +-int eventnum; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct event *thisevent; +- REAL eventx, eventy; +- int leftchild, rightchild; +- int smallest; +- int notdone; +- +- thisevent = heap[eventnum]; +- eventx = thisevent->xkey; +- eventy = thisevent->ykey; +- leftchild = 2 * eventnum + 1; +- notdone = leftchild < heapsize; +- while (notdone) { +- if ((heap[leftchild]->ykey < eventy) || +- ((heap[leftchild]->ykey == eventy) +- && (heap[leftchild]->xkey < eventx))) { +- smallest = leftchild; +- } else { +- smallest = eventnum; +- } +- rightchild = leftchild + 1; +- if (rightchild < heapsize) { +- if ((heap[rightchild]->ykey < heap[smallest]->ykey) || +- ((heap[rightchild]->ykey == heap[smallest]->ykey) +- && (heap[rightchild]->xkey < heap[smallest]->xkey))) { +- smallest = rightchild; +- } +- } +- if (smallest == eventnum) { +- notdone = 0; +- } else { +- heap[eventnum] = heap[smallest]; +- heap[eventnum]->heapposition = eventnum; +- heap[smallest] = thisevent; +- thisevent->heapposition = smallest; +- +- eventnum = smallest; +- leftchild = 2 * eventnum + 1; +- notdone = leftchild < heapsize; +- } +- } +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void eventheapdelete(struct event **heap, int heapsize, int eventnum) +-#else /* not ANSI_DECLARATORS */ +-void eventheapdelete(heap, heapsize, eventnum) +-struct event **heap; +-int heapsize; +-int eventnum; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct event *moveevent; +- REAL eventx, eventy; +- int parent; +- int notdone; +- +- moveevent = heap[heapsize - 1]; +- if (eventnum > 0) { +- eventx = moveevent->xkey; +- eventy = moveevent->ykey; +- do { +- parent = (eventnum - 1) >> 1; +- if ((heap[parent]->ykey < eventy) || +- ((heap[parent]->ykey == eventy) +- && (heap[parent]->xkey <= eventx))) { +- notdone = 0; +- } else { +- heap[eventnum] = heap[parent]; +- heap[eventnum]->heapposition = eventnum; +- +- eventnum = parent; +- notdone = eventnum > 0; +- } +- } while (notdone); +- } +- heap[eventnum] = moveevent; +- moveevent->heapposition = eventnum; +- eventheapify(heap, heapsize - 1, eventnum); +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void createeventheap(struct mesh *m, struct event ***eventheap, +- struct event **events, struct event **freeevents) +-#else /* not ANSI_DECLARATORS */ +-void createeventheap(m, eventheap, events, freeevents) +-struct mesh *m; +-struct event ***eventheap; +-struct event **events; +-struct event **freeevents; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex thisvertex; +- int maxevents; +- int i; +- +- maxevents = (3 * m->invertices) / 2; +- *eventheap = (struct event **) trimalloc(maxevents * +- (int) sizeof(struct event *)); +- *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event)); +- traversalinit(&m->vertices); +- for (i = 0; i < m->invertices; i++) { +- thisvertex = vertextraverse(m); +- (*events)[i].eventptr = (void *) thisvertex; +- (*events)[i].xkey = thisvertex[0]; +- (*events)[i].ykey = thisvertex[1]; +- eventheapinsert(*eventheap, i, *events + i); +- } +- *freeevents = (struct event *) NULL; +- for (i = maxevents - 1; i >= m->invertices; i--) { +- (*events)[i].eventptr = (void *) *freeevents; +- *freeevents = *events + i; +- } +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite) +-#else /* not ANSI_DECLARATORS */ +-int rightofhyperbola(m, fronttri, newsite) +-struct mesh *m; +-struct otri *fronttri; +-vertex newsite; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex leftvertex, rightvertex; +- REAL dxa, dya, dxb, dyb; +- +- m->hyperbolacount++; +- +- dest(*fronttri, leftvertex); +- apex(*fronttri, rightvertex); +- if ((leftvertex[1] < rightvertex[1]) || +- ((leftvertex[1] == rightvertex[1]) && +- (leftvertex[0] < rightvertex[0]))) { +- if (newsite[0] >= rightvertex[0]) { +- return 1; +- } +- } else { +- if (newsite[0] <= leftvertex[0]) { +- return 0; +- } +- } +- dxa = leftvertex[0] - newsite[0]; +- dya = leftvertex[1] - newsite[1]; +- dxb = rightvertex[0] - newsite[0]; +- dyb = rightvertex[1] - newsite[1]; +- return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya); +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-REAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc) +-#else /* not ANSI_DECLARATORS */ +-REAL circletop(m, pa, pb, pc, ccwabc) +-struct mesh *m; +-vertex pa; +-vertex pb; +-vertex pc; +-REAL ccwabc; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL xac, yac, xbc, ybc, xab, yab; +- REAL aclen2, bclen2, ablen2; +- +- m->circletopcount++; +- +- xac = pa[0] - pc[0]; +- yac = pa[1] - pc[1]; +- xbc = pb[0] - pc[0]; +- ybc = pb[1] - pc[1]; +- xab = pa[0] - pb[0]; +- yab = pa[1] - pb[1]; +- aclen2 = xac * xac + yac * yac; +- bclen2 = xbc * xbc + ybc * ybc; +- ablen2 = xab * xab + yab * yab; +- return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) +- / (2.0 * ccwabc); +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-void check4deadevent(struct otri *checktri, struct event **freeevents, +- struct event **eventheap, int *heapsize) +-#else /* not ANSI_DECLARATORS */ +-void check4deadevent(checktri, freeevents, eventheap, heapsize) +-struct otri *checktri; +-struct event **freeevents; +-struct event **eventheap; +-int *heapsize; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct event *deadevent; +- vertex eventvertex; +- int eventnum; +- +- org(*checktri, eventvertex); +- if (eventvertex != (vertex) NULL) { +- deadevent = (struct event *) eventvertex; +- eventnum = deadevent->heapposition; +- deadevent->eventptr = (void *) *freeevents; +- *freeevents = deadevent; +- eventheapdelete(eventheap, *heapsize, eventnum); +- (*heapsize)--; +- setorg(*checktri, NULL); +- } +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-struct splaynode *splay(struct mesh *m, struct splaynode *splaytree, +- vertex searchpoint, struct otri *searchtri) +-#else /* not ANSI_DECLARATORS */ +-struct splaynode *splay(m, splaytree, searchpoint, searchtri) +-struct mesh *m; +-struct splaynode *splaytree; +-vertex searchpoint; +-struct otri *searchtri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct splaynode *child, *grandchild; +- struct splaynode *lefttree, *righttree; +- struct splaynode *leftright; +- vertex checkvertex; +- int rightofroot, rightofchild; +- +- if (splaytree == (struct splaynode *) NULL) { +- return (struct splaynode *) NULL; +- } +- dest(splaytree->keyedge, checkvertex); +- if (checkvertex == splaytree->keydest) { +- rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint); +- if (rightofroot) { +- otricopy(splaytree->keyedge, *searchtri); +- child = splaytree->rchild; +- } else { +- child = splaytree->lchild; +- } +- if (child == (struct splaynode *) NULL) { +- return splaytree; +- } +- dest(child->keyedge, checkvertex); +- if (checkvertex != child->keydest) { +- child = splay(m, child, searchpoint, searchtri); +- if (child == (struct splaynode *) NULL) { +- if (rightofroot) { +- splaytree->rchild = (struct splaynode *) NULL; +- } else { +- splaytree->lchild = (struct splaynode *) NULL; +- } +- return splaytree; +- } +- } +- rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint); +- if (rightofchild) { +- otricopy(child->keyedge, *searchtri); +- grandchild = splay(m, child->rchild, searchpoint, searchtri); +- child->rchild = grandchild; +- } else { +- grandchild = splay(m, child->lchild, searchpoint, searchtri); +- child->lchild = grandchild; +- } +- if (grandchild == (struct splaynode *) NULL) { +- if (rightofroot) { +- splaytree->rchild = child->lchild; +- child->lchild = splaytree; +- } else { +- splaytree->lchild = child->rchild; +- child->rchild = splaytree; +- } +- return child; +- } +- if (rightofchild) { +- if (rightofroot) { +- splaytree->rchild = child->lchild; +- child->lchild = splaytree; +- } else { +- splaytree->lchild = grandchild->rchild; +- grandchild->rchild = splaytree; +- } +- child->rchild = grandchild->lchild; +- grandchild->lchild = child; +- } else { +- if (rightofroot) { +- splaytree->rchild = grandchild->lchild; +- grandchild->lchild = splaytree; +- } else { +- splaytree->lchild = child->rchild; +- child->rchild = splaytree; +- } +- child->lchild = grandchild->rchild; +- grandchild->rchild = child; +- } +- return grandchild; +- } else { +- lefttree = splay(m, splaytree->lchild, searchpoint, searchtri); +- righttree = splay(m, splaytree->rchild, searchpoint, searchtri); +- +- pooldealloc(&m->splaynodes, (void *) splaytree); +- if (lefttree == (struct splaynode *) NULL) { +- return righttree; +- } else if (righttree == (struct splaynode *) NULL) { +- return lefttree; +- } else if (lefttree->rchild == (struct splaynode *) NULL) { +- lefttree->rchild = righttree->lchild; +- righttree->lchild = lefttree; +- return righttree; +- } else if (righttree->lchild == (struct splaynode *) NULL) { +- righttree->lchild = lefttree->rchild; +- lefttree->rchild = righttree; +- return lefttree; +- } else { +-/* printf("Holy Toledo!!!\n"); */ +- leftright = lefttree->rchild; +- while (leftright->rchild != (struct splaynode *) NULL) { +- leftright = leftright->rchild; +- } +- leftright->rchild = righttree; +- return lefttree; +- } +- } +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot, +- struct otri *newkey, vertex searchpoint) +-#else /* not ANSI_DECLARATORS */ +-struct splaynode *splayinsert(m, splayroot, newkey, searchpoint) +-struct mesh *m; +-struct splaynode *splayroot; +-struct otri *newkey; +-vertex searchpoint; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct splaynode *newsplaynode; +- +- newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes); +- otricopy(*newkey, newsplaynode->keyedge); +- dest(*newkey, newsplaynode->keydest); +- if (splayroot == (struct splaynode *) NULL) { +- newsplaynode->lchild = (struct splaynode *) NULL; +- newsplaynode->rchild = (struct splaynode *) NULL; +- } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) { +- newsplaynode->lchild = splayroot; +- newsplaynode->rchild = splayroot->rchild; +- splayroot->rchild = (struct splaynode *) NULL; +- } else { +- newsplaynode->lchild = splayroot->lchild; +- newsplaynode->rchild = splayroot; +- splayroot->lchild = (struct splaynode *) NULL; +- } +- return newsplaynode; +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-struct splaynode *circletopinsert(struct mesh *m, struct behavior *b, +- struct splaynode *splayroot, +- struct otri *newkey, +- vertex pa, vertex pb, vertex pc, REAL topy) +-#else /* not ANSI_DECLARATORS */ +-struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy) +-struct mesh *m; +-struct behavior *b; +-struct splaynode *splayroot; +-struct otri *newkey; +-vertex pa; +-vertex pb; +-vertex pc; +-REAL topy; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL ccwabc; +- REAL xac, yac, xbc, ybc; +- REAL aclen2, bclen2; +- REAL searchpoint[2]; +- struct otri dummytri; +- +- ccwabc = counterclockwise(m, b, pa, pb, pc); +- xac = pa[0] - pc[0]; +- yac = pa[1] - pc[1]; +- xbc = pb[0] - pc[0]; +- ybc = pb[1] - pc[1]; +- aclen2 = xac * xac + yac * yac; +- bclen2 = xbc * xbc + ybc * ybc; +- searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); +- searchpoint[1] = topy; +- return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri), +- newkey, (vertex) searchpoint); +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot, +- struct otri *bottommost, vertex searchvertex, +- struct otri *searchtri, int *farright) +-#else /* not ANSI_DECLARATORS */ +-struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex, +- searchtri, farright) +-struct mesh *m; +-struct splaynode *splayroot; +-struct otri *bottommost; +-vertex searchvertex; +-struct otri *searchtri; +-int *farright; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int farrightflag; +- triangle ptr; /* Temporary variable used by onext(). */ +- +- otricopy(*bottommost, *searchtri); +- splayroot = splay(m, splayroot, searchvertex, searchtri); +- +- farrightflag = 0; +- while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) { +- onextself(*searchtri); +- farrightflag = otriequal(*searchtri, *bottommost); +- } +- *farright = farrightflag; +- return splayroot; +-} +- +-#endif /* not REDUCED */ +- +-#ifndef REDUCED +- +-#ifdef ANSI_DECLARATORS +-long sweeplinedelaunay(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-long sweeplinedelaunay(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct event **eventheap; +- struct event *events; +- struct event *freeevents; +- struct event *nextevent; +- struct event *newevent; +- struct splaynode *splayroot; +- struct otri bottommost; +- struct otri searchtri; +- struct otri fliptri; +- struct otri lefttri, righttri, farlefttri, farrighttri; +- struct otri inserttri; +- vertex firstvertex, secondvertex; +- vertex nextvertex, lastvertex; +- vertex connectvertex; +- vertex leftvertex, midvertex, rightvertex; +- REAL lefttest, righttest; +- int heapsize; +- int check4events, farrightflag; +- triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ +- +- poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, +- SPLAYNODEPERBLOCK, 0); +- splayroot = (struct splaynode *) NULL; +- +- if (b->verbose) { +- printf(" Placing vertices in event heap.\n"); +- } +- createeventheap(m, &eventheap, &events, &freeevents); +- heapsize = m->invertices; +- +- if (b->verbose) { +- printf(" Forming triangulation.\n"); +- } +- maketriangle(m, b, &lefttri); +- maketriangle(m, b, &righttri); +- bond(lefttri, righttri); +- lnextself(lefttri); +- lprevself(righttri); +- bond(lefttri, righttri); +- lnextself(lefttri); +- lprevself(righttri); +- bond(lefttri, righttri); +- firstvertex = (vertex) eventheap[0]->eventptr; +- eventheap[0]->eventptr = (void *) freeevents; +- freeevents = eventheap[0]; +- eventheapdelete(eventheap, heapsize, 0); +- heapsize--; +- do { +- if (heapsize == 0) { +- printf("Error: Input vertices are all identical.\n"); +- triexit(1); +- } +- secondvertex = (vertex) eventheap[0]->eventptr; +- eventheap[0]->eventptr = (void *) freeevents; +- freeevents = eventheap[0]; +- eventheapdelete(eventheap, heapsize, 0); +- heapsize--; +- if ((firstvertex[0] == secondvertex[0]) && +- (firstvertex[1] == secondvertex[1])) { +- if (!b->quiet) { +- printf( +-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", +- secondvertex[0], secondvertex[1]); +- } +- setvertextype(secondvertex, UNDEADVERTEX); +- m->undeads++; +- } +- } while ((firstvertex[0] == secondvertex[0]) && +- (firstvertex[1] == secondvertex[1])); +- setorg(lefttri, firstvertex); +- setdest(lefttri, secondvertex); +- setorg(righttri, secondvertex); +- setdest(righttri, firstvertex); +- lprev(lefttri, bottommost); +- lastvertex = secondvertex; +- while (heapsize > 0) { +- nextevent = eventheap[0]; +- eventheapdelete(eventheap, heapsize, 0); +- heapsize--; +- check4events = 1; +- if (nextevent->xkey < m->xmin) { +- decode(nextevent->eventptr, fliptri); +- oprev(fliptri, farlefttri); +- check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); +- onext(fliptri, farrighttri); +- check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); +- +- if (otriequal(farlefttri, bottommost)) { +- lprev(fliptri, bottommost); +- } +- flip(m, b, &fliptri); +- setapex(fliptri, NULL); +- lprev(fliptri, lefttri); +- lnext(fliptri, righttri); +- sym(lefttri, farlefttri); +- +- if (randomnation(SAMPLERATE) == 0) { +- symself(fliptri); +- dest(fliptri, leftvertex); +- apex(fliptri, midvertex); +- org(fliptri, rightvertex); +- splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex, +- midvertex, rightvertex, nextevent->ykey); +- } +- } else { +- nextvertex = (vertex) nextevent->eventptr; +- if ((nextvertex[0] == lastvertex[0]) && +- (nextvertex[1] == lastvertex[1])) { +- if (!b->quiet) { +- printf( +-"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", +- nextvertex[0], nextvertex[1]); +- } +- setvertextype(nextvertex, UNDEADVERTEX); +- m->undeads++; +- check4events = 0; +- } else { +- lastvertex = nextvertex; +- +- splayroot = frontlocate(m, splayroot, &bottommost, nextvertex, +- &searchtri, &farrightflag); +-/* +- otricopy(bottommost, searchtri); +- farrightflag = 0; +- while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { +- onextself(searchtri); +- farrightflag = otriequal(searchtri, bottommost); +- } +-*/ +- +- check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); +- +- otricopy(searchtri, farrighttri); +- sym(searchtri, farlefttri); +- maketriangle(m, b, &lefttri); +- maketriangle(m, b, &righttri); +- dest(farrighttri, connectvertex); +- setorg(lefttri, connectvertex); +- setdest(lefttri, nextvertex); +- setorg(righttri, nextvertex); +- setdest(righttri, connectvertex); +- bond(lefttri, righttri); +- lnextself(lefttri); +- lprevself(righttri); +- bond(lefttri, righttri); +- lnextself(lefttri); +- lprevself(righttri); +- bond(lefttri, farlefttri); +- bond(righttri, farrighttri); +- if (!farrightflag && otriequal(farrighttri, bottommost)) { +- otricopy(lefttri, bottommost); +- } +- +- if (randomnation(SAMPLERATE) == 0) { +- splayroot = splayinsert(m, splayroot, &lefttri, nextvertex); +- } else if (randomnation(SAMPLERATE) == 0) { +- lnext(righttri, inserttri); +- splayroot = splayinsert(m, splayroot, &inserttri, nextvertex); +- } +- } +- } +- nextevent->eventptr = (void *) freeevents; +- freeevents = nextevent; +- +- if (check4events) { +- apex(farlefttri, leftvertex); +- dest(lefttri, midvertex); +- apex(lefttri, rightvertex); +- lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); +- if (lefttest > 0.0) { +- newevent = freeevents; +- freeevents = (struct event *) freeevents->eventptr; +- newevent->xkey = m->xminextreme; +- newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, +- lefttest); +- newevent->eventptr = (void *) encode(lefttri); +- eventheapinsert(eventheap, heapsize, newevent); +- heapsize++; +- setorg(lefttri, newevent); +- } +- apex(righttri, leftvertex); +- org(righttri, midvertex); +- apex(farrighttri, rightvertex); +- righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); +- if (righttest > 0.0) { +- newevent = freeevents; +- freeevents = (struct event *) freeevents->eventptr; +- newevent->xkey = m->xminextreme; +- newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, +- righttest); +- newevent->eventptr = (void *) encode(farrighttri); +- eventheapinsert(eventheap, heapsize, newevent); +- heapsize++; +- setorg(farrighttri, newevent); +- } +- } +- } +- +- pooldeinit(&m->splaynodes); +- lprevself(bottommost); +- return removeghosts(m, b, &bottommost); +-} +- +-#endif /* not REDUCED */ +- +-/** **/ +-/** **/ +-/********* Sweepline Delaunay triangulation ends here *********/ +- +-/********* General mesh construction routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* delaunay() Form a Delaunay triangulation. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-long delaunay(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-long delaunay(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- long hulledges; +- +- m->eextras = 0; +- initializetrisubpools(m, b); +- +-#ifdef REDUCED +- if (!b->quiet) { +- printf( +- "Constructing Delaunay triangulation by divide-and-conquer method.\n"); +- } +- hulledges = divconqdelaunay(m, b); +-#else /* not REDUCED */ +- if (!b->quiet) { +- printf("Constructing Delaunay triangulation "); +- if (b->incremental) { +- printf("by incremental method.\n"); +- } else if (b->sweepline) { +- printf("by sweepline method.\n"); +- } else { +- printf("by divide-and-conquer method.\n"); +- } +- } +- if (b->incremental) { +- hulledges = incrementaldelaunay(m, b); +- } else if (b->sweepline) { +- hulledges = sweeplinedelaunay(m, b); +- } else { +- hulledges = divconqdelaunay(m, b); +- } +-#endif /* not REDUCED */ +- +- if (m->triangles.items == 0) { +- /* The input vertices were all collinear, so there are no triangles. */ +- return 0l; +- } else { +- return hulledges; +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */ +-/* .poly) file. Used when the -r switch is used. */ +-/* */ +-/* Reads an .ele file and reconstructs the original mesh. If the -p switch */ +-/* is used, this procedure will also read a .poly file and reconstruct the */ +-/* subsegments of the original mesh. If the -a switch is used, this */ +-/* procedure will also read an .area file and set a maximum area constraint */ +-/* on each triangle. */ +-/* */ +-/* Vertices that are not corners of triangles, such as nodes on edges of */ +-/* subparametric elements, are discarded. */ +-/* */ +-/* This routine finds the adjacencies between triangles (and subsegments) */ +-/* by forming one stack of triangles for each vertex. Each triangle is on */ +-/* three different stacks simultaneously. Each triangle's subsegment */ +-/* pointers are used to link the items in each stack. This memory-saving */ +-/* feature makes the code harder to read. The most important thing to keep */ +-/* in mind is that each triangle is removed from a stack precisely when */ +-/* the corresponding pointer is adjusted to refer to a subsegment rather */ +-/* than the next triangle of the stack. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist, +- REAL *triangleattriblist, REAL *trianglearealist, +- int elements, int corners, int attribs, +- int *segmentlist,int *segmentmarkerlist, int numberofsegments) +-#else /* not ANSI_DECLARATORS */ +-int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist, +- elements, corners, attribs, segmentlist, segmentmarkerlist, +- numberofsegments) +-struct mesh *m; +-struct behavior *b; +-int *trianglelist; +-REAL *triangleattriblist; +-REAL *trianglearealist; +-int elements; +-int corners; +-int attribs; +-int *segmentlist; +-int *segmentmarkerlist; +-int numberofsegments; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-long reconstruct(struct mesh *m, struct behavior *b, char *elefilename, +- char *areafilename, char *polyfilename, FILE *polyfile) +-#else /* not ANSI_DECLARATORS */ +-long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile) +-struct mesh *m; +-struct behavior *b; +-char *elefilename; +-char *areafilename; +-char *polyfilename; +-FILE *polyfile; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- int vertexindex; +- int attribindex; +-#else /* not TRILIBRARY */ +- FILE *elefile; +- FILE *areafile; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int areaelements; +-#endif /* not TRILIBRARY */ +- struct otri triangleloop; +- struct otri triangleleft; +- struct otri checktri; +- struct otri checkleft; +- struct otri checkneighbor; +- struct osub subsegloop; +- triangle *vertexarray; +- triangle *prevlink; +- triangle nexttri; +- vertex tdest, tapex; +- vertex checkdest, checkapex; +- vertex shorg; +- vertex killvertex; +- vertex segmentorg, segmentdest; +- REAL area; +- int corner[3]; +- int end[2]; +- int killvertexindex; +- int incorners; +- int segmentmarkers; +- int boundmarker; +- int aroundvertex; +- long hullsize; +- int notfound; +- long elementnumber, segmentnumber; +- int i, j; +- triangle ptr; /* Temporary variable used by sym(). */ +- +-#ifdef TRILIBRARY +- m->inelements = elements; +- incorners = corners; +- if (incorners < 3) { +- printf("Error: Triangles must have at least 3 vertices.\n"); +- triexit(1); +- } +- m->eextras = attribs; +-#else /* not TRILIBRARY */ +- /* Read the triangles from an .ele file. */ +- if (!b->quiet) { +- printf("Opening %s.\n", elefilename); +- } +- elefile = fopen(elefilename, "r"); +- if (elefile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", elefilename); +- triexit(1); +- } +- /* Read number of triangles, number of vertices per triangle, and */ +- /* number of triangle attributes from .ele file. */ +- stringptr = readline(inputline, elefile, elefilename); +- m->inelements = (int) strtol(stringptr, &stringptr, 0); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- incorners = 3; +- } else { +- incorners = (int) strtol(stringptr, &stringptr, 0); +- if (incorners < 3) { +- printf("Error: Triangles in %s must have at least 3 vertices.\n", +- elefilename); +- triexit(1); +- } +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- m->eextras = 0; +- } else { +- m->eextras = (int) strtol(stringptr, &stringptr, 0); +- } +-#endif /* not TRILIBRARY */ +- +- initializetrisubpools(m, b); +- +- /* Create the triangles. */ +- for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) { +- maketriangle(m, b, &triangleloop); +- /* Mark the triangle as living. */ +- triangleloop.tri[3] = (triangle) triangleloop.tri; +- } +- +- segmentmarkers = 0; +- if (b->poly) { +-#ifdef TRILIBRARY +- m->insegments = numberofsegments; +- segmentmarkers = segmentmarkerlist != (int *) NULL; +-#else /* not TRILIBRARY */ +- /* Read number of segments and number of segment */ +- /* boundary markers from .poly file. */ +- stringptr = readline(inputline, polyfile, b->inpolyfilename); +- m->insegments = (int) strtol(stringptr, &stringptr, 0); +- stringptr = findfield(stringptr); +- if (*stringptr != '\0') { +- segmentmarkers = (int) strtol(stringptr, &stringptr, 0); +- } +-#endif /* not TRILIBRARY */ +- +- /* Create the subsegments. */ +- for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) { +- makesubseg(m, &subsegloop); +- /* Mark the subsegment as living. */ +- subsegloop.ss[2] = (subseg) subsegloop.ss; +- } +- } +- +-#ifdef TRILIBRARY +- vertexindex = 0; +- attribindex = 0; +-#else /* not TRILIBRARY */ +- if (b->vararea) { +- /* Open an .area file, check for consistency with the .ele file. */ +- if (!b->quiet) { +- printf("Opening %s.\n", areafilename); +- } +- areafile = fopen(areafilename, "r"); +- if (areafile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", areafilename); +- triexit(1); +- } +- stringptr = readline(inputline, areafile, areafilename); +- areaelements = (int) strtol(stringptr, &stringptr, 0); +- if (areaelements != m->inelements) { +- printf("Error: %s and %s disagree on number of triangles.\n", +- elefilename, areafilename); +- triexit(1); +- } +- } +-#endif /* not TRILIBRARY */ +- +- if (!b->quiet) { +- printf("Reconstructing mesh.\n"); +- } +- /* Allocate a temporary array that maps each vertex to some adjacent */ +- /* triangle. I took care to allocate all the permanent memory for */ +- /* triangles and subsegments first. */ +- vertexarray = (triangle *) trimalloc(m->vertices.items * +- (int) sizeof(triangle)); +- /* Each vertex is initially unrepresented. */ +- for (i = 0; i < m->vertices.items; i++) { +- vertexarray[i] = (triangle) m->dummytri; +- } +- +- if (b->verbose) { +- printf(" Assembling triangles.\n"); +- } +- /* Read the triangles from the .ele file, and link */ +- /* together those that share an edge. */ +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- elementnumber = b->firstnumber; +- while (triangleloop.tri != (triangle *) NULL) { +-#ifdef TRILIBRARY +- /* Copy the triangle's three corners. */ +- for (j = 0; j < 3; j++) { +- corner[j] = trianglelist[vertexindex++]; +- if ((corner[j] < b->firstnumber) || +- (corner[j] >= b->firstnumber + m->invertices)) { +- printf("Error: Triangle %ld has an invalid vertex index.\n", +- elementnumber); +- triexit(1); +- } +- } +-#else /* not TRILIBRARY */ +- /* Read triangle number and the triangle's three corners. */ +- stringptr = readline(inputline, elefile, elefilename); +- for (j = 0; j < 3; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Triangle %ld is missing vertex %d in %s.\n", +- elementnumber, j + 1, elefilename); +- triexit(1); +- } else { +- corner[j] = (int) strtol(stringptr, &stringptr, 0); +- if ((corner[j] < b->firstnumber) || +- (corner[j] >= b->firstnumber + m->invertices)) { +- printf("Error: Triangle %ld has an invalid vertex index.\n", +- elementnumber); +- triexit(1); +- } +- } +- } +-#endif /* not TRILIBRARY */ +- +- /* Find out about (and throw away) extra nodes. */ +- for (j = 3; j < incorners; j++) { +-#ifdef TRILIBRARY +- killvertexindex = trianglelist[vertexindex++]; +-#else /* not TRILIBRARY */ +- stringptr = findfield(stringptr); +- if (*stringptr != '\0') { +- killvertexindex = (int) strtol(stringptr, &stringptr, 0); +-#endif /* not TRILIBRARY */ +- if ((killvertexindex >= b->firstnumber) && +- (killvertexindex < b->firstnumber + m->invertices)) { +- /* Delete the non-corner vertex if it's not already deleted. */ +- killvertex = getvertex(m, b, killvertexindex); +- if (vertextype(killvertex) != DEADVERTEX) { +- vertexdealloc(m, killvertex); +- } +- } +-#ifndef TRILIBRARY +- } +-#endif /* not TRILIBRARY */ +- } +- +- /* Read the triangle's attributes. */ +- for (j = 0; j < m->eextras; j++) { +-#ifdef TRILIBRARY +- setelemattribute(triangleloop, j, triangleattriblist[attribindex++]); +-#else /* not TRILIBRARY */ +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- setelemattribute(triangleloop, j, 0); +- } else { +- setelemattribute(triangleloop, j, +- (REAL) strtod(stringptr, &stringptr)); +- } +-#endif /* not TRILIBRARY */ +- } +- +- if (b->vararea) { +-#ifdef TRILIBRARY +- area = trianglearealist[elementnumber - b->firstnumber]; +-#else /* not TRILIBRARY */ +- /* Read an area constraint from the .area file. */ +- stringptr = readline(inputline, areafile, areafilename); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- area = -1.0; /* No constraint on this triangle. */ +- } else { +- area = (REAL) strtod(stringptr, &stringptr); +- } +-#endif /* not TRILIBRARY */ +- setareabound(triangleloop, area); +- } +- +- /* Set the triangle's vertices. */ +- triangleloop.orient = 0; +- setorg(triangleloop, getvertex(m, b, corner[0])); +- setdest(triangleloop, getvertex(m, b, corner[1])); +- setapex(triangleloop, getvertex(m, b, corner[2])); +- /* Try linking the triangle to others that share these vertices. */ +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- /* Take the number for the origin of triangleloop. */ +- aroundvertex = corner[triangleloop.orient]; +- /* Look for other triangles having this vertex. */ +- nexttri = vertexarray[aroundvertex - b->firstnumber]; +- /* Link the current triangle to the next one in the stack. */ +- triangleloop.tri[6 + triangleloop.orient] = nexttri; +- /* Push the current triangle onto the stack. */ +- vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop); +- decode(nexttri, checktri); +- if (checktri.tri != m->dummytri) { +- dest(triangleloop, tdest); +- apex(triangleloop, tapex); +- /* Look for other triangles that share an edge. */ +- do { +- dest(checktri, checkdest); +- apex(checktri, checkapex); +- if (tapex == checkdest) { +- /* The two triangles share an edge; bond them together. */ +- lprev(triangleloop, triangleleft); +- bond(triangleleft, checktri); +- } +- if (tdest == checkapex) { +- /* The two triangles share an edge; bond them together. */ +- lprev(checktri, checkleft); +- bond(triangleloop, checkleft); +- } +- /* Find the next triangle in the stack. */ +- nexttri = checktri.tri[6 + checktri.orient]; +- decode(nexttri, checktri); +- } while (checktri.tri != m->dummytri); +- } +- } +- triangleloop.tri = triangletraverse(m); +- elementnumber++; +- } +- +-#ifdef TRILIBRARY +- vertexindex = 0; +-#else /* not TRILIBRARY */ +- fclose(elefile); +- if (b->vararea) { +- fclose(areafile); +- } +-#endif /* not TRILIBRARY */ +- +- hullsize = 0; /* Prepare to count the boundary edges. */ +- if (b->poly) { +- if (b->verbose) { +- printf(" Marking segments in triangulation.\n"); +- } +- /* Read the segments from the .poly file, and link them */ +- /* to their neighboring triangles. */ +- boundmarker = 0; +- traversalinit(&m->subsegs); +- subsegloop.ss = subsegtraverse(m); +- segmentnumber = b->firstnumber; +- while (subsegloop.ss != (subseg *) NULL) { +-#ifdef TRILIBRARY +- end[0] = segmentlist[vertexindex++]; +- end[1] = segmentlist[vertexindex++]; +- if (segmentmarkers) { +- boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber]; +- } +-#else /* not TRILIBRARY */ +- /* Read the endpoints of each segment, and possibly a boundary marker. */ +- stringptr = readline(inputline, polyfile, b->inpolyfilename); +- /* Skip the first (segment number) field. */ +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber, +- polyfilename); +- triexit(1); +- } else { +- end[0] = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %ld is missing its second endpoint in %s.\n", +- segmentnumber, polyfilename); +- triexit(1); +- } else { +- end[1] = (int) strtol(stringptr, &stringptr, 0); +- } +- if (segmentmarkers) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- boundmarker = 0; +- } else { +- boundmarker = (int) strtol(stringptr, &stringptr, 0); +- } +- } +-#endif /* not TRILIBRARY */ +- for (j = 0; j < 2; j++) { +- if ((end[j] < b->firstnumber) || +- (end[j] >= b->firstnumber + m->invertices)) { +- printf("Error: Segment %ld has an invalid vertex index.\n", +- segmentnumber); +- triexit(1); +- } +- } +- +- /* set the subsegment's vertices. */ +- subsegloop.ssorient = 0; +- segmentorg = getvertex(m, b, end[0]); +- segmentdest = getvertex(m, b, end[1]); +- setsorg(subsegloop, segmentorg); +- setsdest(subsegloop, segmentdest); +- setsegorg(subsegloop, segmentorg); +- setsegdest(subsegloop, segmentdest); +- setmark(subsegloop, boundmarker); +- /* Try linking the subsegment to triangles that share these vertices. */ +- for (subsegloop.ssorient = 0; subsegloop.ssorient < 2; +- subsegloop.ssorient++) { +- /* Take the number for the destination of subsegloop. */ +- aroundvertex = end[1 - subsegloop.ssorient]; +- /* Look for triangles having this vertex. */ +- prevlink = &vertexarray[aroundvertex - b->firstnumber]; +- nexttri = vertexarray[aroundvertex - b->firstnumber]; +- decode(nexttri, checktri); +- sorg(subsegloop, shorg); +- notfound = 1; +- /* Look for triangles having this edge. Note that I'm only */ +- /* comparing each triangle's destination with the subsegment; */ +- /* each triangle's apex is handled through a different vertex. */ +- /* Because each triangle appears on three vertices' lists, each */ +- /* occurrence of a triangle on a list can (and does) represent */ +- /* an edge. In this way, most edges are represented twice, and */ +- /* every triangle-subsegment bond is represented once. */ +- while (notfound && (checktri.tri != m->dummytri)) { +- dest(checktri, checkdest); +- if (shorg == checkdest) { +- /* We have a match. Remove this triangle from the list. */ +- *prevlink = checktri.tri[6 + checktri.orient]; +- /* Bond the subsegment to the triangle. */ +- tsbond(checktri, subsegloop); +- /* Check if this is a boundary edge. */ +- sym(checktri, checkneighbor); +- if (checkneighbor.tri == m->dummytri) { +- /* The next line doesn't insert a subsegment (because there's */ +- /* already one there), but it sets the boundary markers of */ +- /* the existing subsegment and its vertices. */ +- insertsubseg(m, b, &checktri, 1); +- hullsize++; +- } +- notfound = 0; +- } +- /* Find the next triangle in the stack. */ +- prevlink = &checktri.tri[6 + checktri.orient]; +- nexttri = checktri.tri[6 + checktri.orient]; +- decode(nexttri, checktri); +- } +- } +- subsegloop.ss = subsegtraverse(m); +- segmentnumber++; +- } +- } +- +- /* Mark the remaining edges as not being attached to any subsegment. */ +- /* Also, count the (yet uncounted) boundary edges. */ +- for (i = 0; i < m->vertices.items; i++) { +- /* Search the stack of triangles adjacent to a vertex. */ +- nexttri = vertexarray[i]; +- decode(nexttri, checktri); +- while (checktri.tri != m->dummytri) { +- /* Find the next triangle in the stack before this */ +- /* information gets overwritten. */ +- nexttri = checktri.tri[6 + checktri.orient]; +- /* No adjacent subsegment. (This overwrites the stack info.) */ +- tsdissolve(checktri); +- sym(checktri, checkneighbor); +- if (checkneighbor.tri == m->dummytri) { +- insertsubseg(m, b, &checktri, 1); +- hullsize++; +- } +- decode(nexttri, checktri); +- } +- } +- +- trifree((void *) vertexarray); +- return hullsize; +-} +- +-#endif /* not CDT_ONLY */ +- +-/** **/ +-/** **/ +-/********* General mesh construction routines end here *********/ +- +-/********* Segment insertion begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* finddirection() Find the first triangle on the path from one point */ +-/* to another. */ +-/* */ +-/* Finds the triangle that intersects a line segment drawn from the */ +-/* origin of `searchtri' to the point `searchpoint', and returns the result */ +-/* in `searchtri'. The origin of `searchtri' does not change, even though */ +-/* the triangle returned may differ from the one passed in. This routine */ +-/* is used to find the direction to move in to get from one point to */ +-/* another. */ +-/* */ +-/* The return value notes whether the destination or apex of the found */ +-/* triangle is collinear with the two points in question. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-enum finddirectionresult finddirection(struct mesh *m, struct behavior *b, +- struct otri *searchtri, +- vertex searchpoint) +-#else /* not ANSI_DECLARATORS */ +-enum finddirectionresult finddirection(m, b, searchtri, searchpoint) +-struct mesh *m; +-struct behavior *b; +-struct otri *searchtri; +-vertex searchpoint; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri checktri; +- vertex startvertex; +- vertex leftvertex, rightvertex; +- REAL leftccw, rightccw; +- int leftflag, rightflag; +- triangle ptr; /* Temporary variable used by onext() and oprev(). */ +- +- org(*searchtri, startvertex); +- dest(*searchtri, rightvertex); +- apex(*searchtri, leftvertex); +- /* Is `searchpoint' to the left? */ +- leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); +- leftflag = leftccw > 0.0; +- /* Is `searchpoint' to the right? */ +- rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); +- rightflag = rightccw > 0.0; +- if (leftflag && rightflag) { +- /* `searchtri' faces directly away from `searchpoint'. We could go left */ +- /* or right. Ask whether it's a triangle or a boundary on the left. */ +- onext(*searchtri, checktri); +- if (checktri.tri == m->dummytri) { +- leftflag = 0; +- } else { +- rightflag = 0; +- } +- } +- while (leftflag) { +- /* Turn left until satisfied. */ +- onextself(*searchtri); +- if (searchtri->tri == m->dummytri) { +- printf("Internal error in finddirection(): Unable to find a\n"); +- printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], +- startvertex[1]); +- printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); +- internalerror(); +- } +- apex(*searchtri, leftvertex); +- rightccw = leftccw; +- leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); +- leftflag = leftccw > 0.0; +- } +- while (rightflag) { +- /* Turn right until satisfied. */ +- oprevself(*searchtri); +- if (searchtri->tri == m->dummytri) { +- printf("Internal error in finddirection(): Unable to find a\n"); +- printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], +- startvertex[1]); +- printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); +- internalerror(); +- } +- dest(*searchtri, rightvertex); +- leftccw = rightccw; +- rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); +- rightflag = rightccw > 0.0; +- } +- if (leftccw == 0.0) { +- return LEFTCOLLINEAR; +- } else if (rightccw == 0.0) { +- return RIGHTCOLLINEAR; +- } else { +- return WITHIN; +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* segmentintersection() Find the intersection of an existing segment */ +-/* and a segment that is being inserted. Insert */ +-/* a vertex at the intersection, splitting an */ +-/* existing subsegment. */ +-/* */ +-/* The segment being inserted connects the apex of splittri to endpoint2. */ +-/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */ +-/* Hence, endpoints of the subsegment being split are the origin and */ +-/* destination of splittri. */ +-/* */ +-/* On completion, splittri is a handle having the newly inserted */ +-/* intersection point as its origin, and endpoint1 as its destination. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void segmentintersection(struct mesh *m, struct behavior *b, +- struct otri *splittri, struct osub *splitsubseg, +- vertex endpoint2) +-#else /* not ANSI_DECLARATORS */ +-void segmentintersection(m, b, splittri, splitsubseg, endpoint2) +-struct mesh *m; +-struct behavior *b; +-struct otri *splittri; +-struct osub *splitsubseg; +-vertex endpoint2; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct osub opposubseg; +- vertex endpoint1; +- vertex torg, tdest; +- vertex leftvertex, rightvertex; +- vertex newvertex; +- enum insertvertexresult success; +- REAL ex, ey; +- REAL tx, ty; +- REAL etx, ety; +- REAL split, denom; +- int i; +- triangle ptr; /* Temporary variable used by onext(). */ +- subseg sptr; /* Temporary variable used by snext(). */ +- +- /* Find the other three segment endpoints. */ +- apex(*splittri, endpoint1); +- org(*splittri, torg); +- dest(*splittri, tdest); +- /* Segment intersection formulae; see the Antonio reference. */ +- tx = tdest[0] - torg[0]; +- ty = tdest[1] - torg[1]; +- ex = endpoint2[0] - endpoint1[0]; +- ey = endpoint2[1] - endpoint1[1]; +- etx = torg[0] - endpoint2[0]; +- ety = torg[1] - endpoint2[1]; +- denom = ty * ex - tx * ey; +- if (denom == 0.0) { +- printf("Internal error in segmentintersection():"); +- printf(" Attempt to find intersection of parallel segments.\n"); +- internalerror(); +- } +- split = (ey * etx - ex * ety) / denom; +- /* Create the new vertex. */ +- newvertex = (vertex) poolalloc(&m->vertices); +- /* Interpolate its coordinate and attributes. */ +- for (i = 0; i < 2 + m->nextras; i++) { +- newvertex[i] = torg[i] + split * (tdest[i] - torg[i]); +- } +- setvertexmark(newvertex, mark(*splitsubseg)); +- setvertextype(newvertex, INPUTVERTEX); +- if (b->verbose > 1) { +- printf( +- " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", +- torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]); +- } +- /* Insert the intersection vertex. This should always succeed. */ +- success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0); +- if (success != SUCCESSFULVERTEX) { +- printf("Internal error in segmentintersection():\n"); +- printf(" Failure to split a segment.\n"); +- internalerror(); +- } +- /* Record a triangle whose origin is the new vertex. */ +- setvertex2tri(newvertex, encode(*splittri)); +- if (m->steinerleft > 0) { +- m->steinerleft--; +- } +- +- /* Divide the segment into two, and correct the segment endpoints. */ +- ssymself(*splitsubseg); +- spivot(*splitsubseg, opposubseg); +- sdissolve(*splitsubseg); +- sdissolve(opposubseg); +- do { +- setsegorg(*splitsubseg, newvertex); +- snextself(*splitsubseg); +- } while (splitsubseg->ss != m->dummysub); +- do { +- setsegorg(opposubseg, newvertex); +- snextself(opposubseg); +- } while (opposubseg.ss != m->dummysub); +- +- /* Inserting the vertex may have caused edge flips. We wish to rediscover */ +- /* the edge connecting endpoint1 to the new intersection vertex. */ +- finddirection(m, b, splittri, endpoint1); +- dest(*splittri, rightvertex); +- apex(*splittri, leftvertex); +- if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) { +- onextself(*splittri); +- } else if ((rightvertex[0] != endpoint1[0]) || +- (rightvertex[1] != endpoint1[1])) { +- printf("Internal error in segmentintersection():\n"); +- printf(" Topological inconsistency after splitting a segment.\n"); +- internalerror(); +- } +- /* `splittri' should have destination endpoint1. */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* scoutsegment() Scout the first triangle on the path from one endpoint */ +-/* to another, and check for completion (reaching the */ +-/* second endpoint), a collinear vertex, or the */ +-/* intersection of two segments. */ +-/* */ +-/* Returns one if the entire segment is successfully inserted, and zero if */ +-/* the job must be finished by conformingedge() or constrainededge(). */ +-/* */ +-/* If the first triangle on the path has the second endpoint as its */ +-/* destination or apex, a subsegment is inserted and the job is done. */ +-/* */ +-/* If the first triangle on the path has a destination or apex that lies on */ +-/* the segment, a subsegment is inserted connecting the first endpoint to */ +-/* the collinear vertex, and the search is continued from the collinear */ +-/* vertex. */ +-/* */ +-/* If the first triangle on the path has a subsegment opposite its origin, */ +-/* then there is a segment that intersects the segment being inserted. */ +-/* Their intersection vertex is inserted, splitting the subsegment. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, +- vertex endpoint2, int newmark) +-#else /* not ANSI_DECLARATORS */ +-int scoutsegment(m, b, searchtri, endpoint2, newmark) +-struct mesh *m; +-struct behavior *b; +-struct otri *searchtri; +-vertex endpoint2; +-int newmark; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri crosstri; +- struct osub crosssubseg; +- vertex leftvertex, rightvertex; +- enum finddirectionresult collinear; +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- collinear = finddirection(m, b, searchtri, endpoint2); +- dest(*searchtri, rightvertex); +- apex(*searchtri, leftvertex); +- if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) || +- ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) { +- /* The segment is already an edge in the mesh. */ +- if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) { +- lprevself(*searchtri); +- } +- /* Insert a subsegment, if there isn't already one there. */ +- insertsubseg(m, b, searchtri, newmark); +- return 1; +- } else if (collinear == LEFTCOLLINEAR) { +- /* We've collided with a vertex between the segment's endpoints. */ +- /* Make the collinear vertex be the triangle's origin. */ +- lprevself(*searchtri); +- insertsubseg(m, b, searchtri, newmark); +- /* Insert the remainder of the segment. */ +- return scoutsegment(m, b, searchtri, endpoint2, newmark); +- } else if (collinear == RIGHTCOLLINEAR) { +- /* We've collided with a vertex between the segment's endpoints. */ +- insertsubseg(m, b, searchtri, newmark); +- /* Make the collinear vertex be the triangle's origin. */ +- lnextself(*searchtri); +- /* Insert the remainder of the segment. */ +- return scoutsegment(m, b, searchtri, endpoint2, newmark); +- } else { +- lnext(*searchtri, crosstri); +- tspivot(crosstri, crosssubseg); +- /* Check for a crossing segment. */ +- if (crosssubseg.ss == m->dummysub) { +- return 0; +- } else { +- /* Insert a vertex at the intersection. */ +- segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2); +- otricopy(crosstri, *searchtri); +- insertsubseg(m, b, searchtri, newmark); +- /* Insert the remainder of the segment. */ +- return scoutsegment(m, b, searchtri, endpoint2, newmark); +- } +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* conformingedge() Force a segment into a conforming Delaunay */ +-/* triangulation by inserting a vertex at its midpoint, */ +-/* and recursively forcing in the two half-segments if */ +-/* necessary. */ +-/* */ +-/* Generates a sequence of subsegments connecting `endpoint1' to */ +-/* `endpoint2'. `newmark' is the boundary marker of the segment, assigned */ +-/* to each new splitting vertex and subsegment. */ +-/* */ +-/* Note that conformingedge() does not always maintain the conforming */ +-/* Delaunay property. Once inserted, segments are locked into place; */ +-/* vertices inserted later (to force other segments in) may render these */ +-/* fixed segments non-Delaunay. The conforming Delaunay property will be */ +-/* restored by enforcequality() by splitting encroached subsegments. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef REDUCED +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void conformingedge(struct mesh *m, struct behavior *b, +- vertex endpoint1, vertex endpoint2, int newmark) +-#else /* not ANSI_DECLARATORS */ +-void conformingedge(m, b, endpoint1, endpoint2, newmark) +-struct mesh *m; +-struct behavior *b; +-vertex endpoint1; +-vertex endpoint2; +-int newmark; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri searchtri1, searchtri2; +- struct osub brokensubseg; +- vertex newvertex; +- vertex midvertex1, midvertex2; +- enum insertvertexresult success; +- int i; +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (b->verbose > 2) { +- printf("Forcing segment into triangulation by recursive splitting:\n"); +- printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], +- endpoint2[0], endpoint2[1]); +- } +- /* Create a new vertex to insert in the middle of the segment. */ +- newvertex = (vertex) poolalloc(&m->vertices); +- /* Interpolate coordinates and attributes. */ +- for (i = 0; i < 2 + m->nextras; i++) { +- newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]); +- } +- setvertexmark(newvertex, newmark); +- setvertextype(newvertex, SEGMENTVERTEX); +- /* No known triangle to search from. */ +- searchtri1.tri = m->dummytri; +- /* Attempt to insert the new vertex. */ +- success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL, +- 0, 0); +- if (success == DUPLICATEVERTEX) { +- if (b->verbose > 2) { +- printf(" Segment intersects existing vertex (%.12g, %.12g).\n", +- newvertex[0], newvertex[1]); +- } +- /* Use the vertex that's already there. */ +- vertexdealloc(m, newvertex); +- org(searchtri1, newvertex); +- } else { +- if (success == VIOLATINGVERTEX) { +- if (b->verbose > 2) { +- printf(" Two segments intersect at (%.12g, %.12g).\n", +- newvertex[0], newvertex[1]); +- } +- /* By fluke, we've landed right on another segment. Split it. */ +- tspivot(searchtri1, brokensubseg); +- success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg, +- 0, 0); +- if (success != SUCCESSFULVERTEX) { +- printf("Internal error in conformingedge():\n"); +- printf(" Failure to split a segment.\n"); +- internalerror(); +- } +- } +- /* The vertex has been inserted successfully. */ +- if (m->steinerleft > 0) { +- m->steinerleft--; +- } +- } +- otricopy(searchtri1, searchtri2); +- /* `searchtri1' and `searchtri2' are fastened at their origins to */ +- /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */ +- /* respectively. First, we must get `searchtri2' out of the way so it */ +- /* won't be invalidated during the insertion of the first half of the */ +- /* segment. */ +- finddirection(m, b, &searchtri2, endpoint2); +- if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) { +- /* The origin of searchtri1 may have changed if a collision with an */ +- /* intervening vertex on the segment occurred. */ +- org(searchtri1, midvertex1); +- conformingedge(m, b, midvertex1, endpoint1, newmark); +- } +- if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) { +- /* The origin of searchtri2 may have changed if a collision with an */ +- /* intervening vertex on the segment occurred. */ +- org(searchtri2, midvertex2); +- conformingedge(m, b, midvertex2, endpoint2, newmark); +- } +-} +- +-#endif /* not CDT_ONLY */ +-#endif /* not REDUCED */ +- +-/*****************************************************************************/ +-/* */ +-/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */ +-/* recursively from an existing vertex. Pay special */ +-/* attention to stacking inverted triangles. */ +-/* */ +-/* This is a support routine for inserting segments into a constrained */ +-/* Delaunay triangulation. */ +-/* */ +-/* The origin of fixuptri is treated as if it has just been inserted, and */ +-/* the local Delaunay condition needs to be enforced. It is only enforced */ +-/* in one sector, however, that being the angular range defined by */ +-/* fixuptri. */ +-/* */ +-/* This routine also needs to make decisions regarding the "stacking" of */ +-/* triangles. (Read the description of constrainededge() below before */ +-/* reading on here, so you understand the algorithm.) If the position of */ +-/* the new vertex (the origin of fixuptri) indicates that the vertex before */ +-/* it on the polygon is a reflex vertex, then "stack" the triangle by */ +-/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */ +-/* triangles are identified.) */ +-/* */ +-/* Otherwise, check whether the vertex before that was a reflex vertex. */ +-/* If so, perform an edge flip, thereby eliminating an inverted triangle */ +-/* (popping it off the stack). The edge flip may result in the creation */ +-/* of a new inverted triangle, depending on whether or not the new vertex */ +-/* is visible to the vertex three edges behind on the polygon. */ +-/* */ +-/* If neither of the two vertices behind the new vertex are reflex */ +-/* vertices, fixuptri and fartri, the triangle opposite it, are not */ +-/* inverted; hence, ensure that the edge between them is locally Delaunay. */ +-/* */ +-/* `leftside' indicates whether or not fixuptri is to the left of the */ +-/* segment being inserted. (Imagine that the segment is pointing up from */ +-/* endpoint1 to endpoint2.) */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void delaunayfixup(struct mesh *m, struct behavior *b, +- struct otri *fixuptri, int leftside) +-#else /* not ANSI_DECLARATORS */ +-void delaunayfixup(m, b, fixuptri, leftside) +-struct mesh *m; +-struct behavior *b; +-struct otri *fixuptri; +-int leftside; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri neartri; +- struct otri fartri; +- struct osub faredge; +- vertex nearvertex, leftvertex, rightvertex, farvertex; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- lnext(*fixuptri, neartri); +- sym(neartri, fartri); +- /* Check if the edge opposite the origin of fixuptri can be flipped. */ +- if (fartri.tri == m->dummytri) { +- return; +- } +- tspivot(neartri, faredge); +- if (faredge.ss != m->dummysub) { +- return; +- } +- /* Find all the relevant vertices. */ +- apex(neartri, nearvertex); +- org(neartri, leftvertex); +- dest(neartri, rightvertex); +- apex(fartri, farvertex); +- /* Check whether the previous polygon vertex is a reflex vertex. */ +- if (leftside) { +- if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) { +- /* leftvertex is a reflex vertex too. Nothing can */ +- /* be done until a convex section is found. */ +- return; +- } +- } else { +- if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) { +- /* rightvertex is a reflex vertex too. Nothing can */ +- /* be done until a convex section is found. */ +- return; +- } +- } +- if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) { +- /* fartri is not an inverted triangle, and farvertex is not a reflex */ +- /* vertex. As there are no reflex vertices, fixuptri isn't an */ +- /* inverted triangle, either. Hence, test the edge between the */ +- /* triangles to ensure it is locally Delaunay. */ +- if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <= +- 0.0) { +- return; +- } +- /* Not locally Delaunay; go on to an edge flip. */ +- } /* else fartri is inverted; remove it from the stack by flipping. */ +- flip(m, b, &neartri); +- lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ +- /* Recursively process the two triangles that result from the flip. */ +- delaunayfixup(m, b, fixuptri, leftside); +- delaunayfixup(m, b, &fartri, leftside); +-} +- +-/*****************************************************************************/ +-/* */ +-/* constrainededge() Force a segment into a constrained Delaunay */ +-/* triangulation by deleting the triangles it */ +-/* intersects, and triangulating the polygons that */ +-/* form on each side of it. */ +-/* */ +-/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */ +-/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */ +-/* boundary marker of the segment. */ +-/* */ +-/* To insert a segment, every triangle whose interior intersects the */ +-/* segment is deleted. The union of these deleted triangles is a polygon */ +-/* (which is not necessarily monotone, but is close enough), which is */ +-/* divided into two polygons by the new segment. This routine's task is */ +-/* to generate the Delaunay triangulation of these two polygons. */ +-/* */ +-/* You might think of this routine's behavior as a two-step process. The */ +-/* first step is to walk from endpoint1 to endpoint2, flipping each edge */ +-/* encountered. This step creates a fan of edges connected to endpoint1, */ +-/* including the desired edge to endpoint2. The second step enforces the */ +-/* Delaunay condition on each side of the segment in an incremental manner: */ +-/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */ +-/* independently on each side of the segment), each vertex is "enforced" */ +-/* as if it had just been inserted, but affecting only the previous */ +-/* vertices. The result is the same as if the vertices had been inserted */ +-/* in the order they appear on the polygon, so the result is Delaunay. */ +-/* */ +-/* In truth, constrainededge() interleaves these two steps. The procedure */ +-/* walks from endpoint1 to endpoint2, and each time an edge is encountered */ +-/* and flipped, the newly exposed vertex (at the far end of the flipped */ +-/* edge) is "enforced" upon the previously flipped edges, usually affecting */ +-/* only one side of the polygon (depending upon which side of the segment */ +-/* the vertex falls on). */ +-/* */ +-/* The algorithm is complicated by the need to handle polygons that are not */ +-/* convex. Although the polygon is not necessarily monotone, it can be */ +-/* triangulated in a manner similar to the stack-based algorithms for */ +-/* monotone polygons. For each reflex vertex (local concavity) of the */ +-/* polygon, there will be an inverted triangle formed by one of the edge */ +-/* flips. (An inverted triangle is one with negative area - that is, its */ +-/* vertices are arranged in clockwise order - and is best thought of as a */ +-/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */ +-/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */ +-/* later. */ +-/* */ +-/* A reflex vertex is popped from the stack when a vertex is inserted that */ +-/* is visible to the reflex vertex. (However, if the vertex behind the */ +-/* reflex vertex is not visible to the reflex vertex, a new inverted */ +-/* triangle will take its place on the stack.) These details are handled */ +-/* by the delaunayfixup() routine above. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void constrainededge(struct mesh *m, struct behavior *b, +- struct otri *starttri, vertex endpoint2, int newmark) +-#else /* not ANSI_DECLARATORS */ +-void constrainededge(m, b, starttri, endpoint2, newmark) +-struct mesh *m; +-struct behavior *b; +-struct otri *starttri; +-vertex endpoint2; +-int newmark; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri fixuptri, fixuptri2; +- struct osub crosssubseg; +- vertex endpoint1; +- vertex farvertex; +- REAL area; +- int collision; +- int done; +- triangle ptr; /* Temporary variable used by sym() and oprev(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- org(*starttri, endpoint1); +- lnext(*starttri, fixuptri); +- flip(m, b, &fixuptri); +- /* `collision' indicates whether we have found a vertex directly */ +- /* between endpoint1 and endpoint2. */ +- collision = 0; +- done = 0; +- do { +- org(fixuptri, farvertex); +- /* `farvertex' is the extreme point of the polygon we are "digging" */ +- /* to get from endpoint1 to endpoint2. */ +- if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) { +- oprev(fixuptri, fixuptri2); +- /* Enforce the Delaunay condition around endpoint2. */ +- delaunayfixup(m, b, &fixuptri, 0); +- delaunayfixup(m, b, &fixuptri2, 1); +- done = 1; +- } else { +- /* Check whether farvertex is to the left or right of the segment */ +- /* being inserted, to decide which edge of fixuptri to dig */ +- /* through next. */ +- area = counterclockwise(m, b, endpoint1, endpoint2, farvertex); +- if (area == 0.0) { +- /* We've collided with a vertex between endpoint1 and endpoint2. */ +- collision = 1; +- oprev(fixuptri, fixuptri2); +- /* Enforce the Delaunay condition around farvertex. */ +- delaunayfixup(m, b, &fixuptri, 0); +- delaunayfixup(m, b, &fixuptri2, 1); +- done = 1; +- } else { +- if (area > 0.0) { /* farvertex is to the left of the segment. */ +- oprev(fixuptri, fixuptri2); +- /* Enforce the Delaunay condition around farvertex, on the */ +- /* left side of the segment only. */ +- delaunayfixup(m, b, &fixuptri2, 1); +- /* Flip the edge that crosses the segment. After the edge is */ +- /* flipped, one of its endpoints is the fan vertex, and the */ +- /* destination of fixuptri is the fan vertex. */ +- lprevself(fixuptri); +- } else { /* farvertex is to the right of the segment. */ +- delaunayfixup(m, b, &fixuptri, 0); +- /* Flip the edge that crosses the segment. After the edge is */ +- /* flipped, one of its endpoints is the fan vertex, and the */ +- /* destination of fixuptri is the fan vertex. */ +- oprevself(fixuptri); +- } +- /* Check for two intersecting segments. */ +- tspivot(fixuptri, crosssubseg); +- if (crosssubseg.ss == m->dummysub) { +- flip(m, b, &fixuptri); /* May create inverted triangle at left. */ +- } else { +- /* We've collided with a segment between endpoint1 and endpoint2. */ +- collision = 1; +- /* Insert a vertex at the intersection. */ +- segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2); +- done = 1; +- } +- } +- } +- } while (!done); +- /* Insert a subsegment to make the segment permanent. */ +- insertsubseg(m, b, &fixuptri, newmark); +- /* If there was a collision with an interceding vertex, install another */ +- /* segment connecting that vertex with endpoint2. */ +- if (collision) { +- /* Insert the remainder of the segment. */ +- if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) { +- constrainededge(m, b, &fixuptri, endpoint2, newmark); +- } +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* insertsegment() Insert a PSLG segment into a triangulation. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void insertsegment(struct mesh *m, struct behavior *b, +- vertex endpoint1, vertex endpoint2, int newmark) +-#else /* not ANSI_DECLARATORS */ +-void insertsegment(m, b, endpoint1, endpoint2, newmark) +-struct mesh *m; +-struct behavior *b; +-vertex endpoint1; +-vertex endpoint2; +-int newmark; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri searchtri1, searchtri2; +- triangle encodedtri; +- vertex checkvertex; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- if (b->verbose > 1) { +- printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", +- endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); +- } +- +- /* Find a triangle whose origin is the segment's first endpoint. */ +- checkvertex = (vertex) NULL; +- encodedtri = vertex2tri(endpoint1); +- if (encodedtri != (triangle) NULL) { +- decode(encodedtri, searchtri1); +- org(searchtri1, checkvertex); +- } +- if (checkvertex != endpoint1) { +- /* Find a boundary triangle to search from. */ +- searchtri1.tri = m->dummytri; +- searchtri1.orient = 0; +- symself(searchtri1); +- /* Search for the segment's first endpoint by point location. */ +- if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) { +- printf( +- "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); +- printf(" (%.12g, %.12g) in triangulation.\n", +- endpoint1[0], endpoint1[1]); +- internalerror(); +- } +- } +- /* Remember this triangle to improve subsequent point location. */ +- otricopy(searchtri1, m->recenttri); +- /* Scout the beginnings of a path from the first endpoint */ +- /* toward the second. */ +- if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) { +- /* The segment was easily inserted. */ +- return; +- } +- /* The first endpoint may have changed if a collision with an intervening */ +- /* vertex on the segment occurred. */ +- org(searchtri1, endpoint1); +- +- /* Find a triangle whose origin is the segment's second endpoint. */ +- checkvertex = (vertex) NULL; +- encodedtri = vertex2tri(endpoint2); +- if (encodedtri != (triangle) NULL) { +- decode(encodedtri, searchtri2); +- org(searchtri2, checkvertex); +- } +- if (checkvertex != endpoint2) { +- /* Find a boundary triangle to search from. */ +- searchtri2.tri = m->dummytri; +- searchtri2.orient = 0; +- symself(searchtri2); +- /* Search for the segment's second endpoint by point location. */ +- if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) { +- printf( +- "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); +- printf(" (%.12g, %.12g) in triangulation.\n", +- endpoint2[0], endpoint2[1]); +- internalerror(); +- } +- } +- /* Remember this triangle to improve subsequent point location. */ +- otricopy(searchtri2, m->recenttri); +- /* Scout the beginnings of a path from the second endpoint */ +- /* toward the first. */ +- if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) { +- /* The segment was easily inserted. */ +- return; +- } +- /* The second endpoint may have changed if a collision with an intervening */ +- /* vertex on the segment occurred. */ +- org(searchtri2, endpoint2); +- +-#ifndef REDUCED +-#ifndef CDT_ONLY +- if (b->splitseg) { +- /* Insert vertices to force the segment into the triangulation. */ +- conformingedge(m, b, endpoint1, endpoint2, newmark); +- } else { +-#endif /* not CDT_ONLY */ +-#endif /* not REDUCED */ +- /* Insert the segment directly into the triangulation. */ +- constrainededge(m, b, &searchtri1, endpoint2, newmark); +-#ifndef REDUCED +-#ifndef CDT_ONLY +- } +-#endif /* not CDT_ONLY */ +-#endif /* not REDUCED */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* markhull() Cover the convex hull of a triangulation with subsegments. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void markhull(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void markhull(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri hulltri; +- struct otri nexttri; +- struct otri starttri; +- triangle ptr; /* Temporary variable used by sym() and oprev(). */ +- +- /* Find a triangle handle on the hull. */ +- hulltri.tri = m->dummytri; +- hulltri.orient = 0; +- symself(hulltri); +- /* Remember where we started so we know when to stop. */ +- otricopy(hulltri, starttri); +- /* Go once counterclockwise around the convex hull. */ +- do { +- /* Create a subsegment if there isn't already one here. */ +- insertsubseg(m, b, &hulltri, 1); +- /* To find the next hull edge, go clockwise around the next vertex. */ +- lnextself(hulltri); +- oprev(hulltri, nexttri); +- while (nexttri.tri != m->dummytri) { +- otricopy(nexttri, hulltri); +- oprev(hulltri, nexttri); +- } +- } while (!otriequal(hulltri, starttri)); +-} +- +-/*****************************************************************************/ +-/* */ +-/* formskeleton() Create the segments of a triangulation, including PSLG */ +-/* segments and edges on the convex hull. */ +-/* */ +-/* The PSLG segments are read from a .poly file. The return value is the */ +-/* number of segments in the file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, +- int *segmentmarkerlist, int numberofsegments) +-#else /* not ANSI_DECLARATORS */ +-void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments) +-struct mesh *m; +-struct behavior *b; +-int *segmentlist; +-int *segmentmarkerlist; +-int numberofsegments; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void formskeleton(struct mesh *m, struct behavior *b, +- FILE *polyfile, char *polyfilename) +-#else /* not ANSI_DECLARATORS */ +-void formskeleton(m, b, polyfile, polyfilename) +-struct mesh *m; +-struct behavior *b; +-FILE *polyfile; +-char *polyfilename; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- char polyfilename[6]; +- int index; +-#else /* not TRILIBRARY */ +- char inputline[INPUTLINESIZE]; +- char *stringptr; +-#endif /* not TRILIBRARY */ +- vertex endpoint1, endpoint2; +- int segmentmarkers; +- int end1, end2; +- int boundmarker; +- int i; +- +- if (b->poly) { +- if (!b->quiet) { +- printf("Recovering segments in Delaunay triangulation.\n"); +- } +-#ifdef TRILIBRARY +- strcpy(polyfilename, "input"); +- m->insegments = numberofsegments; +- segmentmarkers = segmentmarkerlist != (int *) NULL; +- index = 0; +-#else /* not TRILIBRARY */ +- /* Read the segments from a .poly file. */ +- /* Read number of segments and number of boundary markers. */ +- stringptr = readline(inputline, polyfile, polyfilename); +- m->insegments = (int) strtol(stringptr, &stringptr, 0); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- segmentmarkers = 0; +- } else { +- segmentmarkers = (int) strtol(stringptr, &stringptr, 0); +- } +-#endif /* not TRILIBRARY */ +- /* If the input vertices are collinear, there is no triangulation, */ +- /* so don't try to insert segments. */ +- if (m->triangles.items == 0) { +- return; +- } +- +- /* If segments are to be inserted, compute a mapping */ +- /* from vertices to triangles. */ +- if (m->insegments > 0) { +- makevertexmap(m, b); +- if (b->verbose) { +- printf(" Recovering PSLG segments.\n"); +- } +- } +- +- boundmarker = 0; +- /* Read and insert the segments. */ +- for (i = 0; i < m->insegments; i++) { +-#ifdef TRILIBRARY +- end1 = segmentlist[index++]; +- end2 = segmentlist[index++]; +- if (segmentmarkers) { +- boundmarker = segmentmarkerlist[i]; +- } +-#else /* not TRILIBRARY */ +- stringptr = readline(inputline, polyfile, b->inpolyfilename); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %d has no endpoints in %s.\n", +- b->firstnumber + i, polyfilename); +- triexit(1); +- } else { +- end1 = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Segment %d is missing its second endpoint in %s.\n", +- b->firstnumber + i, polyfilename); +- triexit(1); +- } else { +- end2 = (int) strtol(stringptr, &stringptr, 0); +- } +- if (segmentmarkers) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- boundmarker = 0; +- } else { +- boundmarker = (int) strtol(stringptr, &stringptr, 0); +- } +- } +-#endif /* not TRILIBRARY */ +- if ((end1 < b->firstnumber) || +- (end1 >= b->firstnumber + m->invertices)) { +- if (!b->quiet) { +- printf("Warning: Invalid first endpoint of segment %d in %s.\n", +- b->firstnumber + i, polyfilename); +- } +- } else if ((end2 < b->firstnumber) || +- (end2 >= b->firstnumber + m->invertices)) { +- if (!b->quiet) { +- printf("Warning: Invalid second endpoint of segment %d in %s.\n", +- b->firstnumber + i, polyfilename); +- } +- } else { +- /* Find the vertices numbered `end1' and `end2'. */ +- endpoint1 = getvertex(m, b, end1); +- endpoint2 = getvertex(m, b, end2); +- if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { +- if (!b->quiet) { +- printf("Warning: Endpoints of segment %d are coincident in %s.\n", +- b->firstnumber + i, polyfilename); +- } +- } else { +- insertsegment(m, b, endpoint1, endpoint2, boundmarker); +- } +- } +- } +- } else { +- m->insegments = 0; +- } +- if (b->convex || !b->poly) { +- /* Enclose the convex hull with subsegments. */ +- if (b->verbose) { +- printf(" Enclosing convex hull with segments.\n"); +- } +- markhull(m, b); +- } +-} +- +-/** **/ +-/** **/ +-/********* Segment insertion ends here *********/ +- +-/********* Carving out holes and concavities begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* infecthull() Virally infect all of the triangles of the convex hull */ +-/* that are not protected by subsegments. Where there are */ +-/* subsegments, set boundary markers as appropriate. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void infecthull(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void infecthull(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri hulltri; +- struct otri nexttri; +- struct otri starttri; +- struct osub hullsubseg; +- triangle **deadtriangle; +- vertex horg, hdest; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (b->verbose) { +- printf(" Marking concavities (external triangles) for elimination.\n"); +- } +- /* Find a triangle handle on the hull. */ +- hulltri.tri = m->dummytri; +- hulltri.orient = 0; +- symself(hulltri); +- /* Remember where we started so we know when to stop. */ +- otricopy(hulltri, starttri); +- /* Go once counterclockwise around the convex hull. */ +- do { +- /* Ignore triangles that are already infected. */ +- if (!infected(hulltri)) { +- /* Is the triangle protected by a subsegment? */ +- tspivot(hulltri, hullsubseg); +- if (hullsubseg.ss == m->dummysub) { +- /* The triangle is not protected; infect it. */ +- if (!infected(hulltri)) { +- infect(hulltri); +- deadtriangle = (triangle **) poolalloc(&m->viri); +- *deadtriangle = hulltri.tri; +- } +- } else { +- /* The triangle is protected; set boundary markers if appropriate. */ +- if (mark(hullsubseg) == 0) { +- setmark(hullsubseg, 1); +- org(hulltri, horg); +- dest(hulltri, hdest); +- if (vertexmark(horg) == 0) { +- setvertexmark(horg, 1); +- } +- if (vertexmark(hdest) == 0) { +- setvertexmark(hdest, 1); +- } +- } +- } +- } +- /* To find the next hull edge, go clockwise around the next vertex. */ +- lnextself(hulltri); +- oprev(hulltri, nexttri); +- while (nexttri.tri != m->dummytri) { +- otricopy(nexttri, hulltri); +- oprev(hulltri, nexttri); +- } +- } while (!otriequal(hulltri, starttri)); +-} +- +-/*****************************************************************************/ +-/* */ +-/* plague() Spread the virus from all infected triangles to any neighbors */ +-/* not protected by subsegments. Delete all infected triangles. */ +-/* */ +-/* This is the procedure that actually creates holes and concavities. */ +-/* */ +-/* This procedure operates in two phases. The first phase identifies all */ +-/* the triangles that will die, and marks them as infected. They are */ +-/* marked to ensure that each triangle is added to the virus pool only */ +-/* once, so the procedure will terminate. */ +-/* */ +-/* The second phase actually eliminates the infected triangles. It also */ +-/* eliminates orphaned vertices. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void plague(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void plague(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri testtri; +- struct otri neighbor; +- triangle **virusloop; +- triangle **deadtriangle; +- struct osub neighborsubseg; +- vertex testvertex; +- vertex norg, ndest; +- vertex deadorg, deaddest, deadapex; +- int killorg; +- triangle ptr; /* Temporary variable used by sym() and onext(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (b->verbose) { +- printf(" Marking neighbors of marked triangles.\n"); +- } +- /* Loop through all the infected triangles, spreading the virus to */ +- /* their neighbors, then to their neighbors' neighbors. */ +- traversalinit(&m->viri); +- virusloop = (triangle **) traverse(&m->viri); +- while (virusloop != (triangle **) NULL) { +- testtri.tri = *virusloop; +- /* A triangle is marked as infected by messing with one of its pointers */ +- /* to subsegments, setting it to an illegal value. Hence, we have to */ +- /* temporarily uninfect this triangle so that we can examine its */ +- /* adjacent subsegments. */ +- uninfect(testtri); +- if (b->verbose > 2) { +- /* Assign the triangle an orientation for convenience in */ +- /* checking its vertices. */ +- testtri.orient = 0; +- org(testtri, deadorg); +- dest(testtri, deaddest); +- apex(testtri, deadapex); +- printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- deadorg[0], deadorg[1], deaddest[0], deaddest[1], +- deadapex[0], deadapex[1]); +- } +- /* Check each of the triangle's three neighbors. */ +- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { +- /* Find the neighbor. */ +- sym(testtri, neighbor); +- /* Check for a subsegment between the triangle and its neighbor. */ +- tspivot(testtri, neighborsubseg); +- /* Check if the neighbor is nonexistent or already infected. */ +- if ((neighbor.tri == m->dummytri) || infected(neighbor)) { +- if (neighborsubseg.ss != m->dummysub) { +- /* There is a subsegment separating the triangle from its */ +- /* neighbor, but both triangles are dying, so the subsegment */ +- /* dies too. */ +- subsegdealloc(m, neighborsubseg.ss); +- if (neighbor.tri != m->dummytri) { +- /* Make sure the subsegment doesn't get deallocated again */ +- /* later when the infected neighbor is visited. */ +- uninfect(neighbor); +- tsdissolve(neighbor); +- infect(neighbor); +- } +- } +- } else { /* The neighbor exists and is not infected. */ +- if (neighborsubseg.ss == m->dummysub) { +- /* There is no subsegment protecting the neighbor, so */ +- /* the neighbor becomes infected. */ +- if (b->verbose > 2) { +- org(neighbor, deadorg); +- dest(neighbor, deaddest); +- apex(neighbor, deadapex); +- printf( +- " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- deadorg[0], deadorg[1], deaddest[0], deaddest[1], +- deadapex[0], deadapex[1]); +- } +- infect(neighbor); +- /* Ensure that the neighbor's neighbors will be infected. */ +- deadtriangle = (triangle **) poolalloc(&m->viri); +- *deadtriangle = neighbor.tri; +- } else { /* The neighbor is protected by a subsegment. */ +- /* Remove this triangle from the subsegment. */ +- stdissolve(neighborsubseg); +- /* The subsegment becomes a boundary. Set markers accordingly. */ +- if (mark(neighborsubseg) == 0) { +- setmark(neighborsubseg, 1); +- } +- org(neighbor, norg); +- dest(neighbor, ndest); +- if (vertexmark(norg) == 0) { +- setvertexmark(norg, 1); +- } +- if (vertexmark(ndest) == 0) { +- setvertexmark(ndest, 1); +- } +- } +- } +- } +- /* Remark the triangle as infected, so it doesn't get added to the */ +- /* virus pool again. */ +- infect(testtri); +- virusloop = (triangle **) traverse(&m->viri); +- } +- +- if (b->verbose) { +- printf(" Deleting marked triangles.\n"); +- } +- +- traversalinit(&m->viri); +- virusloop = (triangle **) traverse(&m->viri); +- while (virusloop != (triangle **) NULL) { +- testtri.tri = *virusloop; +- +- /* Check each of the three corners of the triangle for elimination. */ +- /* This is done by walking around each vertex, checking if it is */ +- /* still connected to at least one live triangle. */ +- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { +- org(testtri, testvertex); +- /* Check if the vertex has already been tested. */ +- if (testvertex != (vertex) NULL) { +- killorg = 1; +- /* Mark the corner of the triangle as having been tested. */ +- setorg(testtri, NULL); +- /* Walk counterclockwise about the vertex. */ +- onext(testtri, neighbor); +- /* Stop upon reaching a boundary or the starting triangle. */ +- while ((neighbor.tri != m->dummytri) && +- (!otriequal(neighbor, testtri))) { +- if (infected(neighbor)) { +- /* Mark the corner of this triangle as having been tested. */ +- setorg(neighbor, NULL); +- } else { +- /* A live triangle. The vertex survives. */ +- killorg = 0; +- } +- /* Walk counterclockwise about the vertex. */ +- onextself(neighbor); +- } +- /* If we reached a boundary, we must walk clockwise as well. */ +- if (neighbor.tri == m->dummytri) { +- /* Walk clockwise about the vertex. */ +- oprev(testtri, neighbor); +- /* Stop upon reaching a boundary. */ +- while (neighbor.tri != m->dummytri) { +- if (infected(neighbor)) { +- /* Mark the corner of this triangle as having been tested. */ +- setorg(neighbor, NULL); +- } else { +- /* A live triangle. The vertex survives. */ +- killorg = 0; +- } +- /* Walk clockwise about the vertex. */ +- oprevself(neighbor); +- } +- } +- if (killorg) { +- if (b->verbose > 1) { +- printf(" Deleting vertex (%.12g, %.12g)\n", +- testvertex[0], testvertex[1]); +- } +- setvertextype(testvertex, UNDEADVERTEX); +- m->undeads++; +- } +- } +- } +- +- /* Record changes in the number of boundary edges, and disconnect */ +- /* dead triangles from their neighbors. */ +- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { +- sym(testtri, neighbor); +- if (neighbor.tri == m->dummytri) { +- /* There is no neighboring triangle on this edge, so this edge */ +- /* is a boundary edge. This triangle is being deleted, so this */ +- /* boundary edge is deleted. */ +- m->hullsize--; +- } else { +- /* Disconnect the triangle from its neighbor. */ +- dissolve(neighbor); +- /* There is a neighboring triangle on this edge, so this edge */ +- /* becomes a boundary edge when this triangle is deleted. */ +- m->hullsize++; +- } +- } +- /* Return the dead triangle to the pool of triangles. */ +- triangledealloc(m, testtri.tri); +- virusloop = (triangle **) traverse(&m->viri); +- } +- /* Empty the virus pool. */ +- poolrestart(&m->viri); +-} +- +-/*****************************************************************************/ +-/* */ +-/* regionplague() Spread regional attributes and/or area constraints */ +-/* (from a .poly file) throughout the mesh. */ +-/* */ +-/* This procedure operates in two phases. The first phase spreads an */ +-/* attribute and/or an area constraint through a (segment-bounded) region. */ +-/* The triangles are marked to ensure that each triangle is added to the */ +-/* virus pool only once, so the procedure will terminate. */ +-/* */ +-/* The second phase uninfects all infected triangles, returning them to */ +-/* normal. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void regionplague(struct mesh *m, struct behavior *b, +- REAL attribute, REAL area) +-#else /* not ANSI_DECLARATORS */ +-void regionplague(m, b, attribute, area) +-struct mesh *m; +-struct behavior *b; +-REAL attribute; +-REAL area; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri testtri; +- struct otri neighbor; +- triangle **virusloop; +- triangle **regiontri; +- struct osub neighborsubseg; +- vertex regionorg, regiondest, regionapex; +- triangle ptr; /* Temporary variable used by sym() and onext(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (b->verbose > 1) { +- printf(" Marking neighbors of marked triangles.\n"); +- } +- /* Loop through all the infected triangles, spreading the attribute */ +- /* and/or area constraint to their neighbors, then to their neighbors' */ +- /* neighbors. */ +- traversalinit(&m->viri); +- virusloop = (triangle **) traverse(&m->viri); +- while (virusloop != (triangle **) NULL) { +- testtri.tri = *virusloop; +- /* A triangle is marked as infected by messing with one of its pointers */ +- /* to subsegments, setting it to an illegal value. Hence, we have to */ +- /* temporarily uninfect this triangle so that we can examine its */ +- /* adjacent subsegments. */ +- uninfect(testtri); +- if (b->regionattrib) { +- /* Set an attribute. */ +- setelemattribute(testtri, m->eextras, attribute); +- } +- if (b->vararea) { +- /* Set an area constraint. */ +- setareabound(testtri, area); +- } +- if (b->verbose > 2) { +- /* Assign the triangle an orientation for convenience in */ +- /* checking its vertices. */ +- testtri.orient = 0; +- org(testtri, regionorg); +- dest(testtri, regiondest); +- apex(testtri, regionapex); +- printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- regionorg[0], regionorg[1], regiondest[0], regiondest[1], +- regionapex[0], regionapex[1]); +- } +- /* Check each of the triangle's three neighbors. */ +- for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { +- /* Find the neighbor. */ +- sym(testtri, neighbor); +- /* Check for a subsegment between the triangle and its neighbor. */ +- tspivot(testtri, neighborsubseg); +- /* Make sure the neighbor exists, is not already infected, and */ +- /* isn't protected by a subsegment. */ +- if ((neighbor.tri != m->dummytri) && !infected(neighbor) +- && (neighborsubseg.ss == m->dummysub)) { +- if (b->verbose > 2) { +- org(neighbor, regionorg); +- dest(neighbor, regiondest); +- apex(neighbor, regionapex); +- printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- regionorg[0], regionorg[1], regiondest[0], regiondest[1], +- regionapex[0], regionapex[1]); +- } +- /* Infect the neighbor. */ +- infect(neighbor); +- /* Ensure that the neighbor's neighbors will be infected. */ +- regiontri = (triangle **) poolalloc(&m->viri); +- *regiontri = neighbor.tri; +- } +- } +- /* Remark the triangle as infected, so it doesn't get added to the */ +- /* virus pool again. */ +- infect(testtri); +- virusloop = (triangle **) traverse(&m->viri); +- } +- +- /* Uninfect all triangles. */ +- if (b->verbose > 1) { +- printf(" Unmarking marked triangles.\n"); +- } +- traversalinit(&m->viri); +- virusloop = (triangle **) traverse(&m->viri); +- while (virusloop != (triangle **) NULL) { +- testtri.tri = *virusloop; +- uninfect(testtri); +- virusloop = (triangle **) traverse(&m->viri); +- } +- /* Empty the virus pool. */ +- poolrestart(&m->viri); +-} +- +-/*****************************************************************************/ +-/* */ +-/* carveholes() Find the holes and infect them. Find the area */ +-/* constraints and infect them. Infect the convex hull. */ +-/* Spread the infection and kill triangles. Spread the */ +-/* area constraints. */ +-/* */ +-/* This routine mainly calls other routines to carry out all these */ +-/* functions. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, +- REAL *regionlist, int regions) +-#else /* not ANSI_DECLARATORS */ +-void carveholes(m, b, holelist, holes, regionlist, regions) +-struct mesh *m; +-struct behavior *b; +-REAL *holelist; +-int holes; +-REAL *regionlist; +-int regions; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri searchtri; +- struct otri triangleloop; +- struct otri *regiontris; +- triangle **holetri; +- triangle **regiontri; +- vertex searchorg, searchdest; +- enum locateresult intersect; +- int i; +- triangle ptr; /* Temporary variable used by sym(). */ +- +- if (!(b->quiet || (b->noholes && b->convex))) { +- printf("Removing unwanted triangles.\n"); +- if (b->verbose && (holes > 0)) { +- printf(" Marking holes for elimination.\n"); +- } +- } +- +- if (regions > 0) { +- /* Allocate storage for the triangles in which region points fall. */ +- regiontris = (struct otri *) trimalloc(regions * +- (int) sizeof(struct otri)); +- } else { +- regiontris = (struct otri *) NULL; +- } +- +- if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { +- /* Initialize a pool of viri to be used for holes, concavities, */ +- /* regional attributes, and/or regional area constraints. */ +- poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0); +- } +- +- if (!b->convex) { +- /* Mark as infected any unprotected triangles on the boundary. */ +- /* This is one way by which concavities are created. */ +- infecthull(m, b); +- } +- +- if ((holes > 0) && !b->noholes) { +- /* Infect each triangle in which a hole lies. */ +- for (i = 0; i < 2 * holes; i += 2) { +- /* Ignore holes that aren't within the bounds of the mesh. */ +- if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax) +- && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) { +- /* Start searching from some triangle on the outer boundary. */ +- searchtri.tri = m->dummytri; +- searchtri.orient = 0; +- symself(searchtri); +- /* Ensure that the hole is to the left of this boundary edge; */ +- /* otherwise, locate() will falsely report that the hole */ +- /* falls within the starting triangle. */ +- org(searchtri, searchorg); +- dest(searchtri, searchdest); +- if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) > +- 0.0) { +- /* Find a triangle that contains the hole. */ +- intersect = locate(m, b, &holelist[i], &searchtri); +- if ((intersect != OUTSIDE) && (!infected(searchtri))) { +- /* Infect the triangle. This is done by marking the triangle */ +- /* as infected and including the triangle in the virus pool. */ +- infect(searchtri); +- holetri = (triangle **) poolalloc(&m->viri); +- *holetri = searchtri.tri; +- } +- } +- } +- } +- } +- +- /* Now, we have to find all the regions BEFORE we carve the holes, because */ +- /* locate() won't work when the triangulation is no longer convex. */ +- /* (Incidentally, this is the reason why regional attributes and area */ +- /* constraints can't be used when refining a preexisting mesh, which */ +- /* might not be convex; they can only be used with a freshly */ +- /* triangulated PSLG.) */ +- if (regions > 0) { +- /* Find the starting triangle for each region. */ +- for (i = 0; i < regions; i++) { +- regiontris[i].tri = m->dummytri; +- /* Ignore region points that aren't within the bounds of the mesh. */ +- if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) && +- (regionlist[4 * i + 1] >= m->ymin) && +- (regionlist[4 * i + 1] <= m->ymax)) { +- /* Start searching from some triangle on the outer boundary. */ +- searchtri.tri = m->dummytri; +- searchtri.orient = 0; +- symself(searchtri); +- /* Ensure that the region point is to the left of this boundary */ +- /* edge; otherwise, locate() will falsely report that the */ +- /* region point falls within the starting triangle. */ +- org(searchtri, searchorg); +- dest(searchtri, searchdest); +- if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) > +- 0.0) { +- /* Find a triangle that contains the region point. */ +- intersect = locate(m, b, ®ionlist[4 * i], &searchtri); +- if ((intersect != OUTSIDE) && (!infected(searchtri))) { +- /* Record the triangle for processing after the */ +- /* holes have been carved. */ +- otricopy(searchtri, regiontris[i]); +- } +- } +- } +- } +- } +- +- if (m->viri.items > 0) { +- /* Carve the holes and concavities. */ +- plague(m, b); +- } +- /* The virus pool should be empty now. */ +- +- if (regions > 0) { +- if (!b->quiet) { +- if (b->regionattrib) { +- if (b->vararea) { +- printf("Spreading regional attributes and area constraints.\n"); +- } else { +- printf("Spreading regional attributes.\n"); +- } +- } else { +- printf("Spreading regional area constraints.\n"); +- } +- } +- if (b->regionattrib && !b->refine) { +- /* Assign every triangle a regional attribute of zero. */ +- traversalinit(&m->triangles); +- triangleloop.orient = 0; +- triangleloop.tri = triangletraverse(m); +- while (triangleloop.tri != (triangle *) NULL) { +- setelemattribute(triangleloop, m->eextras, 0.0); +- triangleloop.tri = triangletraverse(m); +- } +- } +- for (i = 0; i < regions; i++) { +- if (regiontris[i].tri != m->dummytri) { +- /* Make sure the triangle under consideration still exists. */ +- /* It may have been eaten by the virus. */ +- if (!deadtri(regiontris[i].tri)) { +- /* Put one triangle in the virus pool. */ +- infect(regiontris[i]); +- regiontri = (triangle **) poolalloc(&m->viri); +- *regiontri = regiontris[i].tri; +- /* Apply one region's attribute and/or area constraint. */ +- regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]); +- /* The virus pool should be empty now. */ +- } +- } +- } +- if (b->regionattrib && !b->refine) { +- /* Note the fact that each triangle has an additional attribute. */ +- m->eextras++; +- } +- } +- +- /* Free up memory. */ +- if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { +- pooldeinit(&m->viri); +- } +- if (regions > 0) { +- trifree((void *) regiontris); +- } +-} +- +-/** **/ +-/** **/ +-/********* Carving out holes and concavities ends here *********/ +- +-/********* Mesh quality maintenance begins here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* tallyencs() Traverse the entire list of subsegments, and check each */ +-/* to see if it is encroached. If so, add it to the list. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void tallyencs(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void tallyencs(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct osub subsegloop; +- +- traversalinit(&m->subsegs); +- subsegloop.ssorient = 0; +- subsegloop.ss = subsegtraverse(m); +- while (subsegloop.ss != (subseg *) NULL) { +- /* If the segment is encroached, add it to the list. */ +- checkseg4encroach(m, b, &subsegloop); +- subsegloop.ss = subsegtraverse(m); +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* precisionerror() Print an error message for precision problems. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-void precisionerror() +-{ +- printf("Try increasing the area criterion and/or reducing the minimum\n"); +- printf(" allowable angle so that tiny triangles are not created.\n"); +-#ifdef SINGLE +- printf("Alternatively, try recompiling me with double precision\n"); +- printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); +- printf(" source file or \"-DSINGLE\" from the makefile).\n"); +-#endif /* SINGLE */ +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* splitencsegs() Split all the encroached subsegments. */ +-/* */ +-/* Each encroached subsegment is repaired by splitting it - inserting a */ +-/* vertex at or near its midpoint. Newly inserted vertices may encroach */ +-/* upon other subsegments; these are also repaired. */ +-/* */ +-/* `triflaws' is a flag that specifies whether one should take note of new */ +-/* bad triangles that result from inserting vertices to repair encroached */ +-/* subsegments. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void splitencsegs(struct mesh *m, struct behavior *b, int triflaws) +-#else /* not ANSI_DECLARATORS */ +-void splitencsegs(m, b, triflaws) +-struct mesh *m; +-struct behavior *b; +-int triflaws; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri enctri; +- struct otri testtri; +- struct osub testsh; +- struct osub currentenc; +- struct badsubseg *encloop; +- vertex eorg, edest, eapex; +- vertex newvertex; +- enum insertvertexresult success; +- REAL segmentlength, nearestpoweroftwo; +- REAL split; +- REAL multiplier, divisor; +- int acuteorg, acuteorg2, acutedest, acutedest2; +- int i; +- triangle ptr; /* Temporary variable used by stpivot(). */ +- subseg sptr; /* Temporary variable used by snext(). */ +- +- /* Note that steinerleft == -1 if an unlimited number */ +- /* of Steiner points is allowed. */ +- while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) { +- traversalinit(&m->badsubsegs); +- encloop = badsubsegtraverse(m); +- while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) { +- sdecode(encloop->encsubseg, currentenc); +- sorg(currentenc, eorg); +- sdest(currentenc, edest); +- /* Make sure that this segment is still the same segment it was */ +- /* when it was determined to be encroached. If the segment was */ +- /* enqueued multiple times (because several newly inserted */ +- /* vertices encroached it), it may have already been split. */ +- if (!deadsubseg(currentenc.ss) && +- (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) { +- /* To decide where to split a segment, we need to know if the */ +- /* segment shares an endpoint with an adjacent segment. */ +- /* The concern is that, if we simply split every encroached */ +- /* segment in its center, two adjacent segments with a small */ +- /* angle between them might lead to an infinite loop; each */ +- /* vertex added to split one segment will encroach upon the */ +- /* other segment, which must then be split with a vertex that */ +- /* will encroach upon the first segment, and so on forever. */ +- /* To avoid this, imagine a set of concentric circles, whose */ +- /* radii are powers of two, about each segment endpoint. */ +- /* These concentric circles determine where the segment is */ +- /* split. (If both endpoints are shared with adjacent */ +- /* segments, split the segment in the middle, and apply the */ +- /* concentric circles for later splittings.) */ +- +- /* Is the origin shared with another segment? */ +- stpivot(currentenc, enctri); +- lnext(enctri, testtri); +- tspivot(testtri, testsh); +- acuteorg = testsh.ss != m->dummysub; +- /* Is the destination shared with another segment? */ +- lnextself(testtri); +- tspivot(testtri, testsh); +- acutedest = testsh.ss != m->dummysub; +- +- /* If we're using Chew's algorithm (rather than Ruppert's) */ +- /* to define encroachment, delete free vertices from the */ +- /* subsegment's diametral circle. */ +- if (!b->conformdel && !acuteorg && !acutedest) { +- apex(enctri, eapex); +- while ((vertextype(eapex) == FREEVERTEX) && +- ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { +- deletevertex(m, b, &testtri); +- stpivot(currentenc, enctri); +- apex(enctri, eapex); +- lprev(enctri, testtri); +- } +- } +- +- /* Now, check the other side of the segment, if there's a triangle */ +- /* there. */ +- sym(enctri, testtri); +- if (testtri.tri != m->dummytri) { +- /* Is the destination shared with another segment? */ +- lnextself(testtri); +- tspivot(testtri, testsh); +- acutedest2 = testsh.ss != m->dummysub; +- acutedest = acutedest || acutedest2; +- /* Is the origin shared with another segment? */ +- lnextself(testtri); +- tspivot(testtri, testsh); +- acuteorg2 = testsh.ss != m->dummysub; +- acuteorg = acuteorg || acuteorg2; +- +- /* Delete free vertices from the subsegment's diametral circle. */ +- if (!b->conformdel && !acuteorg2 && !acutedest2) { +- org(testtri, eapex); +- while ((vertextype(eapex) == FREEVERTEX) && +- ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + +- (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { +- deletevertex(m, b, &testtri); +- sym(enctri, testtri); +- apex(testtri, eapex); +- lprevself(testtri); +- } +- } +- } +- +- /* Use the concentric circles if exactly one endpoint is shared */ +- /* with another adjacent segment. */ +- if (acuteorg || acutedest) { +- segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + +- (edest[1] - eorg[1]) * (edest[1] - eorg[1])); +- /* Find the power of two that most evenly splits the segment. */ +- /* The worst case is a 2:1 ratio between subsegment lengths. */ +- nearestpoweroftwo = 1.0; +- while (segmentlength > 3.0 * nearestpoweroftwo) { +- nearestpoweroftwo *= 2.0; +- } +- while (segmentlength < 1.5 * nearestpoweroftwo) { +- nearestpoweroftwo *= 0.5; +- } +- /* Where do we split the segment? */ +- split = nearestpoweroftwo / segmentlength; +- if (acutedest) { +- split = 1.0 - split; +- } +- } else { +- /* If we're not worried about adjacent segments, split */ +- /* this segment in the middle. */ +- split = 0.5; +- } +- +- /* Create the new vertex. */ +- newvertex = (vertex) poolalloc(&m->vertices); +- /* Interpolate its coordinate and attributes. */ +- for (i = 0; i < 2 + m->nextras; i++) { +- newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]); +- } +- +- if (!b->noexact) { +- /* Roundoff in the above calculation may yield a `newvertex' */ +- /* that is not precisely collinear with `eorg' and `edest'. */ +- /* Improve collinearity by one step of iterative refinement. */ +- multiplier = counterclockwise(m, b, eorg, edest, newvertex); +- divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) + +- (eorg[1] - edest[1]) * (eorg[1] - edest[1])); +- if ((multiplier != 0.0) && (divisor != 0.0)) { +- multiplier = multiplier / divisor; +- /* Watch out for NANs. */ +- if (multiplier == multiplier) { +- newvertex[0] += multiplier * (edest[1] - eorg[1]); +- newvertex[1] += multiplier * (eorg[0] - edest[0]); +- } +- } +- } +- +- setvertexmark(newvertex, mark(currentenc)); +- setvertextype(newvertex, SEGMENTVERTEX); +- if (b->verbose > 1) { +- printf( +- " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", +- eorg[0], eorg[1], edest[0], edest[1], +- newvertex[0], newvertex[1]); +- } +- /* Check whether the new vertex lies on an endpoint. */ +- if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) || +- ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) { +- printf("Error: Ran out of precision at (%.12g, %.12g).\n", +- newvertex[0], newvertex[1]); +- printf("I attempted to split a segment to a smaller size than\n"); +- printf(" can be accommodated by the finite precision of\n"); +- printf(" floating point arithmetic.\n"); +- precisionerror(); +- triexit(1); +- } +- /* Insert the splitting vertex. This should always succeed. */ +- success = insertvertex(m, b, newvertex, &enctri, ¤tenc, +- 1, triflaws); +- if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) { +- printf("Internal error in splitencsegs():\n"); +- printf(" Failure to split a segment.\n"); +- internalerror(); +- } +- if (m->steinerleft > 0) { +- m->steinerleft--; +- } +- /* Check the two new subsegments to see if they're encroached. */ +- checkseg4encroach(m, b, ¤tenc); +- snextself(currentenc); +- checkseg4encroach(m, b, ¤tenc); +- } +- +- badsubsegdealloc(m, encloop); +- encloop = badsubsegtraverse(m); +- } +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* tallyfaces() Test every triangle in the mesh for quality measures. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void tallyfaces(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void tallyfaces(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop; +- +- if (b->verbose) { +- printf(" Making a list of bad triangles.\n"); +- } +- traversalinit(&m->triangles); +- triangleloop.orient = 0; +- triangleloop.tri = triangletraverse(m); +- while (triangleloop.tri != (triangle *) NULL) { +- /* If the triangle is bad, enqueue it. */ +- testtriangle(m, b, &triangleloop); +- triangleloop.tri = triangletraverse(m); +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */ +-/* Deletes the newly inserted vertex if it encroaches */ +-/* upon a segment. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void splittriangle(struct mesh *m, struct behavior *b, +- struct badtriang *badtri) +-#else /* not ANSI_DECLARATORS */ +-void splittriangle(m, b, badtri) +-struct mesh *m; +-struct behavior *b; +-struct badtriang *badtri; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri badotri; +- vertex borg, bdest, bapex; +- vertex newvertex; +- REAL xi, eta; +- enum insertvertexresult success; +- int errorflag; +- int i; +- +- decode(badtri->poortri, badotri); +- org(badotri, borg); +- dest(badotri, bdest); +- apex(badotri, bapex); +- /* Make sure that this triangle is still the same triangle it was */ +- /* when it was tested and determined to be of bad quality. */ +- /* Subsequent transformations may have made it a different triangle. */ +- if (!deadtri(badotri.tri) && (borg == badtri->triangorg) && +- (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { +- if (b->verbose > 1) { +- printf(" Splitting this triangle at its circumcenter:\n"); +- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], +- borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); +- } +- +- errorflag = 0; +- /* Create a new vertex at the triangle's circumcenter. */ +- newvertex = (vertex) poolalloc(&m->vertices); +- findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1); +- +- /* Check whether the new vertex lies on a triangle vertex. */ +- if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) || +- ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) || +- ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) { +- if (!b->quiet) { +- printf( +- "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", +- newvertex[0], newvertex[1]); +- errorflag = 1; +- } +- vertexdealloc(m, newvertex); +- } else { +- for (i = 2; i < 2 + m->nextras; i++) { +- /* Interpolate the vertex attributes at the circumcenter. */ +- newvertex[i] = borg[i] + xi * (bdest[i] - borg[i]) +- + eta * (bapex[i] - borg[i]); +- } +- /* The new vertex must be in the interior, and therefore is a */ +- /* free vertex with a marker of zero. */ +- setvertexmark(newvertex, 0); +- setvertextype(newvertex, FREEVERTEX); +- +- /* Ensure that the handle `badotri' does not represent the longest */ +- /* edge of the triangle. This ensures that the circumcenter must */ +- /* fall to the left of this edge, so point location will work. */ +- /* (If the angle org-apex-dest exceeds 90 degrees, then the */ +- /* circumcenter lies outside the org-dest edge, and eta is */ +- /* negative. Roundoff error might prevent eta from being */ +- /* negative when it should be, so I test eta against xi.) */ +- if (eta < xi) { +- lprevself(badotri); +- } +- +- /* Insert the circumcenter, searching from the edge of the triangle, */ +- /* and maintain the Delaunay property of the triangulation. */ +- success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL, +- 1, 1); +- if (success == SUCCESSFULVERTEX) { +- if (m->steinerleft > 0) { +- m->steinerleft--; +- } +- } else if (success == ENCROACHINGVERTEX) { +- /* If the newly inserted vertex encroaches upon a subsegment, */ +- /* delete the new vertex. */ +- undovertex(m, b); +- if (b->verbose > 1) { +- printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); +- } +- vertexdealloc(m, newvertex); +- } else if (success == VIOLATINGVERTEX) { +- /* Failed to insert the new vertex, but some subsegment was */ +- /* marked as being encroached. */ +- vertexdealloc(m, newvertex); +- } else { /* success == DUPLICATEVERTEX */ +- /* Couldn't insert the new vertex because a vertex is already there. */ +- if (!b->quiet) { +- printf( +- "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", +- newvertex[0], newvertex[1]); +- errorflag = 1; +- } +- vertexdealloc(m, newvertex); +- } +- } +- if (errorflag) { +- if (b->verbose) { +- printf(" The new vertex is at the circumcenter of triangle\n"); +- printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", +- borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); +- } +- printf("This probably means that I am trying to refine triangles\n"); +- printf(" to a smaller size than can be accommodated by the finite\n"); +- printf(" precision of floating point arithmetic. (You can be\n"); +- printf(" sure of this if I fail to terminate.)\n"); +- precisionerror(); +- } +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/*****************************************************************************/ +-/* */ +-/* enforcequality() Remove all the encroached subsegments and bad */ +-/* triangles from the triangulation. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef CDT_ONLY +- +-#ifdef ANSI_DECLARATORS +-void enforcequality(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void enforcequality(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct badtriang *badtri; +- int i; +- +- if (!b->quiet) { +- printf("Adding Steiner points to enforce quality.\n"); +- } +- /* Initialize the pool of encroached subsegments. */ +- poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK, +- BADSUBSEGPERBLOCK, 0); +- if (b->verbose) { +- printf(" Looking for encroached subsegments.\n"); +- } +- /* Test all segments to see if they're encroached. */ +- tallyencs(m, b); +- if (b->verbose && (m->badsubsegs.items > 0)) { +- printf(" Splitting encroached subsegments.\n"); +- } +- /* Fix encroached subsegments without noting bad triangles. */ +- splitencsegs(m, b, 0); +- /* At this point, if we haven't run out of Steiner points, the */ +- /* triangulation should be (conforming) Delaunay. */ +- +- /* Next, we worry about enforcing triangle quality. */ +- if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { +- /* Initialize the pool of bad triangles. */ +- poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK, +- BADTRIPERBLOCK, 0); +- /* Initialize the queues of bad triangles. */ +- for (i = 0; i < 4096; i++) { +- m->queuefront[i] = (struct badtriang *) NULL; +- } +- m->firstnonemptyq = -1; +- /* Test all triangles to see if they're bad. */ +- tallyfaces(m, b); +- /* Initialize the pool of recently flipped triangles. */ +- poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK, +- FLIPSTACKERPERBLOCK, 0); +- m->checkquality = 1; +- if (b->verbose) { +- printf(" Splitting bad triangles.\n"); +- } +- while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) { +- /* Fix one bad triangle by inserting a vertex at its circumcenter. */ +- badtri = dequeuebadtriang(m); +- splittriangle(m, b, badtri); +- if (m->badsubsegs.items > 0) { +- /* Put bad triangle back in queue for another try later. */ +- enqueuebadtriang(m, b, badtri); +- /* Fix any encroached subsegments that resulted. */ +- /* Record any new bad triangles that result. */ +- splitencsegs(m, b, 1); +- } else { +- /* Return the bad triangle to the pool. */ +- pooldealloc(&m->badtriangles, (void *) badtri); +- } +- } +- } +- /* At this point, if the "-D" switch was selected and we haven't run out */ +- /* of Steiner points, the triangulation should be (conforming) Delaunay */ +- /* and have no low-quality triangles. */ +- +- /* Might we have run out of Steiner points too soon? */ +- if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) && +- (m->steinerleft == 0)) { +- printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); +- if (m->badsubsegs.items == 1) { +- printf(" one encroached subsegment, and therefore might not be truly\n" +- ); +- } else { +- printf(" %ld encroached subsegments, and therefore might not be truly\n" +- , m->badsubsegs.items); +- } +- printf(" Delaunay. If the Delaunay property is important to you,\n"); +- printf(" try increasing the number of Steiner points (controlled by\n"); +- printf(" the -S switch) slightly and try again.\n\n"); +- } +-} +- +-#endif /* not CDT_ONLY */ +- +-/** **/ +-/** **/ +-/********* Mesh quality maintenance ends here *********/ +- +-/*****************************************************************************/ +-/* */ +-/* highorder() Create extra nodes for quadratic subparametric elements. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void highorder(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void highorder(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop, trisym; +- struct osub checkmark; +- vertex newvertex; +- vertex torg, tdest; +- int i; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +- if (!b->quiet) { +- printf("Adding vertices for second-order triangles.\n"); +- } +- /* The following line ensures that dead items in the pool of nodes */ +- /* cannot be allocated for the extra nodes associated with high */ +- /* order elements. This ensures that the primary nodes (at the */ +- /* corners of elements) will occur earlier in the output files, and */ +- /* have lower indices, than the extra nodes. */ +- m->vertices.deaditemstack = (void *) NULL; +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- /* To loop over the set of edges, loop over all triangles, and look at */ +- /* the three edges of each triangle. If there isn't another triangle */ +- /* adjacent to the edge, operate on the edge. If there is another */ +- /* adjacent triangle, operate on the edge only if the current triangle */ +- /* has a smaller pointer than its neighbor. This way, each edge is */ +- /* considered only once. */ +- while (triangleloop.tri != (triangle *) NULL) { +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- sym(triangleloop, trisym); +- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { +- org(triangleloop, torg); +- dest(triangleloop, tdest); +- /* Create a new node in the middle of the edge. Interpolate */ +- /* its attributes. */ +- newvertex = (vertex) poolalloc(&m->vertices); +- for (i = 0; i < 2 + m->nextras; i++) { +- newvertex[i] = 0.5 * (torg[i] + tdest[i]); +- } +- /* Set the new node's marker to zero or one, depending on */ +- /* whether it lies on a boundary. */ +- setvertexmark(newvertex, trisym.tri == m->dummytri); +- setvertextype(newvertex, +- trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX); +- if (b->usesegments) { +- tspivot(triangleloop, checkmark); +- /* If this edge is a segment, transfer the marker to the new node. */ +- if (checkmark.ss != m->dummysub) { +- setvertexmark(newvertex, mark(checkmark)); +- setvertextype(newvertex, SEGMENTVERTEX); +- } +- } +- if (b->verbose > 1) { +- printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]); +- } +- /* Record the new node in the (one or two) adjacent elements. */ +- triangleloop.tri[m->highorderindex + triangleloop.orient] = +- (triangle) newvertex; +- if (trisym.tri != m->dummytri) { +- trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex; +- } +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +-} +- +-/********* File I/O routines begin here *********/ +-/** **/ +-/** **/ +- +-/*****************************************************************************/ +-/* */ +-/* readline() Read a nonempty line from a file. */ +-/* */ +-/* A line is considered "nonempty" if it contains something that looks like */ +-/* a number. Comments (prefaced by `#') are ignored. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-char *readline(char *string, FILE *infile, char *infilename) +-#else /* not ANSI_DECLARATORS */ +-char *readline(string, infile, infilename) +-char *string; +-FILE *infile; +-char *infilename; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- char *result; +- +- /* Search for something that looks like a number. */ +- do { +- result = fgets(string, INPUTLINESIZE, infile); +- if (result == (char *) NULL) { +- printf(" Error: Unexpected end of file in %s.\n", infilename); +- triexit(1); +- } +- /* Skip anything that doesn't look like a number, a comment, */ +- /* or the end of a line. */ +- while ((*result != '\0') && (*result != '#') +- && (*result != '.') && (*result != '+') && (*result != '-') +- && ((*result < '0') || (*result > '9'))) { +- result++; +- } +- /* If it's a comment or end of line, read another line and try again. */ +- } while ((*result == '#') || (*result == '\0')); +- return result; +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* findfield() Find the next field of a string. */ +-/* */ +-/* Jumps past the current field by searching for whitespace, then jumps */ +-/* past the whitespace to find the next field. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-char *findfield(char *string) +-#else /* not ANSI_DECLARATORS */ +-char *findfield(string) +-char *string; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- char *result; +- +- result = string; +- /* Skip the current field. Stop upon reaching whitespace. */ +- while ((*result != '\0') && (*result != '#') +- && (*result != ' ') && (*result != '\t')) { +- result++; +- } +- /* Now skip the whitespace and anything else that doesn't look like a */ +- /* number, a comment, or the end of a line. */ +- while ((*result != '\0') && (*result != '#') +- && (*result != '.') && (*result != '+') && (*result != '-') +- && ((*result < '0') || (*result > '9'))) { +- result++; +- } +- /* Check for a comment (prefixed with `#'). */ +- if (*result == '#') { +- *result = '\0'; +- } +- return result; +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* readnodes() Read the vertices from a file, which may be a .node or */ +-/* .poly file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void readnodes(struct mesh *m, struct behavior *b, char *nodefilename, +- char *polyfilename, FILE **polyfile) +-#else /* not ANSI_DECLARATORS */ +-void readnodes(m, b, nodefilename, polyfilename, polyfile) +-struct mesh *m; +-struct behavior *b; +-char *nodefilename; +-char *polyfilename; +-FILE **polyfile; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- FILE *infile; +- vertex vertexloop; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- char *infilename; +- REAL x, y; +- int firstnode; +- int nodemarkers; +- int currentmarker; +- int i, j; +- +- if (b->poly) { +- /* Read the vertices from a .poly file. */ +- if (!b->quiet) { +- printf("Opening %s.\n", polyfilename); +- } +- *polyfile = fopen(polyfilename, "r"); +- if (*polyfile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", polyfilename); +- triexit(1); +- } +- /* Read number of vertices, number of dimensions, number of vertex */ +- /* attributes, and number of boundary markers. */ +- stringptr = readline(inputline, *polyfile, polyfilename); +- m->invertices = (int) strtol(stringptr, &stringptr, 0); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- m->mesh_dim = 2; +- } else { +- m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- m->nextras = 0; +- } else { +- m->nextras = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- nodemarkers = 0; +- } else { +- nodemarkers = (int) strtol(stringptr, &stringptr, 0); +- } +- if (m->invertices > 0) { +- infile = *polyfile; +- infilename = polyfilename; +- m->readnodefile = 0; +- } else { +- /* If the .poly file claims there are zero vertices, that means that */ +- /* the vertices should be read from a separate .node file. */ +- m->readnodefile = 1; +- infilename = nodefilename; +- } +- } else { +- m->readnodefile = 1; +- infilename = nodefilename; +- *polyfile = (FILE *) NULL; +- } +- +- if (m->readnodefile) { +- /* Read the vertices from a .node file. */ +- if (!b->quiet) { +- printf("Opening %s.\n", nodefilename); +- } +- infile = fopen(nodefilename, "r"); +- if (infile == (FILE *) NULL) { +- printf(" Error: Cannot access file %s.\n", nodefilename); +- triexit(1); +- } +- /* Read number of vertices, number of dimensions, number of vertex */ +- /* attributes, and number of boundary markers. */ +- stringptr = readline(inputline, infile, nodefilename); +- m->invertices = (int) strtol(stringptr, &stringptr, 0); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- m->mesh_dim = 2; +- } else { +- m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- m->nextras = 0; +- } else { +- m->nextras = (int) strtol(stringptr, &stringptr, 0); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- nodemarkers = 0; +- } else { +- nodemarkers = (int) strtol(stringptr, &stringptr, 0); +- } +- } +- +- if (m->invertices < 3) { +- printf("Error: Input must have at least three input vertices.\n"); +- triexit(1); +- } +- if (m->mesh_dim != 2) { +- printf("Error: Triangle only works with two-dimensional meshes.\n"); +- triexit(1); +- } +- if (m->nextras == 0) { +- b->weighted = 0; +- } +- +- initializevertexpool(m, b); +- +- /* Read the vertices. */ +- for (i = 0; i < m->invertices; i++) { +- vertexloop = (vertex) poolalloc(&m->vertices); +- stringptr = readline(inputline, infile, infilename); +- if (i == 0) { +- firstnode = (int) strtol(stringptr, &stringptr, 0); +- if ((firstnode == 0) || (firstnode == 1)) { +- b->firstnumber = firstnode; +- } +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i); +- triexit(1); +- } +- x = (REAL) strtod(stringptr, &stringptr); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i); +- triexit(1); +- } +- y = (REAL) strtod(stringptr, &stringptr); +- vertexloop[0] = x; +- vertexloop[1] = y; +- /* Read the vertex attributes. */ +- for (j = 2; j < 2 + m->nextras; j++) { +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- vertexloop[j] = 0.0; +- } else { +- vertexloop[j] = (REAL) strtod(stringptr, &stringptr); +- } +- } +- if (nodemarkers) { +- /* Read a vertex marker. */ +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- setvertexmark(vertexloop, 0); +- } else { +- currentmarker = (int) strtol(stringptr, &stringptr, 0); +- setvertexmark(vertexloop, currentmarker); +- } +- } else { +- /* If no markers are specified in the file, they default to zero. */ +- setvertexmark(vertexloop, 0); +- } +- setvertextype(vertexloop, INPUTVERTEX); +- /* Determine the smallest and largest x and y coordinates. */ +- if (i == 0) { +- m->xmin = m->xmax = x; +- m->ymin = m->ymax = y; +- } else { +- m->xmin = (x < m->xmin) ? x : m->xmin; +- m->xmax = (x > m->xmax) ? x : m->xmax; +- m->ymin = (y < m->ymin) ? y : m->ymin; +- m->ymax = (y > m->ymax) ? y : m->ymax; +- } +- } +- if (m->readnodefile) { +- fclose(infile); +- } +- +- /* Nonexistent x value used as a flag to mark circle events in sweepline */ +- /* Delaunay algorithm. */ +- m->xminextreme = 10 * m->xmin - 9 * m->xmax; +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* transfernodes() Read the vertices from memory. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist, +- REAL *pointattriblist, int *pointmarkerlist, +- int numberofpoints, int numberofpointattribs) +-#else /* not ANSI_DECLARATORS */ +-void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist, +- numberofpoints, numberofpointattribs) +-struct mesh *m; +-struct behavior *b; +-REAL *pointlist; +-REAL *pointattriblist; +-int *pointmarkerlist; +-int numberofpoints; +-int numberofpointattribs; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex vertexloop; +- REAL x, y; +- int i, j; +- int coordindex; +- int attribindex; +- +- m->invertices = numberofpoints; +- m->mesh_dim = 2; +- m->nextras = numberofpointattribs; +- m->readnodefile = 0; +- if (m->invertices < 3) { +- printf("Error: Input must have at least three input vertices.\n"); +- triexit(1); +- } +- if (m->nextras == 0) { +- b->weighted = 0; +- } +- +- initializevertexpool(m, b); +- +- /* Read the vertices. */ +- coordindex = 0; +- attribindex = 0; +- for (i = 0; i < m->invertices; i++) { +- vertexloop = (vertex) poolalloc(&m->vertices); +- /* Read the vertex coordinates. */ +- x = vertexloop[0] = pointlist[coordindex++]; +- y = vertexloop[1] = pointlist[coordindex++]; +- /* Read the vertex attributes. */ +- for (j = 0; j < numberofpointattribs; j++) { +- vertexloop[2 + j] = pointattriblist[attribindex++]; +- } +- if (pointmarkerlist != (int *) NULL) { +- /* Read a vertex marker. */ +- setvertexmark(vertexloop, pointmarkerlist[i]); +- } else { +- /* If no markers are specified, they default to zero. */ +- setvertexmark(vertexloop, 0); +- } +- setvertextype(vertexloop, INPUTVERTEX); +- /* Determine the smallest and largest x and y coordinates. */ +- if (i == 0) { +- m->xmin = m->xmax = x; +- m->ymin = m->ymax = y; +- } else { +- m->xmin = (x < m->xmin) ? x : m->xmin; +- m->xmax = (x > m->xmax) ? x : m->xmax; +- m->ymin = (y < m->ymin) ? y : m->ymin; +- m->ymax = (y > m->ymax) ? y : m->ymax; +- } +- } +- +- /* Nonexistent x value used as a flag to mark circle events in sweepline */ +- /* Delaunay algorithm. */ +- m->xminextreme = 10 * m->xmin - 9 * m->xmax; +-} +- +-#endif /* TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* readholes() Read the holes, and possibly regional attributes and area */ +-/* constraints, from a .poly file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void readholes(struct mesh *m, struct behavior *b, +- FILE *polyfile, char *polyfilename, REAL **hlist, int *holes, +- REAL **rlist, int *regions) +-#else /* not ANSI_DECLARATORS */ +-void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions) +-struct mesh *m; +-struct behavior *b; +-FILE *polyfile; +-char *polyfilename; +-REAL **hlist; +-int *holes; +-REAL **rlist; +-int *regions; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- REAL *holelist; +- REAL *regionlist; +- char inputline[INPUTLINESIZE]; +- char *stringptr; +- int index; +- int i; +- +- /* Read the holes. */ +- stringptr = readline(inputline, polyfile, polyfilename); +- *holes = (int) strtol(stringptr, &stringptr, 0); +- if (*holes > 0) { +- holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL)); +- *hlist = holelist; +- for (i = 0; i < 2 * *holes; i += 2) { +- stringptr = readline(inputline, polyfile, polyfilename); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Hole %d has no x coordinate.\n", +- b->firstnumber + (i >> 1)); +- triexit(1); +- } else { +- holelist[i] = (REAL) strtod(stringptr, &stringptr); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Hole %d has no y coordinate.\n", +- b->firstnumber + (i >> 1)); +- triexit(1); +- } else { +- holelist[i + 1] = (REAL) strtod(stringptr, &stringptr); +- } +- } +- } else { +- *hlist = (REAL *) NULL; +- } +- +-#ifndef CDT_ONLY +- if ((b->regionattrib || b->vararea) && !b->refine) { +- /* Read the area constraints. */ +- stringptr = readline(inputline, polyfile, polyfilename); +- *regions = (int) strtol(stringptr, &stringptr, 0); +- if (*regions > 0) { +- regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL)); +- *rlist = regionlist; +- index = 0; +- for (i = 0; i < *regions; i++) { +- stringptr = readline(inputline, polyfile, polyfilename); +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Region %d has no x coordinate.\n", +- b->firstnumber + i); +- triexit(1); +- } else { +- regionlist[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf("Error: Region %d has no y coordinate.\n", +- b->firstnumber + i); +- triexit(1); +- } else { +- regionlist[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- printf( +- "Error: Region %d has no region attribute or area constraint.\n", +- b->firstnumber + i); +- triexit(1); +- } else { +- regionlist[index++] = (REAL) strtod(stringptr, &stringptr); +- } +- stringptr = findfield(stringptr); +- if (*stringptr == '\0') { +- regionlist[index] = regionlist[index - 1]; +- } else { +- regionlist[index] = (REAL) strtod(stringptr, &stringptr); +- } +- index++; +- } +- } +- } else { +- /* Set `*regions' to zero to avoid an accidental free() later. */ +- *regions = 0; +- *rlist = (REAL *) NULL; +- } +-#endif /* not CDT_ONLY */ +- +- fclose(polyfile); +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* finishfile() Write the command line to the output file so the user */ +-/* can remember how the file was generated. Close the file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void finishfile(FILE *outfile, int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void finishfile(outfile, argc, argv) +-FILE *outfile; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- int i; +- +- fprintf(outfile, "# Generated by"); +- for (i = 0; i < argc; i++) { +- fprintf(outfile, " "); +- fputs(argv[i], outfile); +- } +- fprintf(outfile, "\n"); +- fclose(outfile); +-} +- +-#endif /* not TRILIBRARY */ +- +-/*****************************************************************************/ +-/* */ +-/* writenodes() Number the vertices and write them to a .node file. */ +-/* */ +-/* To save memory, the vertex numbers are written over the boundary markers */ +-/* after the vertices are written to a file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, +- REAL **pointattriblist, int **pointmarkerlist) +-#else /* not ANSI_DECLARATORS */ +-void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist) +-struct mesh *m; +-struct behavior *b; +-REAL **pointlist; +-REAL **pointattriblist; +-int **pointmarkerlist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writenodes(struct mesh *m, struct behavior *b, char *nodefilename, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writenodes(m, b, nodefilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *nodefilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- REAL *plist; +- REAL *palist; +- int *pmlist; +- int coordindex; +- int attribindex; +-#else /* not TRILIBRARY */ +- FILE *outfile; +-#endif /* not TRILIBRARY */ +- vertex vertexloop; +- long outvertices; +- int vertexnumber; +- int i; +- +- if (b->jettison) { +- outvertices = m->vertices.items - m->undeads; +- } else { +- outvertices = m->vertices.items; +- } +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing vertices.\n"); +- } +- /* Allocate memory for output vertices if necessary. */ +- if (*pointlist == (REAL *) NULL) { +- *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL))); +- } +- /* Allocate memory for output vertex attributes if necessary. */ +- if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) { +- *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras * +- sizeof(REAL))); +- } +- /* Allocate memory for output vertex markers if necessary. */ +- if (!b->nobound && (*pointmarkerlist == (int *) NULL)) { +- *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int))); +- } +- plist = *pointlist; +- palist = *pointattriblist; +- pmlist = *pointmarkerlist; +- coordindex = 0; +- attribindex = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", nodefilename); +- } +- outfile = fopen(nodefilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", nodefilename); +- triexit(1); +- } +- /* Number of vertices, number of dimensions, number of vertex attributes, */ +- /* and number of boundary markers (zero or one). */ +- fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim, +- m->nextras, 1 - b->nobound); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->vertices); +- vertexnumber = b->firstnumber; +- vertexloop = vertextraverse(m); +- while (vertexloop != (vertex) NULL) { +- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { +-#ifdef TRILIBRARY +- /* X and y coordinates. */ +- plist[coordindex++] = vertexloop[0]; +- plist[coordindex++] = vertexloop[1]; +- /* Vertex attributes. */ +- for (i = 0; i < m->nextras; i++) { +- palist[attribindex++] = vertexloop[2 + i]; +- } +- if (!b->nobound) { +- /* Copy the boundary marker. */ +- pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop); +- } +-#else /* not TRILIBRARY */ +- /* Vertex number, x and y coordinates. */ +- fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0], +- vertexloop[1]); +- for (i = 0; i < m->nextras; i++) { +- /* Write an attribute. */ +- fprintf(outfile, " %.17g", vertexloop[i + 2]); +- } +- if (b->nobound) { +- fprintf(outfile, "\n"); +- } else { +- /* Write the boundary marker. */ +- fprintf(outfile, " %d\n", vertexmark(vertexloop)); +- } +-#endif /* not TRILIBRARY */ +- +- setvertexmark(vertexloop, vertexnumber); +- vertexnumber++; +- } +- vertexloop = vertextraverse(m); +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* numbernodes() Number the vertices. */ +-/* */ +-/* Each vertex is assigned a marker equal to its number. */ +-/* */ +-/* Used when writenodes() is not called because no .node file is written. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void numbernodes(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void numbernodes(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- vertex vertexloop; +- int vertexnumber; +- +- traversalinit(&m->vertices); +- vertexnumber = b->firstnumber; +- vertexloop = vertextraverse(m); +- while (vertexloop != (vertex) NULL) { +- setvertexmark(vertexloop, vertexnumber); +- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { +- vertexnumber++; +- } +- vertexloop = vertextraverse(m); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* writeelements() Write the triangles to an .ele file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writeelements(struct mesh *m, struct behavior *b, +- int **trianglelist, REAL **triangleattriblist) +-#else /* not ANSI_DECLARATORS */ +-void writeelements(m, b, trianglelist, triangleattriblist) +-struct mesh *m; +-struct behavior *b; +-int **trianglelist; +-REAL **triangleattriblist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writeelements(struct mesh *m, struct behavior *b, char *elefilename, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writeelements(m, b, elefilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *elefilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- int *tlist; +- REAL *talist; +- int vertexindex; +- int attribindex; +-#else /* not TRILIBRARY */ +- FILE *outfile; +-#endif /* not TRILIBRARY */ +- struct otri triangleloop; +- vertex p1, p2, p3; +- vertex mid1, mid2, mid3; +- long elementnumber; +- int i; +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing triangles.\n"); +- } +- /* Allocate memory for output triangles if necessary. */ +- if (*trianglelist == (int *) NULL) { +- *trianglelist = (int *) trimalloc((int) (m->triangles.items * +- ((b->order + 1) * (b->order + 2) / +- 2) * sizeof(int))); +- } +- /* Allocate memory for output triangle attributes if necessary. */ +- if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) { +- *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items * +- m->eextras * +- sizeof(REAL))); +- } +- tlist = *trianglelist; +- talist = *triangleattriblist; +- vertexindex = 0; +- attribindex = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", elefilename); +- } +- outfile = fopen(elefilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", elefilename); +- triexit(1); +- } +- /* Number of triangles, vertices per triangle, attributes per triangle. */ +- fprintf(outfile, "%ld %d %d\n", m->triangles.items, +- (b->order + 1) * (b->order + 2) / 2, m->eextras); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- triangleloop.orient = 0; +- elementnumber = b->firstnumber; +- while (triangleloop.tri != (triangle *) NULL) { +- org(triangleloop, p1); +- dest(triangleloop, p2); +- apex(triangleloop, p3); +- if (b->order == 1) { +-#ifdef TRILIBRARY +- tlist[vertexindex++] = vertexmark(p1); +- tlist[vertexindex++] = vertexmark(p2); +- tlist[vertexindex++] = vertexmark(p3); +-#else /* not TRILIBRARY */ +- /* Triangle number, indices for three vertices. */ +- fprintf(outfile, "%4ld %4d %4d %4d", elementnumber, +- vertexmark(p1), vertexmark(p2), vertexmark(p3)); +-#endif /* not TRILIBRARY */ +- } else { +- mid1 = (vertex) triangleloop.tri[m->highorderindex + 1]; +- mid2 = (vertex) triangleloop.tri[m->highorderindex + 2]; +- mid3 = (vertex) triangleloop.tri[m->highorderindex]; +-#ifdef TRILIBRARY +- tlist[vertexindex++] = vertexmark(p1); +- tlist[vertexindex++] = vertexmark(p2); +- tlist[vertexindex++] = vertexmark(p3); +- tlist[vertexindex++] = vertexmark(mid1); +- tlist[vertexindex++] = vertexmark(mid2); +- tlist[vertexindex++] = vertexmark(mid3); +-#else /* not TRILIBRARY */ +- /* Triangle number, indices for six vertices. */ +- fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber, +- vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1), +- vertexmark(mid2), vertexmark(mid3)); +-#endif /* not TRILIBRARY */ +- } +- +-#ifdef TRILIBRARY +- for (i = 0; i < m->eextras; i++) { +- talist[attribindex++] = elemattribute(triangleloop, i); +- } +-#else /* not TRILIBRARY */ +- for (i = 0; i < m->eextras; i++) { +- fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); +- } +- fprintf(outfile, "\n"); +-#endif /* not TRILIBRARY */ +- +- triangleloop.tri = triangletraverse(m); +- elementnumber++; +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* writepoly() Write the segments and holes to a .poly file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writepoly(struct mesh *m, struct behavior *b, +- int **segmentlist, int **segmentmarkerlist) +-#else /* not ANSI_DECLARATORS */ +-void writepoly(m, b, segmentlist, segmentmarkerlist) +-struct mesh *m; +-struct behavior *b; +-int **segmentlist; +-int **segmentmarkerlist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writepoly(struct mesh *m, struct behavior *b, char *polyfilename, +- REAL *holelist, int holes, REAL *regionlist, int regions, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions, +- argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *polyfilename; +-REAL *holelist; +-int holes; +-REAL *regionlist; +-int regions; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- int *slist; +- int *smlist; +- int index; +-#else /* not TRILIBRARY */ +- FILE *outfile; +- long holenumber, regionnumber; +-#endif /* not TRILIBRARY */ +- struct osub subsegloop; +- vertex endpoint1, endpoint2; +- long subsegnumber; +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing segments.\n"); +- } +- /* Allocate memory for output segments if necessary. */ +- if (*segmentlist == (int *) NULL) { +- *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 * +- sizeof(int))); +- } +- /* Allocate memory for output segment markers if necessary. */ +- if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) { +- *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items * +- sizeof(int))); +- } +- slist = *segmentlist; +- smlist = *segmentmarkerlist; +- index = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", polyfilename); +- } +- outfile = fopen(polyfilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", polyfilename); +- triexit(1); +- } +- /* The zero indicates that the vertices are in a separate .node file. */ +- /* Followed by number of dimensions, number of vertex attributes, */ +- /* and number of boundary markers (zero or one). */ +- fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras, +- 1 - b->nobound); +- /* Number of segments, number of boundary markers (zero or one). */ +- fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->subsegs); +- subsegloop.ss = subsegtraverse(m); +- subsegloop.ssorient = 0; +- subsegnumber = b->firstnumber; +- while (subsegloop.ss != (subseg *) NULL) { +- sorg(subsegloop, endpoint1); +- sdest(subsegloop, endpoint2); +-#ifdef TRILIBRARY +- /* Copy indices of the segment's two endpoints. */ +- slist[index++] = vertexmark(endpoint1); +- slist[index++] = vertexmark(endpoint2); +- if (!b->nobound) { +- /* Copy the boundary marker. */ +- smlist[subsegnumber - b->firstnumber] = mark(subsegloop); +- } +-#else /* not TRILIBRARY */ +- /* Segment number, indices of its two endpoints, and possibly a marker. */ +- if (b->nobound) { +- fprintf(outfile, "%4ld %4d %4d\n", subsegnumber, +- vertexmark(endpoint1), vertexmark(endpoint2)); +- } else { +- fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber, +- vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop)); +- } +-#endif /* not TRILIBRARY */ +- +- subsegloop.ss = subsegtraverse(m); +- subsegnumber++; +- } +- +-#ifndef TRILIBRARY +-#ifndef CDT_ONLY +- fprintf(outfile, "%d\n", holes); +- if (holes > 0) { +- for (holenumber = 0; holenumber < holes; holenumber++) { +- /* Hole number, x and y coordinates. */ +- fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber, +- holelist[2 * holenumber], holelist[2 * holenumber + 1]); +- } +- } +- if (regions > 0) { +- fprintf(outfile, "%d\n", regions); +- for (regionnumber = 0; regionnumber < regions; regionnumber++) { +- /* Region number, x and y coordinates, attribute, maximum area. */ +- fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n", +- b->firstnumber + regionnumber, +- regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1], +- regionlist[4 * regionnumber + 2], +- regionlist[4 * regionnumber + 3]); +- } +- } +-#endif /* not CDT_ONLY */ +- +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* writeedges() Write the edges to an .edge file. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writeedges(struct mesh *m, struct behavior *b, +- int **edgelist, int **edgemarkerlist) +-#else /* not ANSI_DECLARATORS */ +-void writeedges(m, b, edgelist, edgemarkerlist) +-struct mesh *m; +-struct behavior *b; +-int **edgelist; +-int **edgemarkerlist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writeedges(struct mesh *m, struct behavior *b, char *edgefilename, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writeedges(m, b, edgefilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *edgefilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- int *elist; +- int *emlist; +- int index; +-#else /* not TRILIBRARY */ +- FILE *outfile; +-#endif /* not TRILIBRARY */ +- struct otri triangleloop, trisym; +- struct osub checkmark; +- vertex p1, p2; +- long edgenumber; +- triangle ptr; /* Temporary variable used by sym(). */ +- subseg sptr; /* Temporary variable used by tspivot(). */ +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing edges.\n"); +- } +- /* Allocate memory for edges if necessary. */ +- if (*edgelist == (int *) NULL) { +- *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); +- } +- /* Allocate memory for edge markers if necessary. */ +- if (!b->nobound && (*edgemarkerlist == (int *) NULL)) { +- *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int))); +- } +- elist = *edgelist; +- emlist = *edgemarkerlist; +- index = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", edgefilename); +- } +- outfile = fopen(edgefilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", edgefilename); +- triexit(1); +- } +- /* Number of edges, number of boundary markers (zero or one). */ +- fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- edgenumber = b->firstnumber; +- /* To loop over the set of edges, loop over all triangles, and look at */ +- /* the three edges of each triangle. If there isn't another triangle */ +- /* adjacent to the edge, operate on the edge. If there is another */ +- /* adjacent triangle, operate on the edge only if the current triangle */ +- /* has a smaller pointer than its neighbor. This way, each edge is */ +- /* considered only once. */ +- while (triangleloop.tri != (triangle *) NULL) { +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- sym(triangleloop, trisym); +- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { +- org(triangleloop, p1); +- dest(triangleloop, p2); +-#ifdef TRILIBRARY +- elist[index++] = vertexmark(p1); +- elist[index++] = vertexmark(p2); +-#endif /* TRILIBRARY */ +- if (b->nobound) { +-#ifndef TRILIBRARY +- /* Edge number, indices of two endpoints. */ +- fprintf(outfile, "%4ld %d %d\n", edgenumber, +- vertexmark(p1), vertexmark(p2)); +-#endif /* not TRILIBRARY */ +- } else { +- /* Edge number, indices of two endpoints, and a boundary marker. */ +- /* If there's no subsegment, the boundary marker is zero. */ +- if (b->usesegments) { +- tspivot(triangleloop, checkmark); +- if (checkmark.ss == m->dummysub) { +-#ifdef TRILIBRARY +- emlist[edgenumber - b->firstnumber] = 0; +-#else /* not TRILIBRARY */ +- fprintf(outfile, "%4ld %d %d %d\n", edgenumber, +- vertexmark(p1), vertexmark(p2), 0); +-#endif /* not TRILIBRARY */ +- } else { +-#ifdef TRILIBRARY +- emlist[edgenumber - b->firstnumber] = mark(checkmark); +-#else /* not TRILIBRARY */ +- fprintf(outfile, "%4ld %d %d %d\n", edgenumber, +- vertexmark(p1), vertexmark(p2), mark(checkmark)); +-#endif /* not TRILIBRARY */ +- } +- } else { +-#ifdef TRILIBRARY +- emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri; +-#else /* not TRILIBRARY */ +- fprintf(outfile, "%4ld %d %d %d\n", edgenumber, +- vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri); +-#endif /* not TRILIBRARY */ +- } +- } +- edgenumber++; +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */ +-/* file. */ +-/* */ +-/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */ +-/* Hence, the Voronoi vertices are listed by traversing the Delaunay */ +-/* triangles, and the Voronoi edges are listed by traversing the Delaunay */ +-/* edges. */ +-/* */ +-/* WARNING: In order to assign numbers to the Voronoi vertices, this */ +-/* procedure messes up the subsegments or the extra nodes of every */ +-/* element. Hence, you should call this procedure last. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist, +- REAL **vpointattriblist, int **vpointmarkerlist, +- int **vedgelist, int **vedgemarkerlist, REAL **vnormlist) +-#else /* not ANSI_DECLARATORS */ +-void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist, +- vedgelist, vedgemarkerlist, vnormlist) +-struct mesh *m; +-struct behavior *b; +-REAL **vpointlist; +-REAL **vpointattriblist; +-int **vpointmarkerlist; +-int **vedgelist; +-int **vedgemarkerlist; +-REAL **vnormlist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename, +- char *vedgefilename, int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *vnodefilename; +-char *vedgefilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- REAL *plist; +- REAL *palist; +- int *elist; +- REAL *normlist; +- int coordindex; +- int attribindex; +-#else /* not TRILIBRARY */ +- FILE *outfile; +-#endif /* not TRILIBRARY */ +- struct otri triangleloop, trisym; +- vertex torg, tdest, tapex; +- REAL circumcenter[2]; +- REAL xi, eta; +- long vnodenumber, vedgenumber; +- int p1, p2; +- int i; +- triangle ptr; /* Temporary variable used by sym(). */ +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing Voronoi vertices.\n"); +- } +- /* Allocate memory for Voronoi vertices if necessary. */ +- if (*vpointlist == (REAL *) NULL) { +- *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 * +- sizeof(REAL))); +- } +- /* Allocate memory for Voronoi vertex attributes if necessary. */ +- if (*vpointattriblist == (REAL *) NULL) { +- *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items * +- m->nextras * sizeof(REAL))); +- } +- *vpointmarkerlist = (int *) NULL; +- plist = *vpointlist; +- palist = *vpointattriblist; +- coordindex = 0; +- attribindex = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", vnodefilename); +- } +- outfile = fopen(vnodefilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", vnodefilename); +- triexit(1); +- } +- /* Number of triangles, two dimensions, number of vertex attributes, */ +- /* no markers. */ +- fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- triangleloop.orient = 0; +- vnodenumber = b->firstnumber; +- while (triangleloop.tri != (triangle *) NULL) { +- org(triangleloop, torg); +- dest(triangleloop, tdest); +- apex(triangleloop, tapex); +- findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0); +-#ifdef TRILIBRARY +- /* X and y coordinates. */ +- plist[coordindex++] = circumcenter[0]; +- plist[coordindex++] = circumcenter[1]; +- for (i = 2; i < 2 + m->nextras; i++) { +- /* Interpolate the vertex attributes at the circumcenter. */ +- palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) +- + eta * (tapex[i] - torg[i]); +- } +-#else /* not TRILIBRARY */ +- /* Voronoi vertex number, x and y coordinates. */ +- fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0], +- circumcenter[1]); +- for (i = 2; i < 2 + m->nextras; i++) { +- /* Interpolate the vertex attributes at the circumcenter. */ +- fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) +- + eta * (tapex[i] - torg[i])); +- } +- fprintf(outfile, "\n"); +-#endif /* not TRILIBRARY */ +- +- * (int *) (triangleloop.tri + 6) = (int) vnodenumber; +- triangleloop.tri = triangletraverse(m); +- vnodenumber++; +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing Voronoi edges.\n"); +- } +- /* Allocate memory for output Voronoi edges if necessary. */ +- if (*vedgelist == (int *) NULL) { +- *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); +- } +- *vedgemarkerlist = (int *) NULL; +- /* Allocate memory for output Voronoi norms if necessary. */ +- if (*vnormlist == (REAL *) NULL) { +- *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL))); +- } +- elist = *vedgelist; +- normlist = *vnormlist; +- coordindex = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", vedgefilename); +- } +- outfile = fopen(vedgefilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", vedgefilename); +- triexit(1); +- } +- /* Number of edges, zero boundary markers. */ +- fprintf(outfile, "%ld %d\n", m->edges, 0); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- vedgenumber = b->firstnumber; +- /* To loop over the set of edges, loop over all triangles, and look at */ +- /* the three edges of each triangle. If there isn't another triangle */ +- /* adjacent to the edge, operate on the edge. If there is another */ +- /* adjacent triangle, operate on the edge only if the current triangle */ +- /* has a smaller pointer than its neighbor. This way, each edge is */ +- /* considered only once. */ +- while (triangleloop.tri != (triangle *) NULL) { +- for (triangleloop.orient = 0; triangleloop.orient < 3; +- triangleloop.orient++) { +- sym(triangleloop, trisym); +- if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { +- /* Find the number of this triangle (and Voronoi vertex). */ +- p1 = * (int *) (triangleloop.tri + 6); +- if (trisym.tri == m->dummytri) { +- org(triangleloop, torg); +- dest(triangleloop, tdest); +-#ifdef TRILIBRARY +- /* Copy an infinite ray. Index of one endpoint, and -1. */ +- elist[coordindex] = p1; +- normlist[coordindex++] = tdest[1] - torg[1]; +- elist[coordindex] = -1; +- normlist[coordindex++] = torg[0] - tdest[0]; +-#else /* not TRILIBRARY */ +- /* Write an infinite ray. Edge number, index of one endpoint, -1, */ +- /* and x and y coordinates of a vector representing the */ +- /* direction of the ray. */ +- fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber, +- p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]); +-#endif /* not TRILIBRARY */ +- } else { +- /* Find the number of the adjacent triangle (and Voronoi vertex). */ +- p2 = * (int *) (trisym.tri + 6); +- /* Finite edge. Write indices of two endpoints. */ +-#ifdef TRILIBRARY +- elist[coordindex] = p1; +- normlist[coordindex++] = 0.0; +- elist[coordindex] = p2; +- normlist[coordindex++] = 0.0; +-#else /* not TRILIBRARY */ +- fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2); +-#endif /* not TRILIBRARY */ +- } +- vedgenumber++; +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist) +-#else /* not ANSI_DECLARATORS */ +-void writeneighbors(m, b, neighborlist) +-struct mesh *m; +-struct behavior *b; +-int **neighborlist; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writeneighbors(m, b, neighborfilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *neighborfilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +-#ifdef TRILIBRARY +- int *nlist; +- int index; +-#else /* not TRILIBRARY */ +- FILE *outfile; +-#endif /* not TRILIBRARY */ +- struct otri triangleloop, trisym; +- long elementnumber; +- int neighbor1, neighbor2, neighbor3; +- triangle ptr; /* Temporary variable used by sym(). */ +- +-#ifdef TRILIBRARY +- if (!b->quiet) { +- printf("Writing neighbors.\n"); +- } +- /* Allocate memory for neighbors if necessary. */ +- if (*neighborlist == (int *) NULL) { +- *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 * +- sizeof(int))); +- } +- nlist = *neighborlist; +- index = 0; +-#else /* not TRILIBRARY */ +- if (!b->quiet) { +- printf("Writing %s.\n", neighborfilename); +- } +- outfile = fopen(neighborfilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", neighborfilename); +- triexit(1); +- } +- /* Number of triangles, three neighbors per triangle. */ +- fprintf(outfile, "%ld %d\n", m->triangles.items, 3); +-#endif /* not TRILIBRARY */ +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- triangleloop.orient = 0; +- elementnumber = b->firstnumber; +- while (triangleloop.tri != (triangle *) NULL) { +- * (int *) (triangleloop.tri + 6) = (int) elementnumber; +- triangleloop.tri = triangletraverse(m); +- elementnumber++; +- } +- * (int *) (m->dummytri + 6) = -1; +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- elementnumber = b->firstnumber; +- while (triangleloop.tri != (triangle *) NULL) { +- triangleloop.orient = 1; +- sym(triangleloop, trisym); +- neighbor1 = * (int *) (trisym.tri + 6); +- triangleloop.orient = 2; +- sym(triangleloop, trisym); +- neighbor2 = * (int *) (trisym.tri + 6); +- triangleloop.orient = 0; +- sym(triangleloop, trisym); +- neighbor3 = * (int *) (trisym.tri + 6); +-#ifdef TRILIBRARY +- nlist[index++] = neighbor1; +- nlist[index++] = neighbor2; +- nlist[index++] = neighbor3; +-#else /* not TRILIBRARY */ +- /* Triangle number, neighboring triangle numbers. */ +- fprintf(outfile, "%4ld %d %d %d\n", elementnumber, +- neighbor1, neighbor2, neighbor3); +-#endif /* not TRILIBRARY */ +- +- triangleloop.tri = triangletraverse(m); +- elementnumber++; +- } +- +-#ifndef TRILIBRARY +- finishfile(outfile, argc, argv); +-#endif /* not TRILIBRARY */ +-} +- +-/*****************************************************************************/ +-/* */ +-/* writeoff() Write the triangulation to an .off file. */ +-/* */ +-/* OFF stands for the Object File Format, a format used by the Geometry */ +-/* Center's Geomview package. */ +-/* */ +-/*****************************************************************************/ +- +-#ifndef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void writeoff(struct mesh *m, struct behavior *b, char *offfilename, +- int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-void writeoff(m, b, offfilename, argc, argv) +-struct mesh *m; +-struct behavior *b; +-char *offfilename; +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- FILE *outfile; +- struct otri triangleloop; +- vertex vertexloop; +- vertex p1, p2, p3; +- long outvertices; +- +- if (!b->quiet) { +- printf("Writing %s.\n", offfilename); +- } +- +- if (b->jettison) { +- outvertices = m->vertices.items - m->undeads; +- } else { +- outvertices = m->vertices.items; +- } +- +- outfile = fopen(offfilename, "w"); +- if (outfile == (FILE *) NULL) { +- printf(" Error: Cannot create file %s.\n", offfilename); +- triexit(1); +- } +- /* Number of vertices, triangles, and edges. */ +- fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items, +- m->edges); +- +- /* Write the vertices. */ +- traversalinit(&m->vertices); +- vertexloop = vertextraverse(m); +- while (vertexloop != (vertex) NULL) { +- if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { +- /* The "0.0" is here because the OFF format uses 3D coordinates. */ +- fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1], +- 0.0); +- } +- vertexloop = vertextraverse(m); +- } +- +- /* Write the triangles. */ +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- triangleloop.orient = 0; +- while (triangleloop.tri != (triangle *) NULL) { +- org(triangleloop, p1); +- dest(triangleloop, p2); +- apex(triangleloop, p3); +- /* The "3" means a three-vertex polygon. */ +- fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber, +- vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber); +- triangleloop.tri = triangletraverse(m); +- } +- finishfile(outfile, argc, argv); +-} +- +-#endif /* not TRILIBRARY */ +- +-/** **/ +-/** **/ +-/********* File I/O routines end here *********/ +- +-/*****************************************************************************/ +-/* */ +-/* quality_statistics() Print statistics about the quality of the mesh. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void quality_statistics(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void quality_statistics(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- struct otri triangleloop; +- vertex p[3]; +- REAL cossquaretable[8]; +- REAL ratiotable[16]; +- REAL dx[3], dy[3]; +- REAL edgelength[3]; +- REAL dotproduct; +- REAL cossquare; +- REAL triarea; +- REAL shortest, longest; +- REAL trilongest2; +- REAL smallestarea, biggestarea; +- REAL triminaltitude2; +- REAL minaltitude; +- REAL triaspect2; +- REAL worstaspect; +- REAL smallestangle, biggestangle; +- REAL radconst, degconst; +- int angletable[18]; +- int aspecttable[16]; +- int aspectindex; +- int tendegree; +- int acutebiggest; +- int i, ii, j, k; +- +- printf("Mesh quality statistics:\n\n"); +- radconst = PI / 18.0; +- degconst = 180.0 / PI; +- for (i = 0; i < 8; i++) { +- cossquaretable[i] = cos(radconst * (REAL) (i + 1)); +- cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; +- } +- for (i = 0; i < 18; i++) { +- angletable[i] = 0; +- } +- +- ratiotable[0] = 1.5; ratiotable[1] = 2.0; +- ratiotable[2] = 2.5; ratiotable[3] = 3.0; +- ratiotable[4] = 4.0; ratiotable[5] = 6.0; +- ratiotable[6] = 10.0; ratiotable[7] = 15.0; +- ratiotable[8] = 25.0; ratiotable[9] = 50.0; +- ratiotable[10] = 100.0; ratiotable[11] = 300.0; +- ratiotable[12] = 1000.0; ratiotable[13] = 10000.0; +- ratiotable[14] = 100000.0; ratiotable[15] = 0.0; +- for (i = 0; i < 16; i++) { +- aspecttable[i] = 0; +- } +- +- minaltitude = m->xmax - m->xmin + m->ymax - m->ymin; +- minaltitude = minaltitude * minaltitude; +- shortest = minaltitude; +- longest = 0.0; +- smallestarea = minaltitude; +- biggestarea = 0.0; +- worstaspect = 0.0; +- smallestangle = 0.0; +- biggestangle = 2.0; +- acutebiggest = 1; +- +- traversalinit(&m->triangles); +- triangleloop.tri = triangletraverse(m); +- triangleloop.orient = 0; +- while (triangleloop.tri != (triangle *) NULL) { +- org(triangleloop, p[0]); +- dest(triangleloop, p[1]); +- apex(triangleloop, p[2]); +- trilongest2 = 0.0; +- +- for (i = 0; i < 3; i++) { +- j = plus1mod3[i]; +- k = minus1mod3[i]; +- dx[i] = p[j][0] - p[k][0]; +- dy[i] = p[j][1] - p[k][1]; +- edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; +- if (edgelength[i] > trilongest2) { +- trilongest2 = edgelength[i]; +- } +- if (edgelength[i] > longest) { +- longest = edgelength[i]; +- } +- if (edgelength[i] < shortest) { +- shortest = edgelength[i]; +- } +- } +- +- triarea = counterclockwise(m, b, p[0], p[1], p[2]); +- if (triarea < smallestarea) { +- smallestarea = triarea; +- } +- if (triarea > biggestarea) { +- biggestarea = triarea; +- } +- triminaltitude2 = triarea * triarea / trilongest2; +- if (triminaltitude2 < minaltitude) { +- minaltitude = triminaltitude2; +- } +- triaspect2 = trilongest2 / triminaltitude2; +- if (triaspect2 > worstaspect) { +- worstaspect = triaspect2; +- } +- aspectindex = 0; +- while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) +- && (aspectindex < 15)) { +- aspectindex++; +- } +- aspecttable[aspectindex]++; +- +- for (i = 0; i < 3; i++) { +- j = plus1mod3[i]; +- k = minus1mod3[i]; +- dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; +- cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); +- tendegree = 8; +- for (ii = 7; ii >= 0; ii--) { +- if (cossquare > cossquaretable[ii]) { +- tendegree = ii; +- } +- } +- if (dotproduct <= 0.0) { +- angletable[tendegree]++; +- if (cossquare > smallestangle) { +- smallestangle = cossquare; +- } +- if (acutebiggest && (cossquare < biggestangle)) { +- biggestangle = cossquare; +- } +- } else { +- angletable[17 - tendegree]++; +- if (acutebiggest || (cossquare > biggestangle)) { +- biggestangle = cossquare; +- acutebiggest = 0; +- } +- } +- } +- triangleloop.tri = triangletraverse(m); +- } +- +- shortest = sqrt(shortest); +- longest = sqrt(longest); +- minaltitude = sqrt(minaltitude); +- worstaspect = sqrt(worstaspect); +- smallestarea *= 0.5; +- biggestarea *= 0.5; +- if (smallestangle >= 1.0) { +- smallestangle = 0.0; +- } else { +- smallestangle = degconst * acos(sqrt(smallestangle)); +- } +- if (biggestangle >= 1.0) { +- biggestangle = 180.0; +- } else { +- if (acutebiggest) { +- biggestangle = degconst * acos(sqrt(biggestangle)); +- } else { +- biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); +- } +- } +- +- printf(" Smallest area: %16.5g | Largest area: %16.5g\n", +- smallestarea, biggestarea); +- printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", +- shortest, longest); +- printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", +- minaltitude, worstaspect); +- +- printf(" Triangle aspect ratio histogram:\n"); +- printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", +- ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], +- aspecttable[8]); +- for (i = 1; i < 7; i++) { +- printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", +- ratiotable[i - 1], ratiotable[i], aspecttable[i], +- ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); +- } +- printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", +- ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], +- aspecttable[15]); +- printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n"); +- +- printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", +- smallestangle, biggestangle); +- +- printf(" Angle histogram:\n"); +- for (i = 0; i < 9; i++) { +- printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", +- i * 10, i * 10 + 10, angletable[i], +- i * 10 + 90, i * 10 + 100, angletable[i + 9]); +- } +- printf("\n"); +-} +- +-/*****************************************************************************/ +-/* */ +-/* statistics() Print all sorts of cool facts. */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef ANSI_DECLARATORS +-void statistics(struct mesh *m, struct behavior *b) +-#else /* not ANSI_DECLARATORS */ +-void statistics(m, b) +-struct mesh *m; +-struct behavior *b; +-#endif /* not ANSI_DECLARATORS */ +- +-{ +- printf("\nStatistics:\n\n"); +- printf(" Input vertices: %d\n", m->invertices); +- if (b->refine) { +- printf(" Input triangles: %d\n", m->inelements); +- } +- if (b->poly) { +- printf(" Input segments: %d\n", m->insegments); +- if (!b->refine) { +- printf(" Input holes: %d\n", m->holes); +- } +- } +- +- printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads); +- printf(" Mesh triangles: %ld\n", m->triangles.items); +- printf(" Mesh edges: %ld\n", m->edges); +- printf(" Mesh exterior boundary edges: %ld\n", m->hullsize); +- if (b->poly || b->refine) { +- printf(" Mesh interior boundary edges: %ld\n", +- m->subsegs.items - m->hullsize); +- printf(" Mesh subsegments (constrained edges): %ld\n", +- m->subsegs.items); +- } +- printf("\n"); +- +- if (b->verbose) { +- quality_statistics(m, b); +- printf("Memory allocation statistics:\n\n"); +- printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems); +- printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems); +- if (m->subsegs.maxitems > 0) { +- printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems); +- } +- if (m->viri.maxitems > 0) { +- printf(" Maximum number of viri: %ld\n", m->viri.maxitems); +- } +- if (m->badsubsegs.maxitems > 0) { +- printf(" Maximum number of encroached subsegments: %ld\n", +- m->badsubsegs.maxitems); +- } +- if (m->badtriangles.maxitems > 0) { +- printf(" Maximum number of bad triangles: %ld\n", +- m->badtriangles.maxitems); +- } +- if (m->flipstackers.maxitems > 0) { +- printf(" Maximum number of stacked triangle flips: %ld\n", +- m->flipstackers.maxitems); +- } +- if (m->splaynodes.maxitems > 0) { +- printf(" Maximum number of splay tree nodes: %ld\n", +- m->splaynodes.maxitems); +- } +- printf(" Approximate heap memory use (bytes): %ld\n\n", +- m->vertices.maxitems * m->vertices.itembytes + +- m->triangles.maxitems * m->triangles.itembytes + +- m->subsegs.maxitems * m->subsegs.itembytes + +- m->viri.maxitems * m->viri.itembytes + +- m->badsubsegs.maxitems * m->badsubsegs.itembytes + +- m->badtriangles.maxitems * m->badtriangles.itembytes + +- m->flipstackers.maxitems * m->flipstackers.itembytes + +- m->splaynodes.maxitems * m->splaynodes.itembytes); +- +- printf("Algorithmic statistics:\n\n"); +- if (!b->weighted) { +- printf(" Number of incircle tests: %ld\n", m->incirclecount); +- } else { +- printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount); +- } +- printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount); +- if (m->hyperbolacount > 0) { +- printf(" Number of right-of-hyperbola tests: %ld\n", +- m->hyperbolacount); +- } +- if (m->circletopcount > 0) { +- printf(" Number of circle top computations: %ld\n", +- m->circletopcount); +- } +- if (m->circumcentercount > 0) { +- printf(" Number of triangle circumcenter computations: %ld\n", +- m->circumcentercount); +- } +- printf("\n"); +- } +-} +- +-/*****************************************************************************/ +-/* */ +-/* main() or triangulate() Gosh, do everything. */ +-/* */ +-/* The sequence is roughly as follows. Many of these steps can be skipped, */ +-/* depending on the command line switches. */ +-/* */ +-/* - Initialize constants and parse the command line. */ +-/* - Read the vertices from a file and either */ +-/* - triangulate them (no -r), or */ +-/* - read an old mesh from files and reconstruct it (-r). */ +-/* - Insert the PSLG segments (-p), and possibly segments on the convex */ +-/* hull (-c). */ +-/* - Read the holes (-p), regional attributes (-pA), and regional area */ +-/* constraints (-pa). Carve the holes and concavities, and spread the */ +-/* regional attributes and area constraints. */ +-/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */ +-/* Also enforce the conforming Delaunay property (-q and -a). */ +-/* - Compute the number of edges in the resulting mesh. */ +-/* - Promote the mesh's linear triangles to higher order elements (-o). */ +-/* - Write the output files and print the statistics. */ +-/* - Check the consistency and Delaunay property of the mesh (-C). */ +-/* */ +-/*****************************************************************************/ +- +-#ifdef TRILIBRARY +- +-#ifdef ANSI_DECLARATORS +-void triangulate(const char *const triswitches, struct triangulateio *in, +- struct triangulateio *out, struct triangulateio *vorout) +-#else /* not ANSI_DECLARATORS */ +-void triangulate(triswitches, in, out, vorout) +-const char *const triswitches; +-struct triangulateio *in; +-struct triangulateio *out; +-struct triangulateio *vorout; +-#endif /* not ANSI_DECLARATORS */ +- +-#else /* not TRILIBRARY */ +- +-#ifdef ANSI_DECLARATORS +-int main(int argc, char **argv) +-#else /* not ANSI_DECLARATORS */ +-int main(argc, argv) +-int argc; +-char **argv; +-#endif /* not ANSI_DECLARATORS */ +- +-#endif /* not TRILIBRARY */ +- +-{ +- struct mesh m; +- struct behavior b; +- REAL *holearray; /* Array of holes. */ +- REAL *regionarray; /* Array of regional attributes and area constraints. */ +-#ifndef TRILIBRARY +- FILE *polyfile; +-#endif /* not TRILIBRARY */ +-#ifndef NO_TIMER +- /* Variables for timing the performance of Triangle. The types are */ +- /* defined in sys/time.h. */ +- struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; +- struct timezone tz; +-#endif /* not NO_TIMER */ +- +-#ifndef NO_TIMER +- gettimeofday(&tv0, &tz); +-#endif /* not NO_TIMER */ +- +- triangleinit(&m); +-#ifdef TRILIBRARY +- parsecommandline(1, &triswitches, &b); +-#else /* not TRILIBRARY */ +- parsecommandline(argc, argv, &b); +-#endif /* not TRILIBRARY */ +- m.steinerleft = b.steiner; +- +-#ifdef TRILIBRARY +- transfernodes(&m, &b, in->pointlist, in->pointattributelist, +- in->pointmarkerlist, in->numberofpoints, +- in->numberofpointattributes); +-#else /* not TRILIBRARY */ +- readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile); +-#endif /* not TRILIBRARY */ +- +-#ifndef NO_TIMER +- if (!b.quiet) { +- gettimeofday(&tv1, &tz); +- } +-#endif /* not NO_TIMER */ +- +-#ifdef CDT_ONLY +- m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ +-#else /* not CDT_ONLY */ +- if (b.refine) { +- /* Read and reconstruct a mesh. */ +-#ifdef TRILIBRARY +- m.hullsize = reconstruct(&m, &b, in->trianglelist, +- in->triangleattributelist, in->trianglearealist, +- in->numberoftriangles, in->numberofcorners, +- in->numberoftriangleattributes, +- in->segmentlist, in->segmentmarkerlist, +- in->numberofsegments); +-#else /* not TRILIBRARY */ +- m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename, +- b.inpolyfilename, polyfile); +-#endif /* not TRILIBRARY */ +- } else { +- m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ +- } +-#endif /* not CDT_ONLY */ +- +-#ifndef NO_TIMER +- if (!b.quiet) { +- gettimeofday(&tv2, &tz); +- if (b.refine) { +- printf("Mesh reconstruction"); +- } else { +- printf("Delaunay"); +- } +- printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + +- (tv2.tv_usec - tv1.tv_usec) / 1000l); +- } +-#endif /* not NO_TIMER */ +- +- /* Ensure that no vertex can be mistaken for a triangular bounding */ +- /* box vertex in insertvertex(). */ +- m.infvertex1 = (vertex) NULL; +- m.infvertex2 = (vertex) NULL; +- m.infvertex3 = (vertex) NULL; +- +- if (b.usesegments) { +- m.checksegments = 1; /* Segments will be introduced next. */ +- if (!b.refine) { +- /* Insert PSLG segments and/or convex hull segments. */ +-#ifdef TRILIBRARY +- formskeleton(&m, &b, in->segmentlist, +- in->segmentmarkerlist, in->numberofsegments); +-#else /* not TRILIBRARY */ +- formskeleton(&m, &b, polyfile, b.inpolyfilename); +-#endif /* not TRILIBRARY */ +- } +- } +- +-#ifndef NO_TIMER +- if (!b.quiet) { +- gettimeofday(&tv3, &tz); +- if (b.usesegments && !b.refine) { +- printf("Segment milliseconds: %ld\n", +- 1000l * (tv3.tv_sec - tv2.tv_sec) + +- (tv3.tv_usec - tv2.tv_usec) / 1000l); +- } +- } +-#endif /* not NO_TIMER */ +- +- if (b.poly && (m.triangles.items > 0)) { +-#ifdef TRILIBRARY +- holearray = in->holelist; +- m.holes = in->numberofholes; +- regionarray = in->regionlist; +- m.regions = in->numberofregions; +-#else /* not TRILIBRARY */ +- readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes, +- ®ionarray, &m.regions); +-#endif /* not TRILIBRARY */ +- if (!b.refine) { +- /* Carve out holes and concavities. */ +- carveholes(&m, &b, holearray, m.holes, regionarray, m.regions); +- } +- } else { +- /* Without a PSLG, there can be no holes or regional attributes */ +- /* or area constraints. The following are set to zero to avoid */ +- /* an accidental free() later. */ +- m.holes = 0; +- m.regions = 0; +- } +- +-#ifndef NO_TIMER +- if (!b.quiet) { +- gettimeofday(&tv4, &tz); +- if (b.poly && !b.refine) { +- printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + +- (tv4.tv_usec - tv3.tv_usec) / 1000l); +- } +- } +-#endif /* not NO_TIMER */ +- +-#ifndef CDT_ONLY +- if (b.quality && (m.triangles.items > 0)) { +- enforcequality(&m, &b); /* Enforce angle and area constraints. */ +- } +-#endif /* not CDT_ONLY */ +- +-#ifndef NO_TIMER +- if (!b.quiet) { +- gettimeofday(&tv5, &tz); +-#ifndef CDT_ONLY +- if (b.quality) { +- printf("Quality milliseconds: %ld\n", +- 1000l * (tv5.tv_sec - tv4.tv_sec) + +- (tv5.tv_usec - tv4.tv_usec) / 1000l); +- } +-#endif /* not CDT_ONLY */ +- } +-#endif /* not NO_TIMER */ +- +- /* Calculate the number of edges. */ +- m.edges = (3l * m.triangles.items + m.hullsize) / 2l; +- +- if (b.order > 1) { +- highorder(&m, &b); /* Promote elements to higher polynomial order. */ +- } +- if (!b.quiet) { +- printf("\n"); +- } +- +-#ifdef TRILIBRARY +- if (b.jettison) { +- out->numberofpoints = m.vertices.items - m.undeads; +- } else { +- out->numberofpoints = m.vertices.items; +- } +- out->numberofpointattributes = m.nextras; +- out->numberoftriangles = m.triangles.items; +- out->numberofcorners = (b.order + 1) * (b.order + 2) / 2; +- out->numberoftriangleattributes = m.eextras; +- out->numberofedges = m.edges; +- if (b.usesegments) { +- out->numberofsegments = m.subsegs.items; +- } else { +- out->numberofsegments = m.hullsize; +- } +- if (vorout != (struct triangulateio *) NULL) { +- vorout->numberofpoints = m.triangles.items; +- vorout->numberofpointattributes = m.nextras; +- vorout->numberofedges = m.edges; +- } +-#endif /* TRILIBRARY */ +- /* If not using iteration numbers, don't write a .node file if one was */ +- /* read, because the original one would be overwritten! */ +- if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) { +- if (!b.quiet) { +-#ifdef TRILIBRARY +- printf("NOT writing vertices.\n"); +-#else /* not TRILIBRARY */ +- printf("NOT writing a .node file.\n"); +-#endif /* not TRILIBRARY */ +- } +- numbernodes(&m, &b); /* We must remember to number the vertices. */ +- } else { +- /* writenodes() numbers the vertices too. */ +-#ifdef TRILIBRARY +- writenodes(&m, &b, &out->pointlist, &out->pointattributelist, +- &out->pointmarkerlist); +-#else /* not TRILIBRARY */ +- writenodes(&m, &b, b.outnodefilename, argc, argv); +-#endif /* TRILIBRARY */ +- } +- if (b.noelewritten) { +- if (!b.quiet) { +-#ifdef TRILIBRARY +- printf("NOT writing triangles.\n"); +-#else /* not TRILIBRARY */ +- printf("NOT writing an .ele file.\n"); +-#endif /* not TRILIBRARY */ +- } +- } else { +-#ifdef TRILIBRARY +- writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist); +-#else /* not TRILIBRARY */ +- writeelements(&m, &b, b.outelefilename, argc, argv); +-#endif /* not TRILIBRARY */ +- } +- /* The -c switch (convex switch) causes a PSLG to be written */ +- /* even if none was read. */ +- if (b.poly || b.convex) { +- /* If not using iteration numbers, don't overwrite the .poly file. */ +- if (b.nopolywritten || b.noiterationnum) { +- if (!b.quiet) { +-#ifdef TRILIBRARY +- printf("NOT writing segments.\n"); +-#else /* not TRILIBRARY */ +- printf("NOT writing a .poly file.\n"); +-#endif /* not TRILIBRARY */ +- } +- } else { +-#ifdef TRILIBRARY +- writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist); +- out->numberofholes = m.holes; +- out->numberofregions = m.regions; +- if (b.poly) { +- out->holelist = in->holelist; +- out->regionlist = in->regionlist; +- } else { +- out->holelist = (REAL *) NULL; +- out->regionlist = (REAL *) NULL; +- } +-#else /* not TRILIBRARY */ +- writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray, +- m.regions, argc, argv); +-#endif /* not TRILIBRARY */ +- } +- } +-#ifndef TRILIBRARY +-#ifndef CDT_ONLY +- if (m.regions > 0) { +- trifree((void *) regionarray); +- } +-#endif /* not CDT_ONLY */ +- if (m.holes > 0) { +- trifree((void *) holearray); +- } +- if (b.geomview) { +- writeoff(&m, &b, b.offfilename, argc, argv); +- } +-#endif /* not TRILIBRARY */ +- if (b.edgesout) { +-#ifdef TRILIBRARY +- writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist); +-#else /* not TRILIBRARY */ +- writeedges(&m, &b, b.edgefilename, argc, argv); +-#endif /* not TRILIBRARY */ +- } +- if (b.voronoi) { +-#ifdef TRILIBRARY +- writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist, +- &vorout->pointmarkerlist, &vorout->edgelist, +- &vorout->edgemarkerlist, &vorout->normlist); +-#else /* not TRILIBRARY */ +- writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv); +-#endif /* not TRILIBRARY */ +- } +- if (b.neighbors) { +-#ifdef TRILIBRARY +- writeneighbors(&m, &b, &out->neighborlist); +-#else /* not TRILIBRARY */ +- writeneighbors(&m, &b, b.neighborfilename, argc, argv); +-#endif /* not TRILIBRARY */ +- } +- +- if (!b.quiet) { +-#ifndef NO_TIMER +- gettimeofday(&tv6, &tz); +- printf("\nOutput milliseconds: %ld\n", +- 1000l * (tv6.tv_sec - tv5.tv_sec) + +- (tv6.tv_usec - tv5.tv_usec) / 1000l); +- printf("Total running milliseconds: %ld\n", +- 1000l * (tv6.tv_sec - tv0.tv_sec) + +- (tv6.tv_usec - tv0.tv_usec) / 1000l); +-#endif /* not NO_TIMER */ +- +- statistics(&m, &b); +- } +- +-#ifndef REDUCED +- if (b.docheck) { +- checkmesh(&m, &b); +- checkdelaunay(&m, &b); +- } +-#endif /* not REDUCED */ +- +- triangledeinit(&m, &b); +-#ifndef TRILIBRARY +- return 0; +-#endif /* not TRILIBRARY */ +-}; +diff --git a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.h b/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.h +deleted file mode 100644 +index de14cb5395..0000000000 +--- a/Modules/ThirdParty/VNL/src/vxl/v3p/netlib/triangle.h ++++ /dev/null +@@ -1,299 +0,0 @@ +-#ifndef netlib_triangle_h_ +-#define netlib_triangle_h_ +-/*****************************************************************************/ +-/* */ +-/* (triangle.h) */ +-/* */ +-/* Include file for programs that call Triangle. */ +-/* */ +-/* Accompanies Triangle Version 1.6 */ +-/* July 28, 2005 */ +-/* */ +-/* Copyright 1996, 2005 */ +-/* Jonathan Richard Shewchuk */ +-/* 2360 Woolsey #H */ +-/* Berkeley, California 94705-1927 */ +-/* jrs@cs.berkeley.edu */ +-/* */ +-/*****************************************************************************/ +- +-/*****************************************************************************/ +-/* */ +-/* How to call Triangle from another program */ +-/* */ +-/* */ +-/* If you haven't read Triangle's instructions (run "triangle -h" to read */ +-/* them), you won't understand what follows. */ +-/* */ +-/* Triangle must be compiled into an object file (triangle.o) with the */ +-/* TRILIBRARY symbol defined (generally by using the -DTRILIBRARY compiler */ +-/* switch). The makefile included with Triangle will do this for you if */ +-/* you run "make trilibrary". The resulting object file can be called via */ +-/* the procedure triangulate(). */ +-/* */ +-/* If the size of the object file is important to you, you may wish to */ +-/* generate a reduced version of triangle.o. The REDUCED symbol gets rid */ +-/* of all features that are primarily of research interest. Specifically, */ +-/* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */ +-/* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */ +-/* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */ +-/* eliminates Triangle's -r, -q, -a, -u, -D, -Y, -S, and -s switches. */ +-/* */ +-/* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */ +-/* made in the makefile or in triangle.c itself. Putting these definitions */ +-/* in this file (triangle.h) will not create the desired effect. */ +-/* */ +-/* */ +-/* The calling convention for triangulate() follows. */ +-/* */ +-/* void triangulate(triswitches, in, out, vorout) */ +-/* char *triswitches; */ +-/* struct triangulateio *in; */ +-/* struct triangulateio *out; */ +-/* struct triangulateio *vorout; */ +-/* */ +-/* `triswitches' is a string containing the command line switches you wish */ +-/* to invoke. No initial dash is required. Some suggestions: */ +-/* */ +-/* - You'll probably find it convenient to use the `z' switch so that */ +-/* points (and other items) are numbered from zero. This simplifies */ +-/* indexing, because the first item of any type always starts at index */ +-/* [0] of the corresponding array, whether that item's number is zero or */ +-/* one. */ +-/* - You'll probably want to use the `Q' (quiet) switch in your final code, */ +-/* but you can take advantage of Triangle's printed output (including the */ +-/* `V' switch) while debugging. */ +-/* - If you are not using the `q', `a', `u', `D', `j', or `s' switches, */ +-/* then the output points will be identical to the input points, except */ +-/* possibly for the boundary markers. If you don't need the boundary */ +-/* markers, you should use the `N' (no nodes output) switch to save */ +-/* memory. (If you do need boundary markers, but need to save memory, a */ +-/* good nasty trick is to set out->pointlist equal to in->pointlist */ +-/* before calling triangulate(), so that Triangle overwrites the input */ +-/* points with identical copies.) */ +-/* - The `I' (no iteration numbers) and `g' (.off file output) switches */ +-/* have no effect when Triangle is compiled with TRILIBRARY defined. */ +-/* */ +-/* `in', `out', and `vorout' are descriptions of the input, the output, */ +-/* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */ +-/* `vorout' may be NULL. `in' and `out' may never be NULL. */ +-/* */ +-/* Certain fields of the input and output structures must be initialized, */ +-/* as described below. */ +-/* */ +-/*****************************************************************************/ +- +-/*****************************************************************************/ +-/* */ +-/* The `triangulateio' structure. */ +-/* */ +-/* Used to pass data into and out of the triangulate() procedure. */ +-/* */ +-/* */ +-/* Arrays are used to store points, triangles, markers, and so forth. In */ +-/* all cases, the first item in any array is stored starting at index [0]. */ +-/* However, that item is item number `1' unless the `z' switch is used, in */ +-/* which case it is item number `0'. Hence, you may find it easier to */ +-/* index points (and triangles in the neighbor list) if you use the `z' */ +-/* switch. Unless, of course, you're calling Triangle from a Fortran */ +-/* program. */ +-/* */ +-/* Description of fields (except the `numberof' fields, which are obvious): */ +-/* */ +-/* `pointlist': An array of point coordinates. The first point's x */ +-/* coordinate is at index [0] and its y coordinate at index [1], followed */ +-/* by the coordinates of the remaining points. Each point occupies two */ +-/* REALs. */ +-/* `pointattributelist': An array of point attributes. Each point's */ +-/* attributes occupy `numberofpointattributes' REALs. */ +-/* `pointmarkerlist': An array of point markers; one int per point. */ +-/* */ +-/* `trianglelist': An array of triangle corners. The first triangle's */ +-/* first corner is at index [0], followed by its other two corners in */ +-/* counterclockwise order, followed by any other nodes if the triangle */ +-/* represents a nonlinear element. Each triangle occupies */ +-/* `numberofcorners' ints. */ +-/* `triangleattributelist': An array of triangle attributes. Each */ +-/* triangle's attributes occupy `numberoftriangleattributes' REALs. */ +-/* `trianglearealist': An array of triangle area constraints; one REAL per */ +-/* triangle. Input only. */ +-/* `neighborlist': An array of triangle neighbors; three ints per */ +-/* triangle. Output only. */ +-/* */ +-/* `segmentlist': An array of segment endpoints. The first segment's */ +-/* endpoints are at indices [0] and [1], followed by the remaining */ +-/* segments. Two ints per segment. */ +-/* `segmentmarkerlist': An array of segment markers; one int per segment. */ +-/* */ +-/* `holelist': An array of holes. The first hole's x and y coordinates */ +-/* are at indices [0] and [1], followed by the remaining holes. Two */ +-/* REALs per hole. Input only, although the pointer is copied to the */ +-/* output structure for your convenience. */ +-/* */ +-/* `regionlist': An array of regional attributes and area constraints. */ +-/* The first constraint's x and y coordinates are at indices [0] and [1], */ +-/* followed by the regional attribute at index [2], followed by the */ +-/* maximum area at index [3], followed by the remaining area constraints. */ +-/* Four REALs per area constraint. Note that each regional attribute is */ +-/* used only if you select the `A' switch, and each area constraint is */ +-/* used only if you select the `a' switch (with no number following), but */ +-/* omitting one of these switches does not change the memory layout. */ +-/* Input only, although the pointer is copied to the output structure for */ +-/* your convenience. */ +-/* */ +-/* `edgelist': An array of edge endpoints. The first edge's endpoints are */ +-/* at indices [0] and [1], followed by the remaining edges. Two ints per */ +-/* edge. Output only. */ +-/* `edgemarkerlist': An array of edge markers; one int per edge. Output */ +-/* only. */ +-/* `normlist': An array of normal vectors, used for infinite rays in */ +-/* Voronoi diagrams. The first normal vector's x and y magnitudes are */ +-/* at indices [0] and [1], followed by the remaining vectors. For each */ +-/* finite edge in a Voronoi diagram, the normal vector written is the */ +-/* zero vector. Two REALs per edge. Output only. */ +-/* */ +-/* */ +-/* Any input fields that Triangle will examine must be initialized. */ +-/* Furthermore, for each output array that Triangle will write to, you */ +-/* must either provide space by setting the appropriate pointer to point */ +-/* to the space you want the data written to, or you must initialize the */ +-/* pointer to NULL, which tells Triangle to allocate space for the results. */ +-/* The latter option is preferable, because Triangle always knows exactly */ +-/* how much space to allocate. The former option is provided mainly for */ +-/* people who need to call Triangle from Fortran code, though it also makes */ +-/* possible some nasty space-saving tricks, like writing the output to the */ +-/* same arrays as the input. */ +-/* */ +-/* Triangle will not free() any input or output arrays, including those it */ +-/* allocates itself; that's up to you. You should free arrays allocated by */ +-/* Triangle by calling the trifree() procedure defined below. (By default, */ +-/* trifree() just calls the standard free() library procedure, but */ +-/* applications that call triangulate() may replace trimalloc() and */ +-/* trifree() in triangle.c to use specialized memory allocators.) */ +-/* */ +-/* Here's a guide to help you decide which fields you must initialize */ +-/* before you call triangulate(). */ +-/* */ +-/* `in': */ +-/* */ +-/* - `pointlist' must always point to a list of points; `numberofpoints' */ +-/* and `numberofpointattributes' must be properly set. */ +-/* `pointmarkerlist' must either be set to NULL (in which case all */ +-/* markers default to zero), or must point to a list of markers. If */ +-/* `numberofpointattributes' is not zero, `pointattributelist' must */ +-/* point to a list of point attributes. */ +-/* - If the `r' switch is used, `trianglelist' must point to a list of */ +-/* triangles, and `numberoftriangles', `numberofcorners', and */ +-/* `numberoftriangleattributes' must be properly set. If */ +-/* `numberoftriangleattributes' is not zero, `triangleattributelist' */ +-/* must point to a list of triangle attributes. If the `a' switch is */ +-/* used (with no number following), `trianglearealist' must point to a */ +-/* list of triangle area constraints. `neighborlist' may be ignored. */ +-/* - If the `p' switch is used, `segmentlist' must point to a list of */ +-/* segments, `numberofsegments' must be properly set, and */ +-/* `segmentmarkerlist' must either be set to NULL (in which case all */ +-/* markers default to zero), or must point to a list of markers. */ +-/* - If the `p' switch is used without the `r' switch, then */ +-/* `numberofholes' and `numberofregions' must be properly set. If */ +-/* `numberofholes' is not zero, `holelist' must point to a list of */ +-/* holes. If `numberofregions' is not zero, `regionlist' must point to */ +-/* a list of region constraints. */ +-/* - If the `p' switch is used, `holelist', `numberofholes', */ +-/* `regionlist', and `numberofregions' is copied to `out'. (You can */ +-/* nonetheless get away with not initializing them if the `r' switch is */ +-/* used.) */ +-/* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */ +-/* ignored. */ +-/* */ +-/* `out': */ +-/* */ +-/* - `pointlist' must be initialized (NULL or pointing to memory) unless */ +-/* the `N' switch is used. `pointmarkerlist' must be initialized */ +-/* unless the `N' or `B' switch is used. If `N' is not used and */ +-/* `in->numberofpointattributes' is not zero, `pointattributelist' must */ +-/* be initialized. */ +-/* - `trianglelist' must be initialized unless the `E' switch is used. */ +-/* `neighborlist' must be initialized if the `n' switch is used. If */ +-/* the `E' switch is not used and (`in->numberofelementattributes' is */ +-/* not zero or the `A' switch is used), `elementattributelist' must be */ +-/* initialized. `trianglearealist' may be ignored. */ +-/* - `segmentlist' must be initialized if the `p' or `c' switch is used, */ +-/* and the `P' switch is not used. `segmentmarkerlist' must also be */ +-/* initialized under these circumstances unless the `B' switch is used. */ +-/* - `edgelist' must be initialized if the `e' switch is used. */ +-/* `edgemarkerlist' must be initialized if the `e' switch is used and */ +-/* the `B' switch is not. */ +-/* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/ +-/* */ +-/* `vorout' (only needed if `v' switch is used): */ +-/* */ +-/* - `pointlist' must be initialized. If `in->numberofpointattributes' */ +-/* is not zero, `pointattributelist' must be initialized. */ +-/* `pointmarkerlist' may be ignored. */ +-/* - `edgelist' and `normlist' must both be initialized. */ +-/* `edgemarkerlist' may be ignored. */ +-/* - Everything else may be ignored. */ +-/* */ +-/* After a call to triangulate(), the valid fields of `out' and `vorout' */ +-/* will depend, in an obvious way, on the choice of switches used. Note */ +-/* that when the `p' switch is used, the pointers `holelist' and */ +-/* `regionlist' are copied from `in' to `out', but no new space is */ +-/* allocated; be careful that you don't free() the same array twice. On */ +-/* the other hand, Triangle will never copy the `pointlist' pointer (or any */ +-/* others); new space is allocated for `out->pointlist', or if the `N' */ +-/* switch is used, `out->pointlist' remains uninitialized. */ +-/* */ +-/* All of the meaningful `numberof' fields will be properly set; for */ +-/* instance, `numberofedges' will represent the number of edges in the */ +-/* triangulation whether or not the edges were written. If segments are */ +-/* not used, `numberofsegments' will indicate the number of boundary edges. */ +-/* */ +-/*****************************************************************************/ +-#undef REAL +-#ifdef SINGLE +-#define REAL float +-#else /* not SINGLE */ +-#define REAL double +-#endif /* not SINGLE */ +- +-struct triangulateio { +- REAL *pointlist; /* In / out */ +- REAL *pointattributelist; /* In / out */ +- int *pointmarkerlist; /* In / out */ +- int numberofpoints; /* In / out */ +- int numberofpointattributes; /* In / out */ +- +- int *trianglelist; /* In / out */ +- REAL *triangleattributelist; /* In / out */ +- REAL *trianglearealist; /* In only */ +- int *neighborlist; /* Out only */ +- int numberoftriangles; /* In / out */ +- int numberofcorners; /* In / out */ +- int numberoftriangleattributes; /* In / out */ +- +- int *segmentlist; /* In / out */ +- int *segmentmarkerlist; /* In / out */ +- int numberofsegments; /* In / out */ +- +- REAL *holelist; /* In / pointer to array copied out */ +- int numberofholes; /* In / copied out */ +- +- REAL *regionlist; /* In / pointer to array copied out */ +- int numberofregions; /* In / copied out */ +- +- int *edgelist; /* Out only */ +- int *edgemarkerlist; /* Not used with Voronoi diagram; out only */ +- REAL *normlist; /* Used only with Voronoi diagram; out only */ +- int numberofedges; /* Out only */ +-}; +- +-#define ANSI_DECLARATORS +-#ifdef ANSI_DECLARATORS +-void triangulate(const char * const, struct triangulateio *, struct triangulateio *, +- struct triangulateio *); +-void trifree(void *memptr); +-#else /* not ANSI_DECLARATORS */ +-void triangulate(); +-void trifree(); +-#endif /* not ANSI_DECLARATORS */ +-#endif /* netlib_triangle_h_ */ +commit d1066224e3b048650e278f5ebfb648b2a198ba55 +Author: Matt McCormick +Date: Mon Jul 13 14:28:52 2020 -0400 + + BUG: Remove License incompatible netlib files from vxl updates + + Per issue #1913. + +diff --git a/Modules/ThirdParty/VNL/UpdateFromUpstream.sh b/Modules/ThirdParty/VNL/UpdateFromUpstream.sh +index b2665ad167..010d5a2047 100755 +--- a/Modules/ThirdParty/VNL/UpdateFromUpstream.sh ++++ b/Modules/ThirdParty/VNL/UpdateFromUpstream.sh +@@ -8,7 +8,10 @@ upstream_git_branch='master' + snapshot_author_name='VXL Maintainers' + snapshot_author_email='vxl-maintainers@lists.sourceforge.net' + +-snapshot_redact_cmd='' ++snapshot_redact_cmd=' ++ rm v3p/netlib/triangle* ++ rm v3p/netlib/examples/showme.c ++' + snapshot_relative_path='src/vxl' + snapshot_paths=' + CMakeLists.txt diff --git a/insighttoolkit.changes b/insighttoolkit.changes index 691e645..7947163 100644 --- a/insighttoolkit.changes +++ b/insighttoolkit.changes @@ -1,3 +1,10 @@ +------------------------------------------------------------------- +Tue Jul 14 22:09:20 UTC 2020 - Atri Bhattacharya + +- Add insighttoolkit-drop-netlib-triangle-files.patch: Drop netlib + triangle files and any linking to them due to licensing issues; + patch from upstream [gh#InsightSoftwareConsortium/ITK#1913]. + ------------------------------------------------------------------- Wed Jun 3 00:58:31 UTC 2020 - Atri Bhattacharya diff --git a/insighttoolkit.spec b/insighttoolkit.spec index d29529c..7ad421f 100644 --- a/insighttoolkit.spec +++ b/insighttoolkit.spec @@ -26,6 +26,8 @@ Name: insighttoolkit Version: 5.1.0 Release: 0 Summary: Toolkit for scientific image processing, segmentation, and registration +# NON-FREE FILES IN Modules/ThirdParty/VNL/src/vxl/v3p/netlib/ NOT USED BY ITK AND REMOVED BY Patch4 +# SEE NOTICE file, https://github.com/InsightSoftwareConsortium/ITK/pull/1913, and https://github.com/InsightSoftwareConsortium/ITK/pull/1920 License: Apache-2.0 URL: https://www.itk.org Source: https://github.com/InsightSoftwareConsortium/ITK/releases/download/v%{version}/%{tarname}-%{version}.tar.gz @@ -33,6 +35,8 @@ Source: https://github.com/InsightSoftwareConsortium/ITK/releases/downlo Patch1: nrrdio-linking.patch # PATCH-FIX-UPSTREAM proper linking against math library [gh#InsightSoftwareConsortium/ITK#1867, gh#InsightSoftwareConsortium/ITK#1878] Patch3: itklbfgs-linking.patch +# PATCH-FIX-UPSTREAM insighttoolkit-drop-netlib-triangle-files.patch [gh#InsightSoftwareConsortium/ITK#1913] badshah400@gmail.com -- Drop netlib triangle files and any linking to them due to licensing issues; patch from upstream +Patch4: insighttoolkit-drop-netlib-triangle-files.patch BuildRequires: CastXML-devel BuildRequires: bison BuildRequires: cmake @@ -134,6 +138,7 @@ This package provides the modules for ITK's python bindings. -DITK_USE_SYSTEM_GDCM:BOOL=ON \ -DITK_USE_SYSTEM_SWIG:BOOL=ON \ -DITK_USE_SYSTEM_VXL:BOOL=OFF \ + -DVXL_BUILD_CORE_NUMERICS:BOOL=OFF \ -DVCL_INCLUDE_CXX_0X:BOOL=ON \ -DITK_FORBID_DOWNLOADS=ON \ -DITK_WRAP_PYTHON:BOOL=ON @@ -149,10 +154,11 @@ This package provides the modules for ITK's python bindings. %postun -n %{libname} -p /sbin/ldconfig %files -n %{libname} -%license LICENSE +%license LICENSE NOTICE %{_libdir}/*.so.1 %files devel +%license LICENSE NOTICE %{_includedir}/%{name}/ %{_libdir}/lib*.so %{_libdir}/cmake/ @@ -160,6 +166,7 @@ This package provides the modules for ITK's python bindings. %doc %{_docdir}/%{name}/ %files -n python3-itk +%license LICENSE NOTICE %{python3_sitearch}/*.py %{python3_sitearch}/itk/