1Triangle 2A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. 3Version 1.6 4 5Show Me 6A Display Program for Meshes and More. 7Version 1.6 8 9Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk 102360 Woolsey #H 11Berkeley, California 94705-1927 12Please send bugs and comments to jrs@cs.berkeley.edu 13 14Created as part of the Quake project (tools for earthquake simulation). 15Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship. 16There is no warranty whatsoever. Use at your own risk. 17 18 19Triangle generates exact Delaunay triangulations, constrained Delaunay 20triangulations, conforming Delaunay triangulations, Voronoi diagrams, and 21high-quality triangular meshes. The latter can be generated with no small 22or large angles, and are thus suitable for finite element analysis. 23Show Me graphically displays the contents of the geometric files used by 24Triangle. Show Me can also write images in PostScript form. 25 26Information on the algorithms used by Triangle, including complete 27references, can be found in the comments at the beginning of the triangle.c 28source file. Another listing of these references, with PostScript copies 29of some of the papers, is available from the Web page 30 31 http://www.cs.cmu.edu/~quake/triangle.research.html 32 33------------------------------------------------------------------------------ 34 35These programs may be freely redistributed under the condition that the 36copyright notices (including the copy of this notice in the code comments 37and the copyright notice printed when the `-h' switch is selected) are 38not removed, and no compensation is received. Private, research, and 39institutional use is free. You may distribute modified versions of this 40code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT 41IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH 42SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND 43CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as 44part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT 45WITH THE AUTHOR. (If you are not directly supplying this code to a 46customer, and you are instead telling them how they can obtain it for 47free, then you are not required to make any arrangement with me.) 48 49------------------------------------------------------------------------------ 50 51The files included in this distribution are: 52 53 README The file you're reading now. 54 triangle.c Complete C source code for Triangle. 55 showme.c Complete C source code for Show Me. 56 triangle.h Include file for calling Triangle from another program. 57 tricall.c Sample program that calls Triangle. 58 makefile Makefile for compiling Triangle and Show Me. 59 A.poly A sample input file. 60 61Each of Triangle and Show Me is a single portable C file. The easiest way 62to compile them is to edit and use the included makefile. Before 63compiling, read the makefile, which describes your options, and edit it 64accordingly. You should specify: 65 66 The source and binary directories. 67 68 The C compiler and level of optimization. 69 70 The "correct" directories for include files (especially X include files), 71 if necessary. 72 73 Do you want single precision or double? (The default is double.) Do you 74 want to leave out some of Triangle's features to reduce the size of the 75 executable file? Investigate the SINGLE, REDUCED, and CDT_ONLY symbols. 76 77 If yours is not a Unix system, define the NO_TIMER symbol to remove the 78 Unix-specific timing code. Also, don't try to compile Show Me; it only 79 works with X Windows. 80 81 If you are compiling on an Intel x86 CPU and using gcc w/Linux or 82 Microsoft C, be sure to define the LINUX or CPU86 (for Microsoft) symbol 83 during compilation so that the exact arithmetic works right. 84 85Once you've done this, type "make" to compile the programs. Alternatively, 86the files are usually easy to compile without a makefile: 87 88 cc -O -o triangle triangle.c -lm 89 cc -O -o showme showme.c -lX11 90 91On some systems, the C compiler won't be able to find the X include files 92or libraries, and you'll need to specify an include path or library path: 93 94 cc -O -I/usr/local/include -o showme showme.c -L/usr/local/lib -lX11 95 96Some processors, including Intel x86 family and possibly Motorola 68xxx 97family chips, are IEEE conformant but have extended length internal 98floating-point registers that may defeat Triangle's exact arithmetic 99routines by failing to cause enough roundoff error! Typically, there is a 100way to set these internal registers so that they are rounded off to IEEE 101single or double precision format. I believe (but I'm not certain) that 102Triangle has the right incantations for x86 chips, if you have gcc running 103under Linux (define the LINUX compiler symbol) or Microsoft C (define the 104CPU86 compiler symbol). 105 106If you have a different processor or operating system, or if I got the 107incantations wrong, you should check your C compiler or system manuals to 108find out how to configure these internal registers to the precision you are 109using. Otherwise, the exact arithmetic routines won't be exact at all. 110See http://www.cs.cmu.edu/~quake/robust.pc.html for details. Triangle's 111exact arithmetic hasn't a hope of working on machines like the Cray C90 or 112Y-MP, which are not IEEE conformant and have inaccurate rounding. 113 114Triangle and Show Me have both text and HTML documentation. The latter is 115illustrated. Find it on the Web at 116 117 http://www.cs.cmu.edu/~quake/triangle.html 118 http://www.cs.cmu.edu/~quake/showme.html 119 120Complete text instructions are printed by invoking each program with the 121`-h' switch: 122 123 triangle -h 124 showme -h 125 126The instructions are long; you'll probably want to pipe the output to 127`more' or `lpr' or redirect it to a file. 128 129Both programs give a short list of command line options if they are invoked 130without arguments (that is, just type `triangle' or `showme'). 131 132Try out Triangle on the enclosed sample file, A.poly: 133 134 triangle -p A 135 showme A.poly & 136 137Triangle will read the Planar Straight Line Graph defined by A.poly, and 138write its constrained Delaunay triangulation to A.1.node and A.1.ele. 139Show Me will display the figure defined by A.poly. There are two buttons 140marked "ele" in the Show Me window; click on the top one. This will cause 141Show Me to load and display the triangulation. 142 143For contrast, try running 144 145 triangle -pq A 146 147Now, click on the same "ele" button. A new triangulation will be loaded; 148this one having no angles smaller than 20 degrees. 149 150To see a Voronoi diagram, try this: 151 152 cp A.poly A.node 153 triangle -v A 154 155Click the "ele" button again. You will see the Delaunay triangulation of 156the points in A.poly, without the segments. Now click the top "voro" button. 157You will see the Voronoi diagram corresponding to that Delaunay triangulation. 158Click the "Reset" button to see the full extent of the diagram. 159 160------------------------------------------------------------------------------ 161 162If you wish to call Triangle from another program, instructions for doing 163so are contained in the file `triangle.h' (but read Triangle's regular 164instructions first!). Also look at `tricall.c', which provides an example 165of how to call Triangle. 166 167Type "make trilibrary" to create triangle.o, a callable object file. 168Alternatively, the object file is usually easy to compile without a 169makefile: 170 171 cc -DTRILIBRARY -O -c triangle.c 172 173Type "make distclean" to remove all the object and executable files created 174by make. 175 176------------------------------------------------------------------------------ 177 178If you use Triangle, and especially if you use it to accomplish real work, 179I would like very much to hear from you. A short letter or email (to 180jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot to me. 181The more people I know are using this program, the more easily I can 182justify spending time on improvements and on the three-dimensional 183successor to Triangle, which in turn will benefit you. Also, I can put you 184on a list to receive email whenever a new version of Triangle is available. 185 186If you use a mesh generated by Triangle or plotted by Show Me in a 187publication, please include an acknowledgment as well. And please spell 188Triangle with a capital `T'! If you want to include a citation, use 189`Jonathan Richard Shewchuk, ``Triangle: Engineering a 2D Quality Mesh 190Generator and Delaunay Triangulator,'' in Applied Computational Geometry: 191Towards Geometric Engineering (Ming C. Lin and Dinesh Manocha, editors), 192volume 1148 of Lecture Notes in Computer Science, pages 203-222, 193Springer-Verlag, Berlin, May 1996. (From the First ACM Workshop on Applied 194Computational Geometry.)' 195 196 197Jonathan Richard Shewchuk 198July 27, 2005 199