199 lines
8.5 KiB
Plaintext
199 lines
8.5 KiB
Plaintext
Triangle
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A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.
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Version 1.6
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Show Me
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A Display Program for Meshes and More.
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Version 1.6
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Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk
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2360 Woolsey #H
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Berkeley, California 94705-1927
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Please send bugs and comments to jrs@cs.berkeley.edu
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Created as part of the Quake project (tools for earthquake simulation).
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Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.
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There is no warranty whatsoever. Use at your own risk.
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Triangle generates exact Delaunay triangulations, constrained Delaunay
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triangulations, conforming Delaunay triangulations, Voronoi diagrams, and
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high-quality triangular meshes. The latter can be generated with no small
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or large angles, and are thus suitable for finite element analysis.
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Show Me graphically displays the contents of the geometric files used by
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Triangle. Show Me can also write images in PostScript form.
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Information on the algorithms used by Triangle, including complete
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references, can be found in the comments at the beginning of the triangle.c
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source file. Another listing of these references, with PostScript copies
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of some of the papers, is available from the Web page
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http://www.cs.cmu.edu/~quake/triangle.research.html
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------------------------------------------------------------------------------
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These programs may be freely redistributed under the condition that the
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copyright notices (including the copy of this notice in the code comments
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and the copyright notice printed when the `-h' switch is selected) are
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not removed, and no compensation is received. Private, research, and
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institutional use is free. You may distribute modified versions of this
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code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT
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IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH
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SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND
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CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as
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part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT
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WITH THE AUTHOR. (If you are not directly supplying this code to a
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customer, and you are instead telling them how they can obtain it for
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free, then you are not required to make any arrangement with me.)
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------------------------------------------------------------------------------
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The files included in this distribution are:
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README The file you're reading now.
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triangle.c Complete C source code for Triangle.
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showme.c Complete C source code for Show Me.
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triangle.h Include file for calling Triangle from another program.
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tricall.c Sample program that calls Triangle.
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makefile Makefile for compiling Triangle and Show Me.
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A.poly A sample input file.
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Each of Triangle and Show Me is a single portable C file. The easiest way
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to compile them is to edit and use the included makefile. Before
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compiling, read the makefile, which describes your options, and edit it
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accordingly. You should specify:
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The source and binary directories.
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The C compiler and level of optimization.
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The "correct" directories for include files (especially X include files),
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if necessary.
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Do you want single precision or double? (The default is double.) Do you
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want to leave out some of Triangle's features to reduce the size of the
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executable file? Investigate the SINGLE, REDUCED, and CDT_ONLY symbols.
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If yours is not a Unix system, define the NO_TIMER symbol to remove the
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Unix-specific timing code. Also, don't try to compile Show Me; it only
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works with X Windows.
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If you are compiling on an Intel x86 CPU and using gcc w/Linux or
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Microsoft C, be sure to define the LINUX or CPU86 (for Microsoft) symbol
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during compilation so that the exact arithmetic works right.
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Once you've done this, type "make" to compile the programs. Alternatively,
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the files are usually easy to compile without a makefile:
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cc -O -o triangle triangle.c -lm
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cc -O -o showme showme.c -lX11
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On some systems, the C compiler won't be able to find the X include files
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or libraries, and you'll need to specify an include path or library path:
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cc -O -I/usr/local/include -o showme showme.c -L/usr/local/lib -lX11
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Some processors, including Intel x86 family and possibly Motorola 68xxx
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family chips, are IEEE conformant but have extended length internal
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floating-point registers that may defeat Triangle's exact arithmetic
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routines by failing to cause enough roundoff error! Typically, there is a
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way to set these internal registers so that they are rounded off to IEEE
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single or double precision format. I believe (but I'm not certain) that
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Triangle has the right incantations for x86 chips, if you have gcc running
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under Linux (define the LINUX compiler symbol) or Microsoft C (define the
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CPU86 compiler symbol).
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If you have a different processor or operating system, or if I got the
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incantations wrong, you should check your C compiler or system manuals to
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find out how to configure these internal registers to the precision you are
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using. Otherwise, the exact arithmetic routines won't be exact at all.
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See http://www.cs.cmu.edu/~quake/robust.pc.html for details. Triangle's
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exact arithmetic hasn't a hope of working on machines like the Cray C90 or
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Y-MP, which are not IEEE conformant and have inaccurate rounding.
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Triangle and Show Me have both text and HTML documentation. The latter is
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illustrated. Find it on the Web at
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http://www.cs.cmu.edu/~quake/triangle.html
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http://www.cs.cmu.edu/~quake/showme.html
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Complete text instructions are printed by invoking each program with the
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`-h' switch:
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triangle -h
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showme -h
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The instructions are long; you'll probably want to pipe the output to
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`more' or `lpr' or redirect it to a file.
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Both programs give a short list of command line options if they are invoked
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without arguments (that is, just type `triangle' or `showme').
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Try out Triangle on the enclosed sample file, A.poly:
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triangle -p A
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showme A.poly &
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Triangle will read the Planar Straight Line Graph defined by A.poly, and
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write its constrained Delaunay triangulation to A.1.node and A.1.ele.
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Show Me will display the figure defined by A.poly. There are two buttons
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marked "ele" in the Show Me window; click on the top one. This will cause
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Show Me to load and display the triangulation.
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For contrast, try running
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triangle -pq A
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Now, click on the same "ele" button. A new triangulation will be loaded;
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this one having no angles smaller than 20 degrees.
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To see a Voronoi diagram, try this:
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cp A.poly A.node
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triangle -v A
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Click the "ele" button again. You will see the Delaunay triangulation of
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the points in A.poly, without the segments. Now click the top "voro" button.
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You will see the Voronoi diagram corresponding to that Delaunay triangulation.
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Click the "Reset" button to see the full extent of the diagram.
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------------------------------------------------------------------------------
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If you wish to call Triangle from another program, instructions for doing
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so are contained in the file `triangle.h' (but read Triangle's regular
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instructions first!). Also look at `tricall.c', which provides an example
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of how to call Triangle.
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Type "make trilibrary" to create triangle.o, a callable object file.
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Alternatively, the object file is usually easy to compile without a
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makefile:
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cc -DTRILIBRARY -O -c triangle.c
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Type "make distclean" to remove all the object and executable files created
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by make.
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------------------------------------------------------------------------------
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If you use Triangle, and especially if you use it to accomplish real work,
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I would like very much to hear from you. A short letter or email (to
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jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot to me.
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The more people I know are using this program, the more easily I can
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justify spending time on improvements and on the three-dimensional
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successor to Triangle, which in turn will benefit you. Also, I can put you
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on a list to receive email whenever a new version of Triangle is available.
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If you use a mesh generated by Triangle or plotted by Show Me in a
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publication, please include an acknowledgment as well. And please spell
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Triangle with a capital `T'! If you want to include a citation, use
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`Jonathan Richard Shewchuk, ``Triangle: Engineering a 2D Quality Mesh
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Generator and Delaunay Triangulator,'' in Applied Computational Geometry:
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Towards Geometric Engineering (Ming C. Lin and Dinesh Manocha, editors),
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volume 1148 of Lecture Notes in Computer Science, pages 203-222,
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Springer-Verlag, Berlin, May 1996. (From the First ACM Workshop on Applied
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Computational Geometry.)'
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Jonathan Richard Shewchuk
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July 27, 2005
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