Triangle
A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.
Version 1.3

Show Me
A Display Program for Meshes and More.
Version 1.3

Copyright 1996 Jonathan Richard Shewchuk
School of Computer Science
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, Pennsylvania  15213-3891
Please send bugs and comments to jrs@cs.cmu.edu

Created as part of the Archimedes project (tools for parallel FEM).
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, and quality conforming Delaunay triangulations.  The
latter can be generated with no small 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

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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.)

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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 data file.

Triangle and Show Me are each 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.

  Do you want single precision or double?  Do you want to leave out some of
  Triangle's features to reduce the size of the executable file?

  The "correct" directories for include files (especially X include files),
  if necessary.

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

However, on other systems (like my workstation), the latter incantation
will cause the wrong files to be read, and the Show Me mouse buttons won't
work properly in the main window.  Hence, try the "-I" and "-L" switches
ONLY if the compiler fails without it.  (If you're using the makefile, you
may edit it to add this switch.)

Some processors, possibly including Intel x86 family and 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.  If you have such a processor,
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.
Unfortunately, I don't have access to any such systems, and can't give
advice on how to configure them.  These problems don't occur on any
workstations I am aware of.  However, 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 both produce their own documentation.  Complete
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').  Alternatively, you may want to read
the instructions on the World Wide Web.  The appropriate URLs are:

  http://www.cs.cmu.edu/~quake/triangle.html
  http://www.cs.cmu.edu/~quake/showme.html

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.

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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.

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

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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.cmu.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.


Jonathan Richard Shewchuk
July 20, 1996
