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<html>
<head>
<title>
TEST_TRIANGULATION - Mesh Generation Test Regions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_TRIANGULATION <br> Mesh Generation Test Regions
</h1>
<hr>
<p>
<b>TEST_TRIANGULATION</b>
is a FORTRAN90 library which
sets up a number of triangulation test problems.
</p>
<p>
As far as possible, a uniform and abstract approach has been used.
For each test region, a number of routines are provided, via which
it is possible for the user to determine many things about the region.
Often, just one or two routines would be needed for a particular
purpose. The names of the routines, and their purposes are:
<ul>
<li>
<b>BOUNDARY_NEAREST:</b> returns the nearest point on the boundary
of the region to a given point or set of points;
</li>
<li>
<b>BOUNDARY_PROJECT:</b> projects exterior points onto the boundary.
</li>
<li>
<b>BOUNDARY_SEGMENT:</b> returns a sequence of roughly equally spaced
points that lie on one particular boundary segment;
</li>
<li>
<b>BOUNDARY_SEGMENT_LENGTH:</b> returns the "length" (number of
nodes) of a particular boundary segment. This simply counts
the number of points needed to trace or approximate the
boundary segment;
</li>
<li>
<b>BOUNDARY_SEGMENT_NUM:</b> returns the number of boundary segments.
Simple regions have one boundary segment. A region with one hole
has two, and so on;
</li>
<li>
<b>BOX:</b> returns a bounding box for the region. All points in
the region are within this box;
</li>
<li>
<b>DENSITY:</b> the value of the mesh density function at any
point in the region. If this is not constant, then high values
correspond to places where many more mesh points should be placed;
is always 2 for this set;
</li>
<li>
<b>ELEMENT_SIZE:</b> returns a requested typical element size. This
refers to the average size of the triangles formed by a triangulation
of the points;
</li>
<li>
<b>FIXED_NUM:</b> returns the number of points which must be
included as nodes of the mesh (which may be zero);
</li>
<li>
<b>FIXED_POINTS:</b> returns the coordinates of the points which
must be included as nodes of the mesh;
</li>
<li>
<b>HEADER:</b> prints a brief description of the problem;
</li>
<li>
<b>HOLE_NUM:</b> returns the number of "holes" in the region;
</li>
<li>
<b>HOLE_POINT:</b> returns the coordinates of one point in a hole
(useful when TRIANGLE is to be invoked);
</li>
<li>
<b>INSIDE:</b> reports which of a given set of points are
inside the region.
</li>
<li>
<b>SAMPLE:</b> returns a set of sample points from the region,
chosen with uniform probability;
</li>
<li>
<b>SAMPLE_H1:</b> returns a set of sample points from the region,
after it has been enlarged by an amount H1;
</li>
<li>
<b>SDIST:</b> returns the signed distance to the boundary of
the region for each of a set of input points.
(a positive distance means the point is outside the region,
a negative distance means it is inside);
<i>(Not ready for problems 4, 5, 6, 7, 8, 9 )</i>
</li>
<li>
<b>TITLE:</b> a title for the problem;
</li>
</ul>
</p>
<p>
The test problems include:
<ol>
<li>
The unit circle;
</li>
<li>
The unit circle with a circular hole;
</li>
<li>
A square with a circular hole;
</li>
<li>
A hexagon with a hexagonal hole;
</li>
<li>
The horn;
</li>
<li>
The superellipse with a superelliptical hole;
</li>
<li>
The bicycle seat;
</li>
<li>
The slice of pie with a circular hole and triangular notch;
</li>
<li>
Jeff Borggaard's square with two hexagonal holes;
</li>
<li>
The unit square;
</li>
<li>
The L-shaped region;
</li>
<li>
John Shadid's H-shaped region;
</li>
<li>
The Sandia fork;
</li>
<li>
Marcus Garvie's Lake Alpha, with Beta Island;
</li>
<li>
Sangbum Kim's forward step;
</li>
</ol>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_TRIANGULATION</b> is available in
<a href = "../../f_src/test_triangulation/test_triangulation.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_triangulation/test_triangulation.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt_triangulation/cvt_triangulation.html">
CVT_TRIANGULATION</a>,
a FORTRAN90 program which
uses routines from the <b>TEST_TRIANGULATION</b> library
to create a CVT-based triangularization.
</p>
<p>
<a href = "../../m_src/distmesh/distmesh.html">
DISTMESH</a>,
a MATLAB program which
takes the definition of
a 2D region, and fills it up with a set of nodes, and triangulates
those nodes to make a triangulation of the region. The region may
be nonconvex and may include holes; the user may request a specific
density for the nodes, and may require certain points to be in the
set of nodes.
</p>
<p>
<a href = "../../f_src/hex_grid_triangulate/hex_grid_triangulate.html">
HEX_GRID_TRIANGULATE</a>,
a FORTRAN90 program which
uses this library of test regions and computes points on a hexagonal grid
inside each region.
</p>
<p>
<a href = "../../f_src/table_io/table_io.html">
TABLE_IO</a>,
a FORTRAN90 library which
is used to write some of the output files.
</p>
<p>
<a href = "../../f_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a FORTRAN90 library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image
using Open GL.
</p>
<p>
<a href = "../../f_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a FORTRAN90 program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a FORTRAN90 program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION ORDER3</a>,
a directory which
describes the format for triangulations of order 3.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION ORDER6</a>,
a directory which
describes the format for
triangulations of order 6.
</p>
<p>
<a href = "../../f_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a FORTRAN90 program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../f_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a FORTRAN90 program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a FORTRAN90 program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../f_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines an ordering
of the nodes that will reduce the bandwidth of the adjacency
matrix, and writes the new triangulation information to a file.
</p>
<p>
<a href = "../../f_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a FORTRAN90 program which
reads data defining a triangulation, replaces each triangle
by four congruent smaller ones, and writes the new triangulation
information to a file.
</p>
<p>
<a href = "../../f_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines the neighboring
triangles of each triangle, and writes that information to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000,<br>
ISBN: 3-540-65620-0.
</li>
<li>
Barry Joe, <br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms, <br>
Advances in Engineering Software,<br>
Volume 13, 1991, pages 325-331.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, June 2004, pages 329-345.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_triangulation.f90">test_triangulation.f90</a>,
the source code.
</li>
<li>
<a href = "test_triangulation.sh">test_triangulation.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
TEST_TRIANGULATION_PRB carries out some simple tasks with the
sample problems.
<ul>
<li>
<a href = "test_triangulation_prb.f90">test_triangulation_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_triangulation_prb.sh">test_triangulation_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_triangulation_prb_output.txt">test_triangulation_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
One of the routines in TEST_TRIANGULATION_PRB calls the appropriate
routines to determine the boundary of each region, and creates
an Encapsulated PostScript image.
<ul>
<li>
<a href = "p01_boundary.png">p01_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #1.
</li>
<li>
<a href = "p02_boundary.png">p02_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #2.
</li>
<li>
<a href = "p03_boundary.png">p03_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #3.
</li>
<li>
<a href = "p04_boundary.png">p04_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #4.
</li>
<li>
<a href = "p05_boundary.png">p05_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #5.
</li>
<li>
<a href = "p06_boundary.png">p06_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #6.
</li>
<li>
<a href = "p07_boundary.png">p07_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #7.
</li>
<li>
<a href = "p08_boundary.png">p08_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #8.
</li>
<li>
<a href = "p09_boundary.png">p09_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #9.
</li>
<li>
<a href = "p10_boundary.png">p10_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #10.
</li>
<li>
<a href = "p11_boundary.png">p11_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #11.
</li>
<li>
<a href = "p12_boundary.png">p12_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #12.
</li>
<li>
<a href = "p13_boundary.png">p13_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #13.
</li>
<li>
<a href = "p14_boundary.png">p14_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #14.
</li>
<li>
<a href = "p15_boundary.png">p15_boundary.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the boundary of the problem #15.
</li>
</ul>
</p>
<p>
One of the routines in TEST_TRIANGULATION_PRB creates an EPS
image of 200 sample points in each region.
<ul>
<li>
<a href = "p01_points.png">p01_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #1.
</li>
<li>
<a href = "p02_points.png">p02_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #2.
</li>
<li>
<a href = "p03_points.png">p03_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #3.
</li>
<li>
<a href = "p04_points.png">p04_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #4.
</li>
<li>
<a href = "p05_points.png">p05_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #5.
</li>
<li>
<a href = "p06_points.png">p06_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #6.
</li>
<li>
<a href = "p07_points.png">p07_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #7.
</li>
<li>
<a href = "p08_points.png">p08_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #8.
</li>
<li>
<a href = "p09_points.png">p09_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #9.
</li>
<li>
<a href = "p10_points.png">p10_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #10.
</li>
<li>
<a href = "p11_points.png">p11_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #11.
</li>
<li>
<a href = "p12_points.png">p12_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #12.
</li>
<li>
<a href = "p13_points.png">p13_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #13.
</li>
<li>
<a href = "p14_points.png">p14_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #14.
</li>
<li>
<a href = "p15_points.png">p15_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
sample points for problem #15.
</li>
</ul>
</p>
<p>
One of the routines in TEST_TRIANGULATION_PRB calls the appropriate
routine to create a
<a href = "../../data/poly/poly.html">POLY file</a>, which can be
displayed by the
<a href = "../../g_src/showme/showme.html">SHOWME</a> program,
or used as the start of a triangulation process involving
<a href = "../../cpp_src/triangle/triangle.html">TRIANGLE</a>.
<ul>
<li>
<a href = "../../data/poly/p01.poly">p01.poly</a>,
TEST_TRIANGULATION problem #1.
</li>
<li>
<a href = "../../data/p02.poly">p02.poly</a>,
TEST_TRIANGULATION problem #2.
</li>
<li>
<a href = "../../data/p03.poly">p03.poly</a>,
TEST_TRIANGULATION problem #3.
</li>
<li>
<a href = "../../data/p04.poly">p04.poly</a>,
TEST_TRIANGULATION problem #4.
</li>
<li>
<a href = "../../data/p05.poly">p05.poly</a>,
TEST_TRIANGULATION problem #5.
</li>
<li>
<a href = "../../data/p06.poly">p06.poly</a>,
TEST_TRIANGULATION problem #6.
</li>
<li>
<a href = "../../data/p07.poly">p07.poly</a>,
TEST_TRIANGULATION problem #7.
</li>
<li>
<a href = "../../data/p08.poly">p08.poly</a>,
TEST_TRIANGULATION problem #8.
</li>
<li>
<a href = "../../data/p09.poly">p09.poly</a>,
TEST_TRIANGULATION problem #9.
</li>
<li>
<a href = "../../data/p10.poly">p10.poly</a>,
TEST_TRIANGULATION problem #10.
</li>
<li>
<a href = "../../data/p11.poly">p11.poly</a>,
TEST_TRIANGULATION problem #11.
</li>
<li>
<a href = "../../data/p12.poly">p12.poly</a>,
TEST_TRIANGULATION problem #12.
</li>
<li>
<a href = "../../data/p13.poly">p13.poly</a>,
TEST_TRIANGULATION problem #13.
</li>
<li>
<a href = "../../data/p14.poly">p14.poly</a>,
TEST_TRIANGULATION problem #14.
</li>
<li>
<a href = "../../data/p15.poly">p15.poly</a>,
TEST_TRIANGULATION problem #15.
</li>
</ul>
</p>
<p>
Simple changes to TEST_TRIANGULATION_PRB can be made so that
a file is created containing pairs of sample points and nearest
points on the boundary. If the file lists these pairs followed by
a blank line, then the
<a href = "../../g_src/plot_points/plot_points.html">
PLOT_POINTS</a> can be used, with the "DASH" option, to illustrate
the results.
<ul>
<li>
<a href = "p06_boundary_nearest.txt">p06_boundary_nearest.txt</a>,
lists pairs of points and nearest boundary points for
problem 6.
</li>
<li>
<a href = "p06_boundary_nearest.png">p06_boundary_nearest.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nearest point on the boundary.
</li>
<li>
<a href = "p07_boundary_nearest.txt">p07_boundary_nearest.txt</a>,
lists pairs of points and nearest boundary points for
problem 7.
</li>
<li>
<a href = "p07_boundary_nearest.png">p07_boundary_nearest.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nearest point on the boundary.
</li>
<li>
<a href = "p08_boundary_nearest.txt">p08_boundary_nearest.txt</a>,
lists pairs of points and nearest boundary points for
problem 8.
</li>
<li>
<a href = "p08_boundary_nearest.png">p08_boundary_nearest.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nearest point on the boundary.
</li>
<li>
<a href = "p09_boundary_nearest.txt">p09_boundary_nearest.txt</a>,
lists pairs of points and nearest boundary points for
problem 9.
</li>
<li>
<a href = "p09_boundary_nearest.png">p09_boundary_nearest.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nearest point on the boundary.
</li>
</ul>
</p>
<p>
One of the routines in TEST_TRIANGULATION_PRB creates a set of
points on a hexagonal grid, contained in a given region. This
dataset is written to a file.
<ul>
<li>
<a href = "p08_hex_grid_points.txt">p08_hex_grid_points.txt</a>,
hex grid points for problem 8.
</li>
<li>
<a href = "p08_hex_grid_points.png">p08_hex_grid_points.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the hex grid points for problem 8.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ANGLE_CONTAINS_POINT_2D</b> determines if an angle contains a point, in 2D.
</li>
<li>
<b>ANGLE_HALF_2D</b> finds half an angle in 2D.
</li>
<li>
<b>ANGLE_RAD_2D</b> returns the angle swept out between two rays in 2D.
</li>
<li>
<b>ATAN4</b> computes the inverse tangent of the ratio Y / X.
</li>
<li>
<b>BOX_CONTAINS_POINT_2D</b> determines if a point is inside a box in 2D.
</li>
<li>
<b>CIRCLE_ARC_POINT_NEAR_2D</b> : nearest point on a circular arc.
</li>
<li>
<b>CIRCLE_IMP_CONTAINS_POINT_2D</b> determines if a circle contains a point in 2D.
</li>
<li>
<b>CIRCLE_IMP_POINT_NEAR_2D:</b> nearest ( implicit circle, point ) in 2D.
</li>
<li>
<b>CIRCLE_SECTOR_CONTAINS_POINT_2D</b> : is a point inside a circular sector?
</li>
<li>
<b>COS_DEG</b> returns the cosine of an angle given in degrees.
</li>
<li>
<b>DTABLE_DATA_WRITE</b> writes data to a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_WRITE</b> writes the header to a double precision table file.
</li>
<li>
<b>DTABLE_WRITE</b> writes a double precision table file.
</li>
<li>
<b>FILE_NAME_INC</b> generates the next filename in a series.
</li>
<li>
<b>FMIN_RC</b> seeks a minimizer of a scalar function of a scalar variable.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HEX_GRID_ANGLE</b> sets the points in an angled hex grid in a box.
</li>
<li>
<b>HEX_GRID_ANGLE_SIZE</b> counts the points in an angled hex grid in a box.
</li>
<li>
<b>HEXAGON_CONTAINS_POINT_2D</b> finds if a point is inside a hexagon in 2D.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>P00_BOUNDARY_EPS</b> draws the boundary of a region as an EPS file.
</li>
<li>
<b>P00_BOUNDARY_NEAREST</b> returns a nearest boundary point for any problem.
</li>
<li>
<b>P00_BOUNDARY_PROJECT</b> projects exterior points to the boundary.
</li>
<li>
<b>P00_BOUNDARY_SEGMENT</b> returns a boundary segment in a problem.
</li>
<li>
<b>P00_BOUNDARY_SEGMENT_LENGTH</b> returns boundary segment lengths in a problem.
</li>
<li>
<b>P00_BOUNDARY_SEGMENT_NUM</b> counts the boundary segments in a problem.
</li>
<li>
<b>P00_BOX</b> returns a bounding box for a problem.
</li>
<li>
<b>P00_DENSITY</b> returns the density for a problem.
</li>
<li>
<b>P00_ELEMENT_SIZE</b> returns a typical element size for a problem.
</li>
<li>
<b>P00_FIXED_NUM</b> returns the number of fixed points in a problem.
</li>
<li>
<b>P00_FIXED_POINTS</b> returns the fixed points in a problem.
</li>
<li>
<b>P00_HEADER</b> prints some information about a problem.
</li>
<li>
<b>P00_HEX_GRID</b> returns hex grid points in a region.
</li>
<li>
<b>P00_HEX_GRID_COUNT</b> counts the number of hex grid points in a region.
</li>
<li>
<b>P00_HOLE_NUM</b> counts the holes in a problem.
</li>
<li>
<b>P00_HOLE_POINT</b> returns a point inside a given hole.
</li>
<li>
<b>P00_INSIDE</b> reports if a point is inside the region in a problem.
</li>
<li>
<b>P00_POINTS_EPS</b> draws points in a region as an EPS file.
</li>
<li>
<b>P00_POLY_WRITE</b> collects data and writes it to a POLY file.
</li>
<li>
<b>P00_SAMPLE</b> samples points from the region in a problem.
</li>
<li>
<b>P00_SAMPLE_H1</b> samples points from the enlarged region in a problem.
</li>
<li>
<b>P00_SDIST</b> returns the signed distance to the region in a problem.
</li>
<li>
<b>P00_TEST_NUM</b> returns the number of available tests.
</li>
<li>
<b>P00_TITLE</b> returns a title for a problem.
</li>
<li>
<b>P01_BOUNDARY_NEAREST</b> returns a nearest boundary point in problem 01.
</li>
<li>
<b>P01_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 01.
</li>
<li>
<b>P01_BOUNDARY_SEGMENT</b> returns a boundary segment in problem 01.
</li>
<li>
<b>P01_BOUNDARY_SEGMENT_LENGTH</b> returns boundary segment lengths in problem 01.
</li>
<li>
<b>P01_BOUNDARY_SEGMENT_NUM</b> counts the boundary segments in problem 01.
</li>
<li>
<b>P01_BOX</b> returns a bounding box for problem 01.
</li>
<li>
<b>P01_DENSITY</b> returns the density for problem 01.
</li>
<li>
<b>P01_ELEMENT_SIZE</b> returns a typical element size for problem 01.
</li>
<li>
<b>P01_FIXED_NUM</b> returns the number of fixed points in problem 01.
</li>
<li>
<b>P01_FIXED_POINTS</b> returns the fixed points in problem 01.
</li>
<li>
<b>P01_HEADER</b> prints some information about problem 01.
</li>
<li>
<b>P01_HOLE_NUM</b> counts the holes in problem 01.
</li>
<li>
<b>P01_HOLE_POINT</b> returns a point inside a given hole in problem 1.
</li>
<li>
<b>P01_INSIDE</b> reports if a point is inside the region in problem 01.
</li>
<li>
<b>P01_SAMPLE</b> samples points from the region in problem 01.
</li>
<li>
<b>P01_SAMPLE_H1</b> samples points from the enlarged region in problem 01.
</li>
<li>
<b>P01_SDIST</b> returns the signed distance to the region in problem 01.
</li>
<li>
<b>P01_TITLE</b> returns a title for problem 01.
</li>
<li>
<b>P02_BOUNDARY_NEAREST</b> returns a nearest boundary point in problem 02.
</li>
<li>
<b>P02_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 02.
</li>
<li>
<b>P02_BOUNDARY_SEGMENT</b> returns a boundary segment in problem 02.
</li>
<li>
<b>P02_BOUNDARY_SEGMENT_LENGTH</b> returns boundary segment lengths in problem 02.
</li>
<li>
<b>P02_BOUNDARY_SEGMENT_NUM</b> counts the boundary segments in problem 02.
</li>
<li>
<b>P02_BOX</b> returns a bounding box for problem 02.
</li>
<li>
<b>P02_DENSITY</b> returns the density for problem 02.
</li>
<li>
<b>P02_ELEMENT_SIZE</b> returns a typical element size for problem 02.
</li>
<li>
<b>P02_FIXED_NUM</b> returns the number of fixed points in problem 02.
</li>
<li>
<b>P02_FIXED_POINTS</b> returns the fixed points in problem 02.
</li>
<li>
<b>P02_HEADER</b> prints some information about problem 02.
</li>
<li>
<b>P02_HOLE_NUM</b> counts the holes in problem 02.
</li>
<li>
<b>P02_HOLE_POINT</b> returns a point inside a given hole in problem 2.
</li>
<li>
<b>P02_INSIDE</b> reports if a point is inside the region in problem 02.
</li>
<li>
<b>P02_SAMPLE</b> samples points from the region in problem 02.
</li>
<li>
<b>P02_SAMPLE_H1</b> samples points from the enlarged region in problem 02.
</li>
<li>
<b>P02_SDIST</b> returns the signed distance to the region in problem 02.
</li>
<li>
<b>P02_TITLE</b> returns a title for problem 02.
</li>
<li>
<b>P03_BOUNDARY_NEAREST</b> returns a nearest boundary point in problem 03.
</li>
<li>
<b>P03_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 03.
</li>
<li>
<b>P03_BOUNDARY_SEGMENT</b> returns a boundary segment in problem 03.
</li>
<li>
<b>P03_BOUNDARY_SEGMENT_LENGTH</b> returns boundary segment lengths in problem 03.
</li>
<li>
<b>P03_BOUNDARY_SEGMENT_NUM</b> counts the boundary segments in problem 03.
</li>
<li>
<b>P03_BOX</b> returns a bounding box for problem 03.
</li>
<li>
<b>P03_DENSITY</b> returns the density for problem 03.
</li>
<li>
<b>P03_ELEMENT_SIZE</b> returns a typical element size for problem 03.
</li>
<li>
<b>P03_FIXED_NUM</b> returns the number of fixed points in problem 03.
</li>
<li>
<b>P03_FIXED_POINTS</b> returns the fixed points in problem 03.
</li>
<li>
<b>P03_HEADER</b> prints some information about problem 03.
</li>
<li>