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<html>
<head>
<title>
STRIPACK - Delaunay Triangulation on a Sphere
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
STRIPACK <br> Delaunay Triangulation on a Sphere
</h1>
<hr>
<p>
<b>STRIPACK</b>
is a FORTRAN90 library which
carries out some computational geometry tasks on the unit sphere in 3D,
by Robert Renka.
</p>
<p>
<b>STRIPACK</b> can compute the Delaunay triangulation or the
Voronoi diagram of a set of points on the unit sphere.
</p>
<p>
<b>STRIPACK</b> can make a PostScript plot
of the Delaunay triangulation or the Voronoi diagram from a given
point of view.
</p>
<p>
<b>STRIPACK</b> is a generalization of Robert Renka's code
<a href = "../../f_src/tripack/tripack.html">TRIPACK</a>, which computes
Delaunay triangulations and Voronoi diagrams for a set of points
in the plane.
</p>
<p>
<b>STRIPACK</b> is a FORTRAN90 "translation" of the original
FORTRAN77 code written by Robert Renka and published in the
ACM Transactions on Mathematical Software.
</p>
<p>
<b>STRIPACK</b> is ACM TOMS Algorithm 772. The text of the
original FORTRAN77 version is available online
through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>.
</p>
<p>
According to Steven Fortune, it is possible to compute the Delaunay triangulation
of points on a sphere by computing their convex hull. If the sphere is the unit
sphere at the origin, the facet normals are the Voronoi vertices.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/delaunay_lmap_2d/delaunay_lmap_2d.html">
DELAUNAY_LMAP_2D</a>,
a FORTRAN90 program which
can compute the Delaunay triangulation
of points in
the plane subject to a linear mapping.
</p>
<p>
<a href = "../../f_src/geometry/geometry.html">
GEOMETRY</a>,
a FORTRAN90 library which
computes various geometric quantities, including grids on spheres.
</p>
<p>
<a href = "../../f_src/geompack/geompack.html">
GEOMPACK</a>,
a FORTRAN90 library which
includes Delaunay triangulation routines, by Barry Joe.
</p>
<p>
<a href = "../../f_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a FORTRAN90 library which
creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi
Tessellations.
</p>
<p>
<a href = "../../f_src/sphere_delaunay/sphere_delaunay.html">
SPHERE_DELAUNAY</a>,
a FORTRAN90 program which
computes the Delaunay triangulation of points on a sphere.
</p>
<p>
<a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
SPHERE_DESIGN_RULE</a>,
a FORTRAN90 library which
returns point sets on the surface of the unit sphere, known as "designs",
which can be useful for estimating integrals on the surface, among other uses.
</p>
<p>
<a href = "../../f_src/sphere_quad/sphere_quad.html">
SPHERE_QUAD</a>,
a FORTRAN90 library which
estimates the integral of a function defined on the sphere.
</p>
<p>
<a href = "../../f_src/sphere_stereograph/sphere_stereograph.html">
SPHERE_STEREOGRAPH</a>,
a FORTRAN90 library which
computes the stereographic mapping between points on the unit sphere
and points on the plane Z = 1; a generalized mapping is also available.
</p>
<p>
<a href = "../../f_src/sphere_voronoi/sphere_voronoi.html">
SPHERE_VORONOI</a>,
a FORTRAN90 program which
computes and plots the Voronoi diagram of points on the unit sphere.
</p>
<p>
<a href = "../../cpp_src/sphere_voronoi_display_opengl/sphere_voronoi_display_opengl.html">
SPHERE_VORONOI_DISPLAY_OPENGL</a>,
a C++ program which
displays a sphere and randomly selected generator points, and then
gradually colors in points in the sphere that are closest to each generator.
</p>
<p>
<a href = "../../f_src/stripack_interactive/stripack_interactive.html">
STRIPACK_INTERACTIVE</a>,
a FORTRAN90 program which
reads an XYZ file of 3D points on
the unit sphere, computes the Delaunay triangulation, and writes it
to a file.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
reads a file of point coordinates in the TABLE format and writes out
the Delaunay triangulation.
</p>
<p>
<a href = "../../f77_src/toms772/toms772.html">
TOMS772</a>,
a FORTRAN77 library which
is the original text of the STRIPACK program.
</p>
<p>
<a href = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
may be used to make a PostScript image of
a triangulation of points.
</p>
<p>
<a href = "../../f_src/tripack/tripack.html">
TRIPACK</a>,
a FORTRAN90 library which
computes the Delaunay triangulation of points in the plane.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Robert Renka
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, pages 345-405, September 1991.
</li>
<li>
Thomas Ericson, Victor Zinoviev,<br>
Codes on Euclidean Spheres,<br>
Elsevier, 2001,<br>
ISBN: 0444503293,<br>
LC: QA166.7E75
</li>
<li>
Gerald Folland,<br>
How to Integrate a Polynomial Over a Sphere,<br>
American Mathematical Monthly,<br>
Volume 108, Number 5, May 2001, pages 446-448.
</li>
<li>
Jacob Goodman, Joseph ORourke, editors,<br>
Handbook of Discrete and Computational Geometry,<br>
Second Edition,<br>
CRC/Chapman and Hall, 2004,<br>
ISBN: 1-58488-301-4,<br>
LC: QA167.H36.
</li>
<li>
AD McLaren,<br>
Optimal Numerical Integration on a Sphere,<br>
Mathematics of Computation,<br>
Volume 17, Number 84, October 1963, pages 361-383.
</li>
<li>
Robert Renka,<br>
Algorithm 772: <br>
STRIPACK:
Delaunay Triangulation and Voronoi Diagram on the Surface
of a Sphere,<br>
ACM Transactions on Mathematical Software,<br>
Volume 23, Number 3, September 1997, pages 416-434.
</li>
<li>
Edward Saff, Arno Kuijlaars,<br>
Distributing Many Points on a Sphere,<br>
The Mathematical Intelligencer,<br>
Volume 19, Number 1, 1997, pages 5-11.
</li>
<li>
Brian Wichmann, David Hill,<br>
An Efficient and Portable Pseudo-random Number Generator,<br>
Applied Statistics,<br>
Volume 31, Number 2, 1982, pages 188-190.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "stripack.f90">stripack.f90</a>, the source code.
</li>
<li>
<a href = "stripack.sh">stripack.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>STRIPACK_PRB</b> is a sample problem which tests or demonstrates
many of the functions in STRIPACK.
<ul>
<li>
<a href = "stripack_prb.f90">stripack_prb.f90</a>,
the source code.
</li>
<li>
<a href = "stripack_prb.sh">stripack_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "stripack_prb_output.txt">stripack_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "stripack_prb_del.png">stripack_prb_del.png</a>,
a PNG image of the Delaunay triangulation.
</li>
<li>
<a href = "stripack_prb_vor.png">stripack_prb_vor.png</a>,
a PNG image of the Voronoi diagram.
</li>
</ul>
</p>
<p>
<b>STRIPACK_PRB2</b> is a program which examines the creation
of a Voronoi diagram for a given set of data:
<ul>
<li>
<a href = "stripack_prb2.f90">stripack_prb2.f90</a>,
the source code.
</li>
<li>
<a href = "stripack_prb2.sh">stripack_prb2.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "stripack_prb2_output.txt">stripack_prb2_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>STRIPACK_PRB3</b> is a program which examines the creation
of a Delaunay triangulation for a given set of data:
<ul>
<li>
<a href = "stripack_prb3.f90">stripack_prb3.f90</a>,
the source code.
</li>
<li>
<a href = "stripack_prb3.sh">stripack_prb3.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "stripack_prb3_output.txt">stripack_prb3_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ADDNOD</b> adds a node to a triangulation.
</li>
<li>
<b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>AREAS</b> computes the area of a spherical triangle on the unit sphere.
</li>
<li>
<b>BDYADD</b> adds a boundary node to a triangulation.
</li>
<li>
<b>BNODES</b> returns the boundary nodes of a triangulation.
</li>
<li>
<b>CIRCUM</b> returns the circumcenter of a spherical triangle.
</li>
<li>
<b>COVSPH</b> connects an exterior node to boundary nodes, covering the sphere.
</li>
<li>
<b>CRLIST</b> returns triangle circumcenters and other information.
</li>
<li>
<b>DELARC</b> deletes a boundary arc from a triangulation.
</li>
<li>
<b>DELNB</b> deletes a neighbor from the adjacency list.
</li>
<li>
<b>DELNOD</b> deletes a node from a triangulation.
</li>
<li>
<b>EDGE</b> swaps arcs to force two nodes to be adjacent.
</li>
<li>
<b>GETNP</b> gets the next nearest node to a given node.
</li>
<li>
<b>INSERT</b> inserts K as a neighbor of N1.
</li>
<li>
<b>INSIDE</b> determines if a point is inside a polygonal region.
</li>
<li>
<b>INTADD</b> adds an interior node to a triangulation.
</li>
<li>
<b>INTSRC</b> finds the intersection of two great circles.
</li>
<li>
<b>JRAND</b> returns a random integer between 1 and N.
</li>
<li>
<b>LEFT</b> determines whether a node is to the left of a plane through the origin.
</li>
<li>
<b>LSTPTR</b> returns the index of NB in the adjacency list.
</li>
<li>
<b>NBCNT</b> returns the number of neighbors of a node.
</li>
<li>
<b>NEARND</b> returns the nearest node to a given point.
</li>
<li>
<b>OPTIM</b> optimizes the quadrilateral portion of a triangulation.
</li>
<li>
<b>R83VEC_NORMALIZE</b> normalizes each R83 in an R83VEC to have unit norm.
</li>
<li>
<b>SCOORD</b> converts from Cartesian to spherical coordinates.
</li>
<li>
<b>STORE</b> forces its argument to be stored.
</li>
<li>
<b>SWAP</b> replaces the diagonal arc of a quadrilateral with the other diagonal.
</li>
<li>
<b>SWPTST</b> decides whether to replace a diagonal arc by the other.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRANS</b> transforms spherical coordinates to Cartesian coordinates.
</li>
<li>
<b>TRFIND</b> locates a point relative to a triangulation.
</li>
<li>
<b>TRLIST</b> converts a triangulation data structure to a triangle list.
</li>
<li>
<b>TRLPRT</b> prints a triangle list.
</li>
<li>
<b>TRMESH</b> creates a Delaunay triangulation on the unit sphere.
</li>
<li>
<b>TRPLOT</b> makes a PostScript image of a triangulation on a unit sphere.
</li>
<li>
<b>TRPRNT</b> prints the triangulation adjacency lists.
</li>
<li>
<b>VORONOI_POLY_COUNT</b> counts the polygons of each size in the Voronoi diagram.
</li>
<li>
<b>VRPLOT</b> makes a PostScript image of a Voronoi diagram on the unit sphere.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 30 April 2010
</i>
<!-- John Burkardt -->
</body>
</html>