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<html>
<head>
<title>
SPHERE_VORONOI - Voronoi Diagram on Unit Sphere
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_VORONOI <br> Voronoi Diagram on Unit Sphere
</h1>
<hr>
<p>
<b>SPHERE_VORONOI</b>
is a FORTRAN90 program which
computes and plots the Voronoi diagram of points on the unit sphere.
</p>
<p>
<b>SPHERE_VORONOI</b> takes as input an XYZ file, containing
coordinates of points on the unit sphere in 3D.
It passes this data to Renka's STRIPACK library which
computes the Voronoi diagram. The program then takes one
"snapshot" of the diagram, which is written to an
EPS image file, and stores the vertex and line information defines
the Voronoi triangulation as XYZ and XYZF files.
</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">
Usage:
</h3>
<p>
<blockquote><code>
<b>sphere_voronoi</b> <i>file.xyz</i>
</code></blockquote>
reads the XYZ file <i>file.xyz</i> containing the point coordinates,
creates an EPS file <i>file.eps</i> containing a 2D projection of the Voronoi
diagram, and creates an XYZ file <i>file.voronoi.xyz</i> and an XYZF file
<i>file.xyzf</i> which can be used, in conjunction with <i>file_voronoi.xyz</i>
to display the 3D Voronoi diagram.
</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>SPHERE_VORONOI</b> is available in
<a href = "../../f_src/sphere_voronoi/sphere_voronoi.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sphere_voronoi/sphere_voronoi.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<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 and plots the Delaunay triangulation of points on the unit 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 = "../../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 = "../../cpp_src/sphere_xyz_display_opengl/sphere_xyz_display_opengl.html">
SPHERE_XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads XYZ information defining points in 3D,
and displays a unit sphere and the points, using OpenGL.
</p>
<p>
<a href = "../../f_src/stripack/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
is used by <b>SPHERE_VORONOI</b> to compute the Voronoi tessellation
and Delaunay triangulation of the points on the sphere.
</p>
<p>
<a href = "../../f_src/stripack_interactive/stripack_interactive.html">
STRIPACK_INTERACTIVE</a>,
a FORTRAN90 program which
reads a set of points on the unit sphere, computes the Delaunay triangulation,
and writes it to a file.
</p>
<p>
<a href = "../../data/xyz/xyz.html">
XYZ</a>,
a data directory which
contains examples of XYZ files,
a simple 3D graphics point format;
</p>
<p>
<a href = "../../f_src/xyz_io/xyz_io.html">
XYZ_IO</a>,
a FORTRAN90 library which
reads and writes XYZ files.
</p>
<p>
<a href = "../../data/xyzf/xyzf.html">
XYZF</a>,
a data directory which
contains examples of XYZF files,
a simple 3D graphics point and face format;
</p>
<p>
<a href = "../../m_src/xyzf_display/xyzf_display.html">
XYZF_DISPLAY</a>,
a MATLAB program which
reads XYZF information defining points and faces in 3D,
and displays an image using OpenGL.
</p>
<p>
<a href = "../../cpp_src/xyzf_display_opengl/xyzf_display_opengl.html">
XYZF_DISPLAY_OPENGL</a>,
a C++ program which
reads XYZF information defining points and faces in 3D,
and displays an image using OpenGL.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<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>
Robert Renka,<br>
Algorithm 772: STRIPACK, <br>
Delaunay Triangulation and Voronoi Diagram on the Surface
of a Sphere,<br>
ACM Transactions on Mathematical Software,<br>
Volume 23, Number 3, 1997.
</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>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sphere_voronoi.f90">sphere_voronoi.f90</a>, the source code.
</li>
<li>
<a href = "sphere_voronoi.sh">sphere_voronoi.sh</a>,
commands to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>GEN_00010</b> is a test set of 10 points:
<ul>
<li>
<a href = "gen_00010.xyz">gen_00010.xyz</a>,
the point coordinates.
</li>
<li>
<a href = "gen_00010.png">gen_00010.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the Voronoi diagram for the data.
</li>
<li>
<a href = "gen_00010.voronoi.xyz">gen_00010.voronoi.xyz</a>,
the coordinates of the Voronoi vertices.
</li>
<li>
<a href = "gen_00010.voronoi.xyzf">gen_00010.voronoi.xyzf</a>,
the indices of the Voronoi vertices that form each face.
</li>
</ul>
</p>
<p>
<b>GEN_00100</b> is a test set of 100 points:
<ul>
<li>
<a href = "gen_00100.xyz">gen_00100.xyz</a>,
the point coordinates.
</li>
<li>
<a href = "gen_00100.png">gen_00100.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the Voronoi diagram for the data.
</li>
<li>
<a href = "gen_00100.voronoi.xyz">gen_00100.voronoi.xyz</a>,
the coordinates of the Voronoi vertices.
</li>
<li>
<a href = "gen_00100.voronoi.xyzf">gen_00100.voronoi.xyzf</a>,
the indices of the Voronoi vertices that form each face.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for SPHERE_VORONOI.
</li>
<li>
<b>STRIPACK_INTERFACE</b> calls STRIPACK routines.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the numeric value of a base 10 digit.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_NAME_EXT_SWAP</b> replaces the current "extension" of a file name.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of rows in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>POLY_COUNT</b> counts the number of polygons of each size in the diagram.
</li>
<li>
<b>POLY_COUNT_MAX</b> determines the highest order polygon.
</li>
<li>
<b>S_INDEX_LAST_C</b> finds the LAST occurrence of a given character.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>VR_TO_XYZF</b> makes an XYZF file of Voronoi diagram data.
</li>
<li>
<b>WORD_NEXT_READ</b> "reads" words from a string, one at a time.
</li>
<li>
<b>XYZ_READ</b> reads graphics information from an XYZ file.
</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 19 December 2008.
</i>
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