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<html>
<head>
<title>
STRIPACK_INTERACTIVE - Interactive Delaunay Diagrams on Unit Spheres
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
STRIPACK_INTERACTIVE <br> Interactive Delaunay Diagrams on Unit Spheres
</h1>
<hr>
<p>
<b>STRIPACK_INTERACTIVE</b>
is a FORTRAN90 program which
interactively determines the Delaunay diagram of a set of points
on a sphere.
</p>
<p>
The set of points is read from a file, and the Delaunay triangulation,
once computed, is written out to another file, described as a series
of triplets of point indexes.
</p>
<p>
According to Steven Fortune, it is possible to compute the Delaunay
triangulation of points on the surface of a sphere by computing their
convex hull, regarded as a 3D pointset. 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>
<b>stripack_interactive</b> <i>node_filename</i>
</blockquote>
where
<ul>
<li>
<i>node_filename</i> is the name of a file containing the (X,Y,Z) coordinates of
points on the unit sphere.
</li>
</ul>
</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">
Related Data and Programs:
</h3>
<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/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 = "../../m_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a MATLAB library which
creates a mesh of well-separated points on a unit sphere by applying the
Centroidal Voronoi Tessellation (CVT) iteration.
</p>
<p>
<a href = "../../m_src/sphere_delaunay/sphere_delaunay.html">
SPHERE_DELAUNAY</a>,
a MATLAB 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 = "../../datasets/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a dataset directory containing files which
describe sets of
points on the unit sphere.
</p>
<p>
<a href = "../../f_src/sphere_quad/sphere_quad.html">
SPHERE_QUAD</a>,
a FORTRAN90 library which
approximates an integral over the surface of the unit sphere
by applying a triangulation to the surface;
</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/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
can compute the Delaunay triangulation or Voronoi diagram of a set of points
on the unit sphere.
</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/xyz_io/xyz_io.html">
XYZ_IO</a>,
a FORTRAN90 library which
reads and writes XYZ files.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<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>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "stripack_interactive.f90">stripack_interactive.f90</a>, the source code.
</li>
<li>
<a href = "stripack_interactive.sh">stripack_interactive.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>SPHERE_GRID_ICOS1_F1</b> is a grid of 12 points based on an icosahedron.
<ul>
<li>
<a href = "sphere_grid_icos1_f1,xyz">
sphere_grid_icos1_f1.xyz</a>,
the point coordinates.
</li>
<li>
<a href = "sphere_grid_icos1_f1.xyzf">
sphere_grid_icos1_f1.xyzf</a>,
the triangles forming the Delaunay triangulation.
</li>
<li>
<a href = "sphere_grid_icos1_f1_output.txt">
sphere_grid_icos1_f1_output.txt</a>,
the output from the program.
</li>
</ul>
</p>
<p>
<b>SPHERE_GRID_ICOS1_F2</b> is a grid of 42 points based on an icosahedron.
<ul>
<li>
<a href = "sphere_grid_icos1_f2.xyz">
sphere_grid_icos1_f2.xyz</a>,
the point coordinates.
</li>
<li>
<a href = "sphere_grid_icos1_f2.xyzf">
sphere_grid_icos1_f2.xyzf</a>,
the triangles forming the Delaunay triangulation.
</li>
<li>
<a href = "sphere_grid_icos1_f2_output.txt">
sphere_grid_icos1_f2_output.txt</a>,
the output from the program.
</li>
</ul>
</p>
<p>
<b>SPHERE_GRID_ICOS1_F3</b> is a grid of 92 points based on an icosahedron.
<ul>
<li>
<a href = "sphere_grid_icos1_f3.xyz">
sphere_grid_icos1_f3.xyz</a>,
the point coordinates.
</li>
<li>
<a href = "sphere_grid_icos1_f3.xyzf">
sphere_grid_icos1_f3.xyzf</a>,
the triangles forming the Delaunay triangulation.
</li>
<li>
<a href = "sphere_grid_icos1_f3_output.txt">
sphere_grid_icos1_f3_output.txt</a>,
the output from the program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for STRIPACK_INTERACTIVE
</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 integer value of a base 10 digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 31 August 2010.
</i>
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