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<html>
<head>
<title>
HYPERSPHERE_PROPERTIES - Properties of the M-dimensional Sphere
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HYPERSPHERE_PROPERTIES <br> Properties of the M-dimensional Sphere
</h1>
<hr>
<p>
<b>HYPERSPHERE_PROPERTIES</b>
is a C++ library which
carries out various operations for an M-dimensional hypersphere, including
converting between Cartesian and spherical coordinates,
stereographic projection, sampling the surface of the sphere, and
computing the surface area and volume.
</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>HYPERSPHERE_PROPERTIES</b> is available in
<a href = "../../c_src/hypersphere_properties/hypersphere_properties.html">a C version</a> and
<a href = "../../cpp_src/hypersphere_properties/hypersphere_properties.html">a C++ version</a> and
<a href = "../../f77_src/hypersphere_properties/hypersphere_properties.html">a FORTRAN77 version</a> and
<a href = "../../f_src/hypersphere_properties/hypersphere_properties.html">a FORTRAN90 version</a> and
<a href = "../../m_src/hypersphere_properties/hypersphere_properties.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/geometry/geometry.html">
GEOMETRY</a>,
a C++ library which
performs geometric calculations in 2, 3 and M dimensional space.
</p>
<p>
<a href = "../../cpp_src/hypersphere_monte_carlo/hypersphere_monte_carlo.html">
HYPERSPHERE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in M dimensions;
</p>
<p>
<a href = "../../cpp_src/random_data/random_data.html">
RANDOM_DATA</a>,
a C++ library which
generates sample points for
various probability distributions, spatial dimensions, and geometries,
including the M-dimensional cube, ellipsoid, simplex and sphere.
</p>
<p>
<a href = "../../cpp_src/sphere_stereograph/sphere_stereograph.html">
SPHERE_STEREOGRAPH</a>,
a C++ 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>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
George Marsaglia,<br>
Choosing a point from the surface of a sphere,<br>
Annals of Mathematical Statistics,<br>
Volume 43, Number 2, April 1972, pages 645-646.
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "hypersphere_properties.cpp">hypersphere_properties.cpp</a>, the source code.
</li>
<li>
<a href = "hypersphere_properties.hpp">hypersphere_properties.hpp</a>, the include file.
</li>
<li>
<a href = "hypersphere_properties.sh">hypersphere_properties.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "hypersphere_properties_prb.cpp">hypersphere_properties_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "hypersphere_properties_prb.sh">hypersphere_properties_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "hypersphere_properties_prb_output.txt">hypersphere_properties_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CARTESIAN_TO_HYPERSPHERE:</b> Cartesian to hypersphere coordinate transform.
</li>
<li>
<b>HYPERSPHERE_01_AREA</b> computes the surface area of a unit sphere in ND.
</li>
<li>
<b>HYPERSPHERE_01_AREA_VALUES</b> returns some areas of the unit sphere in ND.
</li>
<li>
<b>HYPERSPHERE_01_INTERIOR_UNIFORM:</b> uniform points inside unit hypersphere.
</li>
<li>
<b>HYPERSPHERE_01_SURFACE_UNIFORM:</b> uniform points on unit hypersphere surface.
</li>
<li>
<b>HYPERSPHERE_01_VOLUME</b> computes the volume of a unit sphere in ND.
</li>
<li>
<b>HYPERSPHERE_01_VOLUME_VALUES</b> returns some volumes of the unit sphere in ND.
</li>
<li>
<b>HYPERSPHERE_AREA</b> computes the surface area of an implicit sphere in ND.
</li>
<li>
<b>HYPERSPHERE_STEREOGRAPH:</b> stereographic mapping of points on a hypersphere.
</li>
<li>
<b>HYPERSPHERE_STEREOGRAPH_INVERSE</b> inverts a stereographic map.
</li>
<li>
<b>HYPERSPHERE_SURFACE_UNIFORM:</b> uniform hypersphere surface samples
</li>
<li>
<b>HYPERSPHERE_TO_CARTESIAN:</b> hypersphere to Cartesian coordinate transform.
</li>
<li>
<b>HYPERSPHERE_VOLUME</b> computes the volume of a hypersphere.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_NORMAL_01</b> returns a unit pseudonormal R8MAT.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_TRANSPOSE_PRINT</b> prints an R8VEC "transposed".
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>SPHERE_STEREOGRAPH</b> computes the stereographic image of points on a sphere.
</li>
<li>
<b>SPHERE_STEREOGRAPH_INVERSE</b> computes stereographic preimages of points.
</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 = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 11 May 2014.
</i>
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