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HYPERSPHERE_PROPERTIES\ Properties of the M-dimensional Sphere {#hypersphere_properties-properties-of-the-m-dimensional-sphere align=”center”} ======================================

HYPERSPHERE_PROPERTIES 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.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

HYPERSPHERE_PROPERTIES is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

GEOMETRY, a C++ library which performs geometric calculations in 2, 3 and M dimensional space.

HYPERSPHERE_MONTE_CARLO, 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;

RANDOM_DATA, a C++ library which generates sample points for various probability distributions, spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.

SPHERE_STEREOGRAPH, 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

Reference: {#reference align=”center”}

Source Code: {#source-code align=”center”}

hypersphere_properties.cpp, the source code.
hypersphere_properties.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

hypersphere_properties_prb.cpp, a sample calling program.
hypersphere_properties_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

CARTESIAN_TO_HYPERSPHERE: Cartesian to hypersphere coordinate transform.
HYPERSPHERE_01_AREA computes the surface area of a unit sphere in ND.
HYPERSPHERE_01_AREA_VALUES returns some areas of the unit sphere in ND.
HYPERSPHERE_01_INTERIOR_UNIFORM: uniform points inside unit hypersphere.
HYPERSPHERE_01_SURFACE_UNIFORM: uniform points on unit hypersphere surface.
HYPERSPHERE_01_VOLUME computes the volume of a unit sphere in ND.
HYPERSPHERE_01_VOLUME_VALUES returns some volumes of the unit sphere in ND.
HYPERSPHERE_AREA computes the surface area of an implicit sphere in ND.
HYPERSPHERE_STEREOGRAPH: stereographic mapping of points on a hypersphere.
HYPERSPHERE_STEREOGRAPH_INVERSE inverts a stereographic map.
HYPERSPHERE_SURFACE_UNIFORM: uniform hypersphere surface samples
HYPERSPHERE_TO_CARTESIAN: hypersphere to Cartesian coordinate transform.
HYPERSPHERE_VOLUME computes the volume of a hypersphere.
R8_UNIFORM_01 returns a unit pseudorandom R8.
R8MAT_NORMAL_01 returns a unit pseudonormal R8MAT.
R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
R8VEC_TRANSPOSE_PRINT prints an R8VEC “transposed”.
R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
SPHERE_STEREOGRAPH computes the stereographic image of points on a sphere.
SPHERE_STEREOGRAPH_INVERSE computes stereographic preimages of points.
TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

Last revised on 11 May 2014.