hypersphere_properties


hypersphere_properties, a MATLAB code 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:

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

Languages:

hypersphere_properties is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

geometry, a MATLAB code which performs geometric calculations in 2, 3 and M dimensional space.

hypersphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

hypersphere_properties_test

hypersphere_surface, a MATLAB code which illustrates a procedure for estimating the location of a hypersurface defined by a characteristic function or a signed function.

random_data, a MATLAB code which generates sample points for various probability distributions, spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.

sphere_stereograph, a MATLAB code which computes the stereographic mapping between points on the unit sphere and points on the plane Z = 1; a generalized mapping is also available

sphere_stereograph_display, a MATLAB code which computes and displays the results of several stereographic projections between a sphere and a plane.

Reference:

    George Marsaglia,
    Choosing a point from the surface of a sphere,
    Annals of Mathematical Statistics,
    Volume 43, Number 2, April 1972, pages 645-646.

Source Code:


Last revised on 01 February 2019.