Properties of the M-dimensional Sphere

HYPERSPHERE_PROPERTIES, a MATLAB 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.


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


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 library which performs geometric calculations in 2, 3 and M dimensional space.

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


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

RANDOM_DATA, a MATLAB 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 MATLAB 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

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


    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.