The M-dimensional Sphere

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.


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 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;

POLYGON_PROPERTIES, a C library which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including interior angles, area, centroid, containment of a point, convexity, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling.

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

TETRAHEDRON_PROPERTIES, a C program which computes properties of a tetrahedron in 3D, including the centroid, circumsphere, dihedral angles, edge lengths, face angles, face areas, insphere, quality, solid angles, and volume.

TRIANGLE_PROPERTIES, a C program which computes properties of a triangle whose vertex coordinates are read from a file.


    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:

Examples and Tests:

List of Routines:

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

Last revised on 10 May 2014.