Visualize the Stereographic Projection

SPHERE_STEREOGRAPH_DISPLAY is a MATLAB program which demonstrates the stereographic projection between a sphere and a plane by displaying a set of points and their images under the mapping.

This program is primarily an auxilliary demonstration of the properties of the SPHERE_STEREOGRAPH library; it is not a standalone application, and while it can be used to understand how to compute and display stereographic projections, a considerable amount of user modifications would be needed to adapt it to each particular problem of interest.


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


SPHERE_STEREOGRAPH_DISPLAY is available in a MATLAB version.

Related Data and Programs:

SPHERE_STEREOGRAPH, a MATLAB library which computes the stereographic mapping between points on the unit sphere and points on the plane Z = 1.

SPHERE_GRID, a MATLAB library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, over the unit sphere.

SPHERE_LEBEDEV_RULE_DISPLAY, a MATLAB program which reads a file defining a Lebedev quadrature rule for the sphere and displays the point locations.

SPHERE_VORONOI_DISPLAY_OPENGL, a C++ program which displays a sphere and randomly selected generator points, and then gradually colors in points in the sphere that are closest to each generator.

SPHERE_XYZ_DISPLAY_OPENGL, a C++ program which reads XYZ information defining points in 3D, and displays a unit sphere and the points, using OpenGL.

SPHERE_XYZF_DISPLAY, a MATLAB program which reads XYZF information defining points and faces, and displays a unit sphere, the points, and the faces, in the MATLAB graphics window. This can be used, for instance, to display Voronoi diagrams or Delaunay triangulations on the unit sphere.


  1. C F Marcus,
    The stereographic projection in vector notation,
    Mathematics Magazine,
    Volume 39, Number 2, March 1966, pages 100-102.

Source Code:

Examples and Tests:

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

Last revised on 11 November 2010.