sphere_delaunay, a MATLAB code which computes the Delaunay triangulation of points on the unit sphere.

According to Steven Fortune, it is possible to compute the Delaunay triangulation of points on a sphere by computing their convex hull. If the sphere is the unit sphere at the origin, the facet normals are the Voronoi vertices.

SPHERE_DELAUNAY uses this approach, by calling MATLAB's convhulln function to generate the convex hull. The information defining the convex hull is actually the desired triangulation of the points. Since this computation is so easy, other parts of the program are designed to analyze the resulting Delaunay triangulation and return other information, such as the areas of the triangles and so on.


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


sphere_delaunay is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

geometry, a MATLAB code which computes various geometric quantities, including grids on spheres.

sphere_cvt, a MATLAB code which creates a mesh of well-separated points on a unit sphere by applying the centroidal voronoi tessellation (cvt) iteration.


sphere_grid, a MATLAB code 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_voronoi, a MATLAB code which computes the voronoi diagram of points on a sphere.


  1. Jacob Goodman, Joseph ORourke, editors,
    Handbook of Discrete and Computational Geometry,
    Second Edition,
    CRC/Chapman and Hall, 2004,
    ISBN: 1-58488-301-4,
    LC: QA167.H36.
  2. Robert Renka,
    Algorithm 772:
    STRIPACK: Delaunay Triangulation and Voronoi Diagram on the Surface of a Sphere,
    ACM Transactions on Mathematical Software,
    Volume 23, Number 3, September 1997, pages 416-434.

Source Code:

Last revised on 25 March 2019.