SPHERE_VORONOI is a FORTRAN90 program which computes and plots the Voronoi diagram of points on the unit sphere.
SPHERE_VORONOI takes as input an XYZ file, containing coordinates of points on the unit sphere in 3D. It passes this data to Renka's STRIPACK library which computes the Voronoi diagram. The program then takes one "snapshot" of the diagram, which is written to an EPS image file, and stores the vertex and line information defines the Voronoi triangulation as XYZ and XYZF files.
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_voronoi file.xyz
reads the XYZ file file.xyz containing the point coordinates,
creates an EPS file file.eps containing a 2D projection of the Voronoi
diagram, and creates an XYZ file file.voronoi.xyz and an XYZF file
file.xyzf which can be used, in conjunction with file_voronoi.xyz
to display the 3D Voronoi diagram.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
SPHERE_VORONOI is available in a FORTRAN90 version and a MATLAB version.
SPHERE_CVT, a FORTRAN90 library which creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi Tessellations.
SPHERE_DELAUNAY, a FORTRAN90 program which computes and plots the Delaunay triangulation of points on the unit sphere.
SPHERE_DESIGN_RULE, a FORTRAN90 library which returns point sets on the surface of the unit sphere, known as "designs", which can be useful for estimating integrals on the surface, among other uses.
SPHERE_QUAD, a FORTRAN90 library which estimates the integral of a function defined on the sphere.
SPHERE_STEREOGRAPH, a FORTRAN90 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_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.
STRIPACK, a FORTRAN90 library which is used by SPHERE_VORONOI to compute the Voronoi tessellation and Delaunay triangulation of the points on the sphere.
STRIPACK_VORONOI, a FORTRAN90 program which reads a set of points on the unit sphere, computes the Voronoi diagram, and writes it to a file.
XYZ, a data directory which contains examples of XYZ files, a simple 3D graphics point format;
XYZ_IO, a FORTRAN90 library which reads and writes XYZ files.
XYZF, a data directory which contains examples of XYZF files, a simple 3D graphics point and face format;
XYZF_DISPLAY, a MATLAB program which reads XYZF information defining points and faces in 3D, and displays an image using OpenGL.
XYZF_DISPLAY_OPENGL, a C++ program which reads XYZF information defining points and faces in 3D, and displays an image using OpenGL.
GEN_00010 is a test set of 10 points:
GEN_00100 is a test set of 100 points:
You can go up one level to the FORTRAN90 source codes.