SPHERE_VORONOI_DISPLAY_OPENGL
Display an Approximate Voronoi Diagram on a Sphere

SPHERE_VORONOI_DISPLAY_OPENGL is a C++ program which picks random points on a sphere as generators, and then gradually colors in neighboring points according to the color of the nearest generator. This, in effect, constructs a Voronoi diagram, or at least, suggests it. The exact calculation of the boundary lines and vertices requires a more precise computation.

The user is allowed to request the number of generators, and OpenGL is used to display the results. Initially, the sphere is rotating, but at least on my machine, once I try to display the neighbors, the rotation becomes very slow.

Usage:

sphere_voronoi_display_opengl gen_num

• gen_num is the number of generators,

Licensing:

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

Languages:

SPHERE_VORONOI_DISPLAY_OPENGL is available in a C++ version.

Related Data and Programs:

FERN_OPENGL, a C++ program which uses OpenGL to display the Barnsley fractal fern.

ROTATING_CUBE_DISPLAY_OPENGL, a C++ program which displays a rotating color cube in 3D, using OpenGL;

SPHERE_CVT, a FORTRAN90 library which creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi Tessellations.

SPHERE_CVT, a MATLAB library which creates a mesh of well-separated points on a unit sphere by applying the Centroidal Voronoi Tessellation (CVT) iteration.

SPHERE_DELAUNAY, a MATLAB program which computes the Delaunay triangulation of points on a 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_VORONOI, a MATLAB program which computes the Voronoi diagram of points on a sphere.

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_VORONOI, a FORTRAN90 program which reads an XYZ file of 3D points on the unit sphere, computes the Voronoi diagram, and writes it to a file.

SXYZ_VORONOI, a FORTRAN90 library which reads an XYZ file of 3D points on the sphere, and computes and plots Delaunay triangulations and Voronoi diagrams.

XYZ_DISPLAY_OPENGL, a C++ program which reads XYZ information defining points in 3D, and displays an image using OpenGL.

Source Code:

• sphere_voronoi_display_opengl.cpp, the source code.
• sphere_voronoi_display_opengl.sh, commands to compile the source code.

Examples and Tests:

• sphere_generators.png, a PNG image of the sphere with just the initial generators indicated.
• sphere_voronoi.png, a PNG image of the sphere, with many points colored the same as the nearest generator.

List of Routines:

• MAIN is the main program for SPHERE_VORONOI_DISPLAY_OPENGL.
• DISPLAY generates the graphics output.
• MOUSE determines the response to mouse input.
• MYINIT initializes OpenGL state variables dealing with viewing and attributes.
• MYRESHAPE determines the window mapping.
• R4MAT_UNIFORM_01 returns a unit pseudorandom R4MAT.
• R4MAT_ZERO_NEW returns a new zeroed R4MAT.
• R4VEC_NORMAL_01 samples the standard normal probability distribution.
• R4VEC_UNIFORM_01 returns a unit unit pseudorandom R4VEC.
• SPIN_IMAGE adjusts the angle of rotation and redisplays the picture.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UNIFORM_ON_SPHERE01_MAP maps uniform points onto the unit sphere.

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