STRIPACK_INTERACTIVE
Interactive Delaunay Diagrams on Unit Spheres

STRIPACK_INTERACTIVE is a FORTRAN90 program which interactively determines the Delaunay diagram of a set of points on a sphere.

The set of points is read from a file, and the Delaunay triangulation, once computed, is written out to another file, described as a series of triplets of point indexes.

Usage:

stripack_interactive node_filename

• node_filename is the name of a file containing the (X,Y,Z) coordinates of points on the unit sphere.

Licensing:

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

Related Data and Programs:

GEOMETRY is a FORTRAN90 library which computes various geometric quantities, including grids on spheres.

SCVT is a FORTRAN90 library which can find a set of well separated points on a sphere using Centroidal Voronoi Tessellations.

SPHERE_DESIGN_RULE is 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_GRID is a dataset directory containing files that describe sets of points on the unit sphere.

SPHERE_VORONOI_DISPLAY_OPEN_GL, 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.

STRI_QUAD is a FORTRAN90 library which estimates the integral of a function defined on the sphere.

STRIPACK is a library of FORTRAN90 routines which can compute the Delaunay triangulation or Voronoi diagram of a set of points on the unit sphere.

SXYZ_VORONOI is a FORTRAN90 library which computes and plots Delaunay triangulations and Voronoi diagrams of points on the sphere.

TOMS772 is a FORTRAN77 library which is the original text of the STRIPACK program.

XYZ_IO is a FORTRAN90 library which reads and writes XYZ files.

Reference:

1. Thomas Ericson, Victor Zinoviev,
   Codes on Euclidean Spheres,
   Elsevier, 2001,
   ISBN: 0444503293,
   LC: QA166.7E75
2. Gerald Folland,
   How to Integrate a Polynomial Over a Sphere,
   American Mathematical Monthly,
   Volume 108, Number 5, May 2001, pages 446-448.
3. AD McLaren,
   Optimal Numerical Integration on a Sphere,
   Mathematics of Computation,
   Volume 17, Number 84, October 1963, pages 361-383.
4. 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.
5. Edward Saff, Arno Kuijlaars,
   Distributing Many Points on a Sphere,
   The Mathematical Intelligencer,
   Volume 19, Number 1, 1997, pages 5-11.

Source Code:

• stripack_interactive.f90, the source code.
• stripack_interactive.csh, commands to compile the source code.

Examples and Tests:

SPHERE_GRID_ICOS1_F1 is a grid of 12 points based on an icosahedron.

• sphere_grid_icos1_f1_xyz.txt, the point coordinates.
• sphere_grid_icos1_f1_triangles.txt, the triangles forming the Delaunay triangulation.
• sphere_grid_icos1_f1_output.txt, the output from the program.

SPHERE_GRID_ICOS1_F2 is a grid of 42 points based on an icosahedron.

• sphere_grid_icos1_f2_xyz.txt, the point coordinates.
• sphere_grid_icos1_f2_triangles.txt, the triangles forming the Delaunay triangulation.
• sphere_grid_icos1_f2_output.txt, the output from the program.

SPHERE_GRID_ICOS1_F3 is a grid of 92 points based on an icosahedron.

• sphere_grid_icos1_f3_xyz.txt, the point coordinates.
• sphere_grid_icos1_f3_triangles.txt, the triangles forming the Delaunay triangulation.
• sphere_grid_icos1_f3_output.txt, the output from the program.

List of Routines:

• MAIN is the main program for STRIPACK_INTERACTIVE
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads data from a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• ITABLE_HEADER_WRITE writes the header to an ITABLE file.
• ITABLE_CLOSE_WRITE closes a file used to write an ITABLE.
• ITABLE_DATA_WRITE writes data to an ITABLE file.
• ITABLE_OPEN_WRITE opens a file to write ITABLE data.
• ITABLE_WRITE writes an ITABLE file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN90 source codes.