STRI_QUAD
Sphere Quadrature via Triangulation

STRI_QUAD is a FORTRAN90 library which estimates the integral of a scalar function F(X,Y,Z) over the surface of a sphere of arbitrary radius centered at the origin.

The estimate is performed by covering the sphere with a triangulation, and then using simple techniques to estimate the integral over each spherical triangle. The code could easily be extended to handle a sphere whose center was arbitrary.

Related Data and Programs:

DESIGN is a FORTRAN90 library which returns pointsets on the sphere that constitute "designs".

SCVT is a FORTRAN90 library of routines which returns well separated pointsets on a sphere computed using a Centroid Voronoi Tessellation.

STRIPACK is a FORTRAN90 library which includes routines to compute the Voronoi diagram or Delaunay triangulation of pointsets on a sphere.

STROUD is a FORTRAN90 library of routines which approximate the integral of a function on the surface or in the interior of a variety of geometric shapes.

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

Source Code:

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

Examples and Tests:

• stri_quad_prb.f90, a sample problem.
• stri_quad_prb.csh, commands to compile and run the problem.
• stri_quad_prb_output.txt, the output file.

List of Routines:

• RANDOM_INITIALIZE initializes the FORTRAN 90 random number seed.
• RTP_TO_XYZ converts spherical coordinates to XYZ coordinates.
• S_CAT concatenates two strings to make a third string.
• SPHERE_AREA_3D computes the surface area of a sphere in 3D.
• SPHERE_QUAD_00 approximates an integral over a sphere in 3D.
• SPHERE_QUAD_01 approximates an integral over a sphere in 3D.
• SPHERE_QUAD_02 approximates an integral over a sphere in 3D.
• SPHERE_QUAD_03 approximates an integral over a sphere in 3D.
• SPHERE_SAMPLE_3D picks a random point on a sphere in 3D.
• STRI_ANGLES_TO_AREA_3D computes the area of a spherical triangle.
• STRI_QUAD_01 approximates an integral over a spherical triangle in 3D.
• STRI_SIDES_TO_ANGLES_3D computes spherical triangle angles in 3D.
• STRI_VERTICES_TO_AREA_3D computes the area of a spherical triangle in 3D.
• STRI_VERTICES_TO_CENTROID_3D gets a spherical triangle "centroid" in 3D.
• STRI_VERTICES_TO_MIDPOINTS_3D gets a spherical triangles midsides in 3D.
• STRI_VERTICES_TO_SIDES_3D computes spherical triangle sides in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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