SPHERE_MAXIMUM_DETERMINANT
Quadrature Rules for the Sphere

SPHERE_MAXIMUM_DETERMINANT is a dataset directory which contains files defining maximum determinant point set on the unit sphere, which can be used for interpolation and quadrature, as computed by Robert Womersley.

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, a C++ library which performs geometric calculations in 2, 3 and M dimensional space.

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_DESIGN_RULE, a dataset directory which contains files defining 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_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.

SPHERE_GRID, a dataset directory which contains grids of points, lines, triangles or quadrilaterals on a sphere;

SPHERE_GRID, a C library 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_LEBEDEV_RULE, a dataset directory which contains files defining Lebedev rules of points on the unit sphere, which can be used for quadrature rules of a known precision;

SPHERE_LEBEDEV_RULE, a C library which computes Lebedev quadrature rules for the unit sphere;

SPHERE_VORONOI, a MATLAB program which computes the Voronoi diagram of points on a sphere.

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, a MATLAB program which reads XYZ information defining points in 3D, and displays a unit sphere and the points in the MATLAB 3D graphics window.

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.

Reference:

1. Ian Sloan, Robert Womersley,
   How good can polynomial interpolation on the sphere be?,
   Advances in Computational Mathematics,
   Volume 14, 2001, pages 195-226.

Sample files

• md01_0004.txt, 4 point rule, precision 1.
• md02_0009.txt, 9 point rule, precision 2.
• md03_0016.txt, 16 point rule, precision 3.
• md04_0025.txt, 25 point rule, precision 4.
• md05_0036.txt, 36 point rule, precision 5.
• md06_0049.txt, 49 point rule, precision 6.
• md07_0064.txt, 64 point rule, precision 7.
• md08_0081.txt, 81 point rule, precision 8.
• md09_0100.txt, 100 point rule, precision 9.
• md10_0121.txt, 121 point rule, precision 10.
• md11_0144.txt, 144 point rule, precision 11.
• md12_0169.txt, 169 point rule, precision 12.
• md13_0196.txt, 196 point rule, precision 13.
• md14_0225.txt, 225 point rule, precision 14.
• md15_0256.txt, 256 point rule, precision 15.
• md16_0289.txt, 289 point rule, precision 16.
• md17_0324.txt, 324 point rule, precision 17.
• md18_0361.txt, 361 point rule, precision 18.
• md19_0400.txt, 400 point rule, precision 19.
• md20_0441.txt, 441 point rule, precision 20.
• md21_0484.txt, 484 point rule, precision 21.
• md22_0529.txt, 529 point rule, precision 22.
• md23_0576.txt, 576 point rule, precision 23.
• md24_0625.txt, 625 point rule, precision 24.
• md25_0676.txt, 676 point rule, precision 25.
• md26_0729.txt, 729 point rule, precision 26.
• md27_0784.txt, 784 point rule, precision 27.
• md28_0841.txt, 841 point rule, precision 28.
• md29_0900.txt, 900 point rule, precision 29.

You can go up one level to the DATASETS page.