SPHERE_GRID
Grids on a Sphere


SPHERE_GRID is a FORTRAN90 library which constructs a variety of sets of points over the surface of the unit sphere in 3D.

A grid on a sphere may mean a set of points, or a set of points and lines that connect them, or a set of points, lines that connect them, and the faces that are bounded by those lines.

A grid may be desired which simply organizes areas. In that case, something like the latitude and longitude lines on a globe may be sufficient, even though "evenly spaced" latitude and longitude lines result in grid cells that are close to rectangular near the equator, but become more asymmetric near the poles.

A grid may also be desired for sampling, that is, for choosing a set of points that are well spread across the sphere. A simple Monte Carlo approach can be used, although this means that the data is only well spread out in the long view; there may be local clusters and gaps.

Other grids are generated by drawing a spiral on the surface of the sphere, and choosing points at regular spacings along that line, or by projecting an icosahedron onto the surface of the sphere, which divides the surface into 20 congruent spherical triangles, and then dealing with the simpler issue of choosing points from the triangles.

The test program uses GNUPLOT to make images of some of the grids.

Licensing:

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

Languages:

SPHERE_GRID is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CUBE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a cube in 3D.

DISK_GRID, a FORTRAN90 library which computes a grid of points over the interior of a disk in 2D.

DISTANCE_TO_POSITION_SPHERE, a MATLAB program which estimates the positions of cities on a sphere (such as the earth) based on a city-to-city distance table.

GNUPLOT, FORTRAN90 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

HYPERCUBE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a hypercube in M dimensions.

LINE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a line segment in 1D.

POLYGON_GRID, a FORTRAN90 library which generates a grid of points over the interior of a polygon in 2D.

PYRAMID_GRID, a FORTRAN90 library which computes a grid of points over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a FORTRAN90 library which generates a regular grid of points over the interior of a simplex in M dimensions.

SPHERE_CUBED_GRID, a FORTRAN90 library which uses the projection of a cube to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.

SPHERE_FIBONACCI_GRID, a FORTRAN90 library which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.

SPHERE_GRID, a FORTRAN90 library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, on the surface of the unit sphere in 3D.

SPHERE_INTEGRALS, a FORTRAN90 library which defines test functions for integration over the surface of the unit sphere in 3D.

SPHERE_LEBEDEV_RULE, a FORTRAN90 library which computes Lebedev quadrature rules for the unit sphere;

SPHERE_LLQ_GRID, a FORTRAN90 library which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.

SPHERE_LLT_GRID, a FORTRAN90 library which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.

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_TRIANGLE_QUAD, a FORTRAN90 library which estimates the integral of a function over a spherical triangle.

SPHERE_VORONOI, a FORTRAN90 program which computes and plots the Voronoi diagram of points on the unit sphere.

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 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.

STRIPACK, a FORTRAN90 library which computes the Delaunay triangulation or Voronoi diagram of points over the surface of the unit sphere in 3D.

STRIPACK_INTERACTIVE, a FORTRAN90 program which reads a set of points on the unit sphere, computes the Delaunay triangulation, and writes it to a file.

WEDGE_GRID, a FORTRAN90 library which computes a grid of points over the interior of the unit wedge in 3D.

XYZ_DISPLAY, a MATLAB program which reads XYZ information defining points in 3D, and displays an image in the MATLAB graphics window.

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

Reference:

  1. Edward Saff, Arno Kuijlaars,
    Distributing Many Points on a Sphere,
    The Mathematical Intelligencer,
    Volume 19, Number 1, 1997, pages 5-11.
  2. Richard Swinbank, James Purser,
    Fibonacci grids: A novel approach to global modelling,
    Quarterly Journal of the Royal Meteorological Society,
    Volume 132, Number 619, July 2006 Part B, pages 1769-1793.

Source Code:

Examples and Tests:

To see the XYZ data files and images of the sphere grids created by this example program, go to the SPHERE_GRID dataset directory.

List of Routines:

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


Last revised on 21 October 2013.