sphere_grid, a C++ code which constructs a grid of points on 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.
The computer code and data files described and made available on this web page are distributed under the MIT license
sphere_grid is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
CUBE_GRID, a C++ code which computes a grid of points over the interior of a cube in 3D.
DISK_GRID, a C++ code which computes a grid of points over the interior of a disk in 2D.
GEOMETRY, a C++ code which performs geometric calculations in 2, 3 and N dimensional space.
gnuplot_test, C++ codes which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.
HYPERCUBE_GRID, a C++ code which computes a grid of points over the interior of a hypercube in M dimensions.
LINE_GRID, a C++ code which computes a grid of points over the interior of a line segment in 1D.
POLYGON_GRID, a C++ code which generates a grid of points over the interior of a polygon in 2D.
PYRAMID_GRID, a C++ code which computes a grid of points over the interior of the unit pyramid in 3D;
SIMPLEX_GRID, a C++ code which generates a grid of points over the interior of a simplex in M dimensions.
SPHERE_FIBONACCI_GRID, a C++ code which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.
SPHERE_LLQ_GRID, a C++ code 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 C++ code which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.
SQUARE_GRID, a C++ code which computes a grid of points over the interior of a square in 2D.
TRIANGLE_GRID, a C++ code which computes a grid of points over the interior of a triangle in 2D.
WEDGE_GRID, a C++ code which computes a grid of points over the interior of the unit wedge in 3D.