SPHERE_FIBONACCI_GRID
Fibonacci Spiral Grid on a Sphere

SPHERE_FIBONACCI_GRID is a FORTRAN90 library which constructs a grid of points using the Fibonacci spiral over the surface of a sphere in 3D.

Licensing:

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

Languages:

SPHERE_FIBONACCI_GRID is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

CIRCLE_ARC_GRID, a FORTRAN90 program which computes points equally spaced along a circular arc;

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.

ELLIPSE_GRID, a FORTRAN90 library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_GRID, a FORTRAN90 library which computes a grid of points over the interior of an ellipsoid in 3D.

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 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_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_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_LEBEDEV_RULE, a FORTRAN90 library which computes Lebedev quadrature rules over the surface of the unit sphere in 3D.

SPHERE_LLQ_GRID, a FORTRAN90 library which computes a grid of quadrilaterals bounded by latitude and longitude lines over the surface of a sphere in 3D.

SPHERE_LLT_GRID, a FORTRAN90 library which computes a grid of triangles bounded by latitude and longitude lines over the surface of a 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.

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

SPHERE_XYZ_DISPLAY, a FORTRAN90 program which reads XYZ information defining points in 3D, and displays a unit sphere and the points in the MATLAB graphics window.

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

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

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

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

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:

• sphere_fibonacci_grid.f90, the source code.

Examples and Tests:

• sphere_fibonacci_grid_test.f90, a sample calling program.
• sphere_fibonacci_grid_test.txt, the output file.
• sphere_fibonacci_grid_n1000.xyz, a text file containing the coordinates of the grid points.
• sphere_fibonacci_grid_n1000.png, a PNG image of a plot of the grid.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• R8MAT_TRANSPOSE_PRINT prints a R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8MAT_WRITE writes an R8MAT file.
• SPHERE_FIBONACCI_GRID_DISPLAY displays sphere points on a Fibonacci spiral.
• SPHERE_FIBONACCI_GRID_POINTS computes sphere points on a Fibonacci spiral.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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