simplex_grid

simplex_grid, a MATLAB code which generates a grid of points over the interior of a simplex in M dimensions.

Licensing:

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

Languages:

simplex_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:

asa299, a MATLAB code which computes the lattice points in an m-dimensional simplex, by chasalow and brand; this is a version of applied statistics algorithm 299;

ball_grid, a MATLAB code which computes a grid of points over the interior of a ball in 3d.

circle_arc_grid, a MATLAB code which computes points equally spaced along a circular arc;

cube_grid, a MATLAB code which computes a grid of points over the interior of a cube in 3d.

disk_grid, a MATLAB code which computes a grid of points over the interior of a disk in 2d.

ellipse_grid, a MATLAB code which computes a grid of points over the interior of an ellipse in 2d.

ellipsoid_grid, a MATLAB code which computes grid points that lie inside a 3d ellipsoid.

fem_basis, a MATLAB code which can define basis functions for the finite element method (fem) for any degree in an m-dimensional simplex (1d interval, 2d triangle, 3d tetrahedron, and higher dimensional generalizations.)

hypercube_grid, a MATLAB code which computes a grid of points over the interior of a hypercube in m dimensions.

line_grid, a MATLAB code which computes a grid of points over the interior of a line segment in 1d.

polygon_grid, a MATLAB code which generates a grid of points over the interior of a polygon in 2d.

pyramid_grid, a MATLAB code which computes a grid of points over the interior of the unit pyramid in 3d;

simplex_coordinates, a MATLAB code which computes the cartesian coordinates of the vertices of a regular simplex in m dimensions.

simplex_gm_rule, a MATLAB code which defines grundmann-moeller quadrature rules over the interior of a simplex in m dimensions.

simplex_grid_test

simplex_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

simplex_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

sphere_fibonacci_grid, a MATLAB code which uses a fibonacci spiral to create a grid of points on the surface of the unit sphere in 3d.

sphere_grid, a MATLAB code 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 MATLAB code which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3d.

square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2d.

tetrahedron_grid, a MATLAB code which computes a grid of points over the interior of a tetrahedron in 3d.

triangle_grid, a MATLAB code which computes a grid of points over the interior of a triangle in 2d.

wedge_grid, a MATLAB code which computes a grid of points over the interior of the unit wedge in 3d.

Source Code:

• comp_next_grlex.m, returns the next composition of an integer N into K parts, using the graded lexicographic ordering.
• comp_random.m, returns a random composition of an integer N into K parts.
• i4_uniform_ab.m, returns a random integer between A and B.
• i4mat_transpose_print.m, prints an I4MAT transposed.
• i4mat_transpose_print_some.m, prints some of an I4MAT transposed.
• ksub_random.m, returns a random subset of K items from a set of N items.
• r8mat_transpose_print.m, prints an R8MAT transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT transposed.
• simplex_grid_index_all.m, returns all the simplex grid indices.
• simplex_grid_index_next.m, returns the next simplex grid index.
• simplex_grid_index_sample.m, returns a random simplex grid index.
• simplex_grid_index_to_point.m, converts a simplex grid index to a physical point.
• simplex_grid_size.m, returns the size of a grid using N subintervals in each of M dimensions.