SIMPLEX_GRID
Regular Grid Within a Simplex

SIMPLEX_GRID, a MATLAB library 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 GNU LGPL 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 library 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 library which computes a grid of points over the interior of a ball in 3D.

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

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

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

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

ELLIPSOID_GRID, a MATLAB library which computes grid points that lie inside a 3D ellipsoid.

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

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

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

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

SIMPLEX_COORDINATES, a MATLAB library which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.

SIMPLEX_GM_RULE, a MATLAB library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

simplex_grid_test

SIMPLEX_INTEGRALS, a MATLAB library 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 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

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

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

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

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

WEDGE_GRID, a MATLAB library 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.
• timestamp.m, prints the current YMDHMS date as a time stamp.