SIMPLEX_GRID
Regular Grid Within a Simplex

SIMPLEX_GRID is a C++ 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA299, a C++ 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 C++ library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a C++ program which computes points equally spaced along a circular arc in 2D.

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

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

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

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

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

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

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

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

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

SIMPLEX_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.

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

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

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

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

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

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

Source Code:

• simplex_grid.cpp, the source code.
• simplex_grid.hpp, the include file.
• simplex_grid.sh, BASH commands to compile the source code.

Examples and Tests:

• simplex_grid_prb.cpp, a sample calling program.
• simplex_grid_prb.sh, BASH commands to compile and run the sample program.
• simplex_grid_prb_output.txt, the output file.

List of Routines:

• COMP_NEXT_GRLEX returns the next composition in grlex order.
• COMP_RANDOM selects a random composition of the integer N into K parts.
• I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• KSUB_RANDOM selects a random subset of size K from a set of size N.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• SIMPLEX_GRID_INDEX_ALL returns all the simplex grid indices.
• SIMPLEX_GRID_INDEX_NEXT returns the next simplex grid index.
• SIMPLEX_GRID_INDEX_SAMPLE returns a random simplex grid index.
• SIMPLEX_GRID_INDEX_TO_POINT returns points corresponding to simplex indices.
• SIMPLEX_GRID_SIZE counts the grid points inside a simplex.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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