Regular Grid Within a Simplex

**SIMPLEX_GRID**,
a C++ code which
generates a grid of points
over the interior of a simplex in M dimensions.

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

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.

- simplex_grid.cpp, the source code.
- simplex_grid.sh, compiles the source code.
- simplex_grid.hpp, the include file.