SIMPLEX_GRID
Regular Grid Within a Simplex

SIMPLEX_GRID is a Python 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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source Code:

• comp_next_grlex.py, returns the next composition of an integer N into K parts, using the graded lexicographic ordering.
• comp_random.py, returns a random composition of an integer N into K parts.
• comp_random_grlex.py, returns a random composition of an integer into K parts, with the integer between 0 and N.
• comp_rank_grlex.py, ranks a composition of an integer into K parts, using grlex order.
• comp_unrank_grlex.py, returns the composition of an integer into K parts of a given rank, using grlex order.
• i4_uniform_ab.py, 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.
• i4vec_print.m, prints an I4VEC.
• ksub_random2.py, 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.
• r8mat_write.py, writes an R8MAT to a file.
• simplex_grid_count.py, returns the size of a grid using N subintervals in each of M dimensions.
• simplex_grid_index_all.m, returns all the simplex grid indices.
• simplex_grid_index_next.py, returns the next simplex grid index.
• simplex_grid_index_sample.py, returns a random simplex grid index.
• simplex_grid_index_to_point.m, converts a simplex grid index to a physical point.
• timestamp.py, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• simplex_grid_test.py, calls all the tests.
• simplex_grid_test.sh, runs all the tests.
• simplex_grid_test.txt, the output file.

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