Tetrahedral Grid of Points

**TETRAHEDRON_GRID**
is a Python library which
generates a grid of points
over the interior of a tetrahedron in 3D.

Starting with any 4 points A, B, C and D that define a tetrahedron, we can divide each edge of the tetrahedron into N subintervals, and create a tetrahedral grid. This defines ((N+1)*(N+2)*(N+3))/6 points that lie on the intersections of grid lines.

The library includes a routine which allows the user to pick an arbitrary tetrahedron and an arbitrary number of subdivisions. It then returns the tetrahedral gridpoints defined by that choice.

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

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

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

CIRCLE_ARC_GRID, a Python library which computes a grid of points along a circle or circular arc in 2D.

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 a grid of points over the interior of an ellipsoid in 3D.

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_GRID, a Python library which generates a regular grid of points over the interior of an arbitrary 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_INTEGRALS, a Python library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TETRAHEDRON_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit 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.

- tetrahedron_grid_count.py, count grid points over the interior of a tetrahedron in 3D.
- tetrahedron_grid_display.py, display points over the interior of a tetrahedron in 3D.
- tetrahedron_grid_points.py, grid points over the interior of a tetrahedron in 3D.
- r83col_print_part.py, prints part of an R83COL.
- r8mat_write.py, writes an R8MAT to a file.
- timestamp.py, prints the current YMDHMS date as a time stamp.

- tetrahedron_grid_test.py, calls all the tests.
- tetrahedron_grid_test.sh, runs all the tests.
- tetrahedron_grid_test.txt, the output file.
- tetrahedron_grid_points.xyz, a sample set of grid points written to a file.
- tetrahedron_grid_points.png, a plot of a sample set of points.
- tetrahedron_grid_display.png, a demonstration of the output of tetrahedron_grid_display().

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