TETRAHEDRON_GRID
Tetrahedral Grid of Points

TETRAHEDRON_GRID is a FORTRAN77 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.

Licensing:

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

Languages:

TETRAHEDRON_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:

BALL_GRID, a FORTRAN77 library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a FORTRAN77 program which computes points equally spaced along a circular arc;

CUBE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a cube in 3D.

DISK_GRID, a FORTRAN77 library which computes a grid of points over the interior of a disk in 2D.

ELLIPSE_GRID, a FORTRAN77 library which computes grid points that lie inside an ellipse.

ELLIPSOID_GRID, a FORTRAN77 library which computes grid points that lie inside a 3D ellipsoid.

HYPERCUBE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a hypercube in M dimensions.

LINE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a line segment in 1D.

PYRAMID_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a FORTRAN77 library which generates a grid of points over the interior of a simplex in M dimensions.

SPHERE_GRID, a FORTRAN77 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.

SQUARE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a square in 2D.

TRIANGLE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a triangle in 2D.

WEDGE_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit wedge in 3D.

Source Code:

• tetrahedron_grid.f, the source code.
• tetrahedron_grid.sh, BASH commands to compile the source code.

Examples and Tests:

• tetrahedron_grid_prb.f, a sample calling program.
• tetrahedron_grid_prb.sh, BASH commands to compile and run the sample program.
• tetrahedron_grid_prb_output.txt, the output file.
• tetrahedron_grid_test01.xyz, a grid of 286 points, generated by subdividing by 10 each side of the (0,0,0), (1,0,0), (0,1,0) and (0,0,1) tetrahedron.
• tetrahedron_grid_test01.png, an image of the points.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• R83VEC_PRINT_PART prints "part" of an R83VEC.
• R8MAT_WRITE writes an R8MAT file.
• TETRAHEDRON_GRID computes points on a tetrahedral grid.
• TETRAHEDRON_GRID_COUNT counts the grid points inside a tetrahedron.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.