TETRAHEDRON_GRID
Tetrahedral Grid of Points

TETRAHEDRON_GRID is a MATLAB library which generates a grid of points inside a 3D tetrahedron.

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.

Related Data and Programs:

BALL_GRID, a MATLAB library which computes grid points that lie inside a 3D ball.

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

CIRCLE_GRID, a MATLAB library which computes grid points that lie inside a circle.

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

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

TRIANGLE_GRID, a MATLAB library which computes a triangular grid of points.

Source Code:

• r83vec_print_part.m, prints part of an R83VEC.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8mat_write.m, writes an R8MAT to a file.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• tetrahedron_grid.m, computes points on a tetrahedral grid.
• tetrahedron_grid_count.m, counts grid points inside a tetrahedron.
• tetrahedron_grid_display.m, displays grid points inside a tetrahedron.

Examples and Tests:

• tetrahedron_grid_test.m, calls all the tests.
• tetrahedron_grid_test_output.txt, the output file.
• tetrahedron_grid_test01.m, sets up a grid of 286 points, generated by subdividing by 10 each side of the (0,0,0), (1,0,0), (0,1,0), (0,0,1) tetrahedron.
• 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.

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