tetrahedron_monte_carlo

tetrahedron_monte_carlo, an Octave code which estimates the integral of a function over a general tetrahedron using the Monte Carlo method.

The library makes it relatively easy to compare different methods of producing sample points in the tetrahedron, and to vary the tetrahedron over which integration is carried out.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

tetrahedron_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

tetrahedron_monte_carlo_test

octave_monte_carlo, an Octave code which uses Monte Carlo sampling to estimate areas and integrals.

tetrahedron_exactness, an Octave code which computes the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

Reference:

1. Claudio Rocchini, Paolo Cignoni,
   Generating Random Points in a Tetrahedron,
   Journal of Graphics Tools,
   Volume 5, Number 4, 2000, pages 9-12.
2. Reuven Rubinstein,
   Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
   Krieger, 1992,
   ISBN: 0894647644,
   LC: QA298.R79.
3. Greg Turk,
   Generating Random Points in a Triangle,
   in Graphics Gems I,
   edited by Andrew Glassner,
   AP Professional, 1990,
   ISBN: 0122861663,
   LC: T385.G697

Source Code:

• r8mat_det_4d.m computes the determinant of a 4x4 R8MAT.
• r8mat_transpose_print.m prints an R8MAT, transposed.
• r8mat_transpose_print_some.m prints some of an R8MAT, transposed.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• reference_to_physical_t3.m maps reference tetrahedron points to physical points.
• s_len_trim.m returns the length of a string to the last nonblank.
• tetrahedron_integrand_01.m evaluates 1 integrand function.
• tetrahedron_integrand_02.m evaluates 3 integrand functions.
• tetrahedron_integrand_03.m evaluates 6 integrand functions.
• tetrahedron_integrand_04.m evaluates 10 integrand functions.
• tetrahedron_integrand_05.m evaluates 15 integrand functions.
• tetrahedron_monte_carlo.m applies the Monte Carlo rule to integrate a function.
• tetrahedron_unit_sample_01.m selects points from the unit tetrahedron.
• tetrahedron_unit_sample_02.m selects points from the unit tetrahedron.
• tetrahedron_unit_sample_03.m selects points from the unit tetrahedron.
• tetrahedron_unit_sample_04.m selects points from the unit tetrahedron.
• tetrahedron_volume.m computes the volume of a tetrahedron.