TRIANGLE_MONTE_CARLO
Monte Carlo Integral Estimates over a General Triangle

TRIANGLE_MONTE_CARLO, a MATLAB library which estimates the integral of a function over a general triangle using the Monte Carlo method.

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

Licensing:

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

Languages:

TRIANGLE_MONTE_CARLO 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_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;

CIRCLE_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

DISK_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

HYPERBALL_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a MATLAB program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERSPHERE_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

SPHERE_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the surface of the unit sphere in 3D;

TETRAHEDRON_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over a tetrahedron.

triangle_monte_carlo_test

TRIANGLE01_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

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_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 T3 reference points to physical points.
• s_len_trim.m returns the length of a string to the last nonblank.
• timestamp.m prints the current YMDHMS date as a time stamp.
• triangle_area.m computes the area of a triangle.
• triangle_integrand_01.m evaluates 1 integrand function.
• triangle_integrand_02.m evaluates 2 integrand functions.
• triangle_integrand_03.m evaluates 3 integrand functions.
• triangle_integrand_04.m evaluates 4 integrand functions.
• triangle_integrand_05.m evaluates 5 integrand functions.
• triangle_monte_carlo.m applies the Monte Carlo rule to integrate a function.
• triangle_unit_sample_01.m selects points from the unit triangle.
• triangle_unit_sample_02.m selects points from the unit triangle.
• triangle_unit_sample_03.m selects points from the unit triangle.
• triangle_unit_sample_04.m selects points from the unit triangle.