TRIANGLE_MONTE_CARLO
Monte Carlo Integral Estimates over a Triangle

TRIANGLE_MONTE_CARLO is a C++ library which estimates the integral of a function over a 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.

Related Data and Programs:

DUNAVANT is a C++ library which defines Dunavant rules for quadrature on a triangle.

FEKETE is a C++ library which defines Fekete rules for interpolation or quadrature on a triangle.

FELIPPA is a C++ library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

GM_RULES is a C++ library which defines Grundmann-Moeller rules for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

NCC_TRIANGLE is a C++ library which defines Newton-Cotes Closed quadrature rules on a triangle.

NCO_TRIANGLE is a C++ library which defines Newton-Cotes Open quadrature rules on a triangle.

NINT_EXACTNESS_TRI is a C++ program which investigates the polynomial exactness of a quadrature rule for the triangle.

RANDOM_DATA, a C++ library which generates sample points for various probability distributions, spatial dimensions, and geometries;

STROUD is a C++ library which defines quadrature rules for a variety of multidimensional reqions.

TEST_TRI_INT is a C++ library which defines test functions for quadrature over the triangle.

TETRAHEDRON_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over a tetrahedron.

TRIANGLE_MONTE_CARLO is available in a C++ version and a FORTRAN90 version and a MATLAB version.

WANDZURA is a C++ library which defines Wandzura rules for quadrature on a triangle.

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:

• triangle_monte_carlo.C, the source code.
• triangle_monte_carlo.H, the include file.
• triangle_monte_carlo.csh, commands to compile the source code.

Examples and Tests:

• triangle_monte_carlo_prb.C, a sample calling program.
• triangle_monte_carlo_prb.csh, commands to compile and run the sample program.
• triangle_monte_carlo_prb_output.txt, the output file.

List of Routines:

• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8VEC_SUM returns the sum of an R8VEC.
• R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
• REFERENCE_TO_PHYSICAL_T3 maps T3 reference points to physical points.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_AREA computes the area of a triangle in 2D.
• TRIANGLE_INTEGRAND_01 evaluates 1 integrand function.
• TRIANGLE_INTEGRAND_02 evaluates 2 integrand functions.
• TRIANGLE_INTEGRAND_03 evaluates 3 integrand functions.
• TRIANGLE_INTEGRAND_04 evaluates 4 integrand functions.
• TRIANGLE_INTEGRAND_05 evaluates 5 integrand functions.
• TRIANGLE_UNIT_SAMPLE_01 selects points from the unit triangle.
• TRIANGLE_UNIT_SAMPLE_02 selects points from the unit triangle.
• TRIANGLE_UNIT_SAMPLE_03 selects points from the unit triangle.
• TRIANGLE_UNIT_SAMPLE_04 selects points from the unit triangle.

You can go up one level to the C++ source codes.