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SPHERE_TRIANGLE_MONTE_CARLO
Monte Carlo Estimates of Integrals over Spherical Triangles {#sphere_triangle_monte_carlo-monte-carlo-estimates-of-integrals-over-spherical-triangles align="center"}

SPHERE_TRIANGLE_MONTE_CARLO is a C++ library which applies the Monte Carlo method to estimate the integral of a function F(X,Y,Z) over a triangle on the surface of the unit sphere in 3D.

Licensing: {#licensing align="center"}

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

Languages: {#languages align="center"}

SPHERE_TRIANGLE_MONTE_CARLO 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: {#related-data-and-programs align="center"}

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

CUBE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

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

DISK_QUARTER_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2D;

ELLIPSE_MONTE_CARLO a C++ library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a C++ library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

HYPERBALL_MONTE_CARLO, a C++ 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 C program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions;

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

LINE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

POLYGON_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

PYRAMID_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

SIMPLEX_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

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

SPHERE_TRIANGLE_QUAD, a C++ library which uses quadrature to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D.

SQUARE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

TETRAHEDRON_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

WEDGE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Reference: {#reference align="center"}

  • Jacob Goodman, Joseph ORourke, editors,
    Handbook of Discrete and Computational Geometry,
    Second Edition,
    CRC/Chapman and Hall, 2004,
    ISBN: 1-58488-301-4,
    LC: QA167.H36.

Source Code: {#source-code align="center"}

Examples and Tests: {#examples-and-tests align="center"}

List of Routines: {#list-of-routines align="center"}

  • ARC_COSINE computes the arc cosine function, with argument truncation.
  • MONOMIAL_VALUE evaluates a monomial.
  • R8_UNIFORM_01 returns a unit pseudorandom R8.
  • R8VEC_NORM returns the L2 norm of an R8VEC.
  • R8VEC_NORMALIZE normalizes an R8VEC in the Euclidean norm.
  • SPHERE01_SAMPLE picks random points on the unit sphere.
  • SPHERE01_TRIANGLE_ANGLES_TO_AREA: area of a triangle on the unit sphere.
  • SPHERE01_TRIANGLE_SAMPLE: sample spherical triangle on unit sphere.
  • SPHERE01_TRIANGLE_SIDES_TO_ANGLES: angles of triangle on unit sphere.
  • SPHERE01_TRIANGLE_VERTICES_TO_AREA: area of triangle on unit sphere.
  • SPHERE01_TRIANGLE_VERTICES_TO_SIDES: sides of triangle on unit sphere.
  • TIMESTAMP prints the current YMDHMS date as a time stamp.

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

Last revised on 22 April 2014.