SPHERE_TRIANGLE_MONTE_CARLO
Monte Carlo Estimates of Integrals over Spherical Triangles

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:

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

Languages:

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

Related Data and Programs:

ANNULUS_MONTE_CARLO a C++ library which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

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 uses the Monte Carlo method to estimate integrals over 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 general disk in 2D;

DISK01_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;

DISK01_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 FORTRAN90 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 hypersphere in M dimensions;

LINE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals 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 on the surface of the unit sphere in 3D;

SPHERE_TRIANGLE_MONTE_CARLO, a C++ library which applies a Monte Carlo method 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 uses the Monte Carlo method to estimate integrals 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 general tetrahedron in 3D.

TETRAHEDRON01_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 general triangle in 2D.

TRIANGLE01_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of the unit 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:

• 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:

• sphere_triangle_monte_carlo.cpp, the source code.
• sphere_triangle_monte_carlo.hpp, the include file.

Examples and Tests:

• sphere_triangle_monte_carlo_test.cpp, a sample calling program.
• sphere_triangle_monte_carlo_test.txt, the output file.

List of Routines:

• 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.

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