sphere_triangle_monte_carlo

sphere_triangle_monte_carlo, an Octave code 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 MIT license

Languages:

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

Related Data and Programs:

sphere_triangle_monte_carlo_test

annulus_monte_carlo an Octave code 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, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3d;

circle_monte_carlo, an Octave code 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, an Octave code 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, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2d.

disk01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2d.

disk01_quarter_monte_carlo, an Octave code 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 an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2d.

ellipsoid_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in m dimensions.

hyperball_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in m dimensions;

hypercube_monte_carlo, an Octave code 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, an Octave code 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, an Octave code 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, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2d.

pyramid_monte_carlo, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

sphere_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the surface of the sphere in 3d;

square_monte_carlo, an Octave code 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, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3d.

triangle_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2d.

triangle01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2d.

wedge_monte_carlo, an Octave code 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:

• monomial_value.m, evaluates a monomial.
• r8_uniform_01.m, returns a unit pseudorandom R8.
• r8vec_normalize.m, normalizes an R8VEC in the Euclidean norm.
• sphere01_sample.m, picks random points on the unit sphere.
• sphere01_triangle_angles_to_area.m, area of a triangle on the unit sphere.
• sphere01_triangle_sample.m, sample spherical triangle on unit sphere.
• sphere01_triangle_sides_to_angles.m, angles of triangle on unit sphere.
• sphere01_triangle_vertices_to_area.m, area of triangle on unit sphere.
• sphere01_triangle_vertices_to_sides.m, sides of triangle on unit sphere.