sphere_triangle_monte_carlo

sphere_triangle_monte_carlo, a MATLAB 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 information on this web page is 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

matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.

sphere_triangle_quad, a MATLAB code which uses quadrature to estimate the integral of a function over a spherical triangle on the surface of the unit sphere 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.