TRIANGLE_MONTE_CARLO is a C++ library which uses the Monte Carlo method to estimate the integral of a function F(X,Y) over the interior of the unit triangle in 2D.
The interior of the unit triangle in 2D is defined by the constraints:
0 <= X 0 <= Y X + Y <= 1The functions F(X,Y) are monomials, having the form
F(X,Y) = X^E(1) * Y^E(2)where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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.
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;
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 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_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.
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 uses the Monte Carlo method to estimate integrals over 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 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 a tetrahedron in 3D.
TRIANGLE_ANALYZE, a C++ program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
TRIANGLE_DUNAVANT_RULE, a C++ library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.
TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
TRIANGLE_LYNESS_RULE, a C++ library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.
TRIANGLE_SYMQ_RULE, a C++ library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
TRIANGLE_WANDZURA_RULE, a C++ library which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 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.
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