triangle01_monte_carlo, an Octave code 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 <= 1
The 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 MIT license
triangle01_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
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 uses the monte carlo method to estimate integrals 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 unit sphere in 3d;
sphere_triangle_monte_carlo, an Octave code 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, 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 a general tetrahedron in 3D.
tetrahedron01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
triangle_dunavant_rule, an Octave code which sets up a dunavant quadrature rule over the interior of a triangle in 2d.
triangle_fekete_rule, an Octave code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.
triangle_felippa_rule, an Octave code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2d.
triangle_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.
triangle_lyness_rule, an Octave code which returns lyness-jespersen quadrature rules over the interior of a triangle in 2d.
triangle_ncc_rule, an Octave code which defines newton-cotes closed quadrature rules on a triangle.
triangle_nco_rule, an Octave code which defines newton-cotes open quadrature rules on a triangle.
triangle_symq_rule, an Octave code 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, an Octave code 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, an Octave code which uses the monte carlo method to estimate integrals over the interior of the unit wedge in 3d.