wedge_integrals

wedge_integrals, a MATLAB code which returns the exact value of the integral of any monomial x^i y^j z^k over the interior of the unit wedge in 3D.

The interior of the unit wedge in 3D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
       -1 <= Z <= +1
      

Licensing:

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

Languages:

wedge_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ball_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

circle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

cube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

disk01_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

hexagon_integrals, a MATLAB code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2D.

hyperball_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.

hypercube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

hypersphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

line_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the unit line segment in 1D.

polygon_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

pyramid_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

simplex_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

sphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

square_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

wedge_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

wedge_felippa_rule, a MATLAB code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

wedge_integrals_test

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Source Code:

• monomial_value.m, evaluates a monomial.
• wedge01_monomial_integral.m, returns the integral of a monomial in the unit wedge in 3D.
• wedge01_sample.m, samples points uniformly from the unit wedge in 3D.
• wedge01_volume.m, returns the volume of the unit wedge in 3D.