pyramid_integrals


pyramid_integrals, a FORTRAN77 code which returns the exact value of the integral of any monomial x^i y^j z^k over the interior of the unit pyramid in 3D.

The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:

        - ( 1 - Z ) <= X <= 1 - Z
        - ( 1 - Z ) <= Y <= 1 - Z
                  0 <= Z <= 1.
      
The volume of the unit pyramid is 4/3.

Licensing:

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

Languages:

pyramid_integrals 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.

Related Data and Programs:

pyramid_integrals_test

ball_integrals, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

circle_integrals, a FORTRAN77 library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

CUBE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

DISK_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.

HYPERCUBE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

HYPERSPHERE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

LINE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the unit line segment in 1D.

POLYGON_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_EXACTNESS, a FORTRAN77 program which investigates the monomial exactness of a quadrature rule over the interior of a pyramid in 3D.

PYRAMID_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit pyramid in 3D;

PYRAMID_MONTE_CARLO, a FORTRAN77 library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

PYRAMID_RULE, a FORTRAN77 program which computes a quadrature rule over the interior of the unit pyramid in 3D;

SIMPLEX_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

SPHERE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

SQUARE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

TETRAHEDRON_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

Source Code:


Last revised on 05 November 2023.