PYRAMID_INTEGRALS is a FORTRAN77 library 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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
PYRAMID_INTEGRALS is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
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.
You can go up one level to the FORTRAN77 source codes.