pyramid_integrals, a C 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.
The computer code and data files described and made available on this web page are distributed under the MIT license
pyramid_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
BALL_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
CIRCLE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
CUBE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
DISK01_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
HYPERBALL_INTEGRALS, a C 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 C 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 C 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 C code which returns the exact value of the integral of any monomial over the unit line segment in 1D.
POLYGON_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
PYRAMID_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_GRID, a C code which computes a grid of points over the interior of the unit pyramid in 3D;
PYRAMID_MONTE_CARLO, a C code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
PYRAMID_RULE, a C code which computes a quadrature rule over the interior of the unit pyramid in 3D;
SIMPLEX_INTEGRALS, a C 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 C code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
SQUARE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
TETRAHEDRON_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
TRIANGLE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
WEDGE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.