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 information on this web page is 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 an Octave 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_exactness, a C code which investigates the monomial exactness of a quadrature rule for the pyramid.
pyramid_felippa_rule, a C code which returns a Felippa quadrature rule 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_jaskowiec_rule, a C code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
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 conical product 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.