**pyramid_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 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 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_felippa_rule, a MATLAB code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.

pyramid_grid, a MATLAB code which computes a grid of points over the interior of the unit pyramid in 3d;

pyramid_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function 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_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.

- monomial_value.m, evaluates a monomial.
- pyramid01_monomial_integral.m, monomial integral in a unit pyramid.
- pyramid01_sample.m, sample the unit pyramid.
- pyramid01_volume.m, volume of a unit pyramid with square base.
- r8_mop.m, returns the I-th power of -1 as an R8.
- r8mat_transpose_print.m, prints an R8MAT, transposed.
- r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.