pyramid_integrals

pyramid_integrals, an Octave 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.
      

Licensing:

The information on this web page is distributed under the MIT 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

octave_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

Source Code:

• 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.