hexagon_integrals

hexagon_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a hexagon.

The code assumes that the hexagon has a "flat" top and bottom:

            *   *
          *       *
            *   *
    

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

hexagon_integrals is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hexagon_integrals_test

hexagon_lyness_rule, a MATLAB code which computes one of 13 Lyness quadrature rules over the interior of the unit hexagon.

hexagon_stroud_rule, a MATLAB code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.

matlab_integrals, a MATLAB 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.

Reference:

1. SF Bockman,
   Generalizing the Formula for Areas of Polygons to Moments,
   American Mathematical Society Monthly,
   Volume 96, Number 2, February 1989, pages 131-132.
2. Carsten Steger,
   On the calculation of arbitrary moments of polygons,
   Technical Report FGBV-96-05,
   Forschungsgruppe Bildverstehen, Informatik IX,
   Technische Universitaet Muenchen, October 1996.

Source Code:

• hexagon01_integrals.m returns the integral of a monomial over the unit hexagon.
• moment_unnormalized.m computes an unnormalized moment of a polygon.
• moment_central.m computes central moments of a polygon.
• moment_normalized.m computes a normalized moment of a polygon.
• r8_mop.m returns the I-th power of -1 as an R8.