hexagon_integrals

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

Licensing:

The computer code and data files described and made available on this web page are 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:

annulus_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of an annulus centered at the origin.

ball_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

circle_integrals, a Python code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2D.

cube_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

disk_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin.

disk01_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

hyperball_integrals, a Python 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 Python 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 Python 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 Python code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

polygon_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

pyramid_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

simplex_integrals, a Python 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 Python code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

square_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

tetrahedron_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

triangle_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of an arbitrary triangle in 2d.

triangle01_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

wedge_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

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:

• hexagon_integrals.py, the source code.
• hexagon_integrals.sh, runs all the tests.
• hexagon_integrals.txt, the output file.