hexagon_rule


hexagon_rule, a MATLAB code which computes a quadrature rule over the interior of the unit hexagon.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

hexagon_rule is available in a MATLAB version.

Related Data and Programs:

annulus_rule, a MATLAB code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

circle_rule, a MATLAB code which computes quadrature rules over the circumference of the unit circle in 2D.

cube_felippa_rule, a MATLAB code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

disk_rule, a MATLAB code which computes a quadrature rule over the interior of the unit disk in 2D, with radius 1 and center (0,0).

disk01_quarter_rule, a MATLAB code which computes a quadrature rule over the interior of the unit quarter disk in 2D, with radius 1 and center (0,0).

disk01_rule, a MATLAB code which computes quadrature rules over the interior of the unit disk in 2D.

hexagon_rule_test

pyramid_felippa_rule, a MATLAB code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

pyramid_rule, a MATLAB code which computes a quadrature rule over the interior of a pyramid in 3D.

sphere_lebedev_rule, a MATLAB code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

square_felippa_rule, a MATLAB code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

stroud, a MATLAB code which defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

tetrahedron_felippa_rule, a MATLAB code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

triangle_fekete_rule, a MATLAB code which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.

triangle_felippa_rule, a MATLAB code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

wedge_felippa_rule, a MATLAB code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

  1. James Lyness, Giovanni Monegato,
    Quadrature rules for regions having regular hexagonal symmetry,
    SIAM Journal on Numerical Analysis.
    Volume 14 Number 2, April 1977, pages 283-295.
  2. Arthur Stroud,
    Approximate Calculation of Multiple Integrals,
    Prentice Hall, 1971.

Source Code:


Last revised on 22 April 2019.