PYRAMID_RULE is a MATLAB program which generates a quadrature rule for a pyramid.
The quadrature rules generated by PYRAMID_RULE are all examples of conical product rules, and involve a kind of direct product of the form:
Legendre rule in X * Legendre rule in Y * Jacobi rule in Zwhere the Jacobi rule includes a factor of (1-Z)^2.
The integration region is:
- ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
When Z is zero, the integration region is a square lying in the (X,Y)
plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the
radius of the square diminishes, and when Z reaches 1, the square has
contracted to the single point (0,0,1).
pyramid_rule ( legendre_order, jacobi_order, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
PYRAMID_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
FELIPPA, a MATLAB library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.
GEOMETRY, a MATLAB library which performs geometric calculations in 2, 3 and N dimensional space.
JACOBI_RULE, a MATLAB program which can compute and print a Gauss-Jacobi quadrature rule.
LEGENDRE_RULE, a MATLAB program which can compute and print a Gauss-Legendre quadrature rule.
PYRAMID_EXACTNESS, a MATLAB program which investigates the polynomial exactness of a quadrature rule for the pyramid.
QUADRATURE_RULES_PYRAMID, a dataset directory which contains quadrature rules for a pyramid with a square base.
QUADRULE, a MATLAB library which defines quadrature rules on a variety of intervals with different weight functions.
STROUD, a MATLAB library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
You can go up one level to the MATLAB source codes.