PYRAMID_RULE, a MATLAB program which generates a quadrature rule over the interior of the unit pyramid in 3D.
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 C++ version and a FORTRAN90 version and a MATLAB version.
ANNULUS_RULE, a MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
CIRCLE_RULE, a MATLAB library which computes a quadrature rule over the circumference of the unit circle in 2D.
CUBE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
DISK_RULE, a MATLAB library which computes quadrature rules over the interior of a disk in 2D.
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 over the interior of the unit pyramid in 3D.
PYRAMID_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_GRID, a MATLAB library which computes a grid of points over the interior of the unit pyramid in 3D;
PYRAMID_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
PYRAMID_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
QUADRATURE_RULES_PYRAMID, a dataset directory which contains quadrature rules over the interior of the unit pyramid in 3D.
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STROUD, a MATLAB library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TETRAHEDRON_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_FEKETE_RULE, a MATLAB library which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a MATLAB library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.