DISK_RULE is a MATLAB library which computes a quadrature rule over the interior of the general disk in 2D, with radius RC and center (XC,YC).
The user specifies values NT and NR, where NT is the number of equally spaced angles, and NR controls the number of radial points, the center of the disk (XC,YC), and the radius of the disk RC. The program returns vectors W(NR*NT), X(NR*NT) and Y(NR*NT), which define the rule Q(f).
To use a rule that is equally powerful in R and T, typically, set NT = 2 * NR.
Given NT, NR, and the quadrature vectors W, X, Y, the integral I(f) is estimated by Q(f) as follows:
s = w' * f(x,y) area = pi * rc ^ 2; q = area * s;
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
DISK_RULE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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DISK01_RULE, a MATLAB library which computes quadrature rules over the interior of the unit disk in 2D.
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PYRAMID_RULE, a MATLAB program which computes a quadrature rule over the interior of a pyramid in 3D.
SPHERE_LEBEDEV_RULE, a MATLAB library which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
SQUARE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a MATLAB library 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.
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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.