DISK01_RULE is a C library which computes a quadrature rule over the interior of the unit disk in 2D.
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 program returns vectors T(1:NT), R(1:NR) and W(1:NR), 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 and NR, and the vectors T, R and W, the integral I(f) of a function f(x,y) is estimated by Q(f) as follows:
s = 0.0 for j = 1, nr for i = 1, nt x = r(j) * cos ( t(i) ) y = r(j) * sin ( t(i) ) s = s + w(j) * f ( x, y ) end end area = pi; q = area * s;
To approximate an integral over a circle with center (XC,YC) and radius RC:
s = 0.0 for j = 1, nr for i = 1, nt x = xc + rc * r(j) * cos ( t(i) ) y = yc + rc * r(j) * sin ( t(i) ) s = s + w(j) * f ( x, y ) end end area = rc * rc * pi; q = area * s;
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
DISK01_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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STROUD, a C 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_FELIPPA_RULE, a C library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
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You can go up one level to the C source codes.