tetrahedron_witherden_rule, a C code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.
The data is given for the tetrahedron: with vertices (0,0,0), (1,0,0), (0,1,0), (0,0,1).
We suppose we are given a tetrahedron T with vertices A, B, C, D. We call a rule with n points, returning barycentric coordinates a, b, c, d, and weights w. Then the integral I of f(x,y,z) over T is approximated by Q as follows:
(x,y,z) = a(1:n) * A + b(1:n) * B + c(1:n) * C + d(1:n) * D
Q = volume(T) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i))
The information on this web page is distributed under the MIT license.
tetrahedron_witherden_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave versionand a Python version.
tetrahedron_witherden_rule_test
c_rule, a C code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
tetrahedron_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
tetrahedron_monte_carlo, a C code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit tetrahedron in 3d.