NCO_TETRAHEDERON is a MATLAB library which defines the weights and abscisass for a sequence of 7 Newton-Cotes open quadrature rules for the tetrahedron.
Newton-Cotes rules have the characteristic that the abscissas are equally spaced. For a tetrahedron, this refers to spacing in the unit reference tetrahedron, or in the barycentric coordinate system. These rules may be mapped to an arbitrary tetrahedron, and will still be valid.
The rules are said to be "open" when they do not include points on the boundary of the tetrahedron.
The use of equally spaced abscissas may be important for your application. That may how your data was collected, for instance. On the other hand, the use of equally spaced abscissas carries a few costs. In particular, for a given degree of polynomial accuracy, there will be rules that achieve this accuracy, but use fewer abscissas than Newton-Cotes. Moreover, the Newton-Cotes approach almost always results in negative weights for some abscissas. This is generally an undesirable feature, particularly when higher order quadrature rules are being used.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
CLENSHAW_CURTIS is a MATLAB library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.
FELIPPA is a MATLAB library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.
GM_RULES is a MATLAB library which defines a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.
KEAST is a MATLAB library which defines a number of quadrature rules for a tetrahedron.
NCC_TETRAHEDRON is a MATLAB library which defines Newton-Cotes closed quadrature rules on a tetrahedron.
NCC_TRIANGLE is a MATLAB library which defines Newton-Cotes closed quadrature rules on a triangle.
NCO_TETRAHEDRON is available in a C++ version and a FORTRAN90 version and a MATLAB version
NCO_TRIANGLE is a MATLAB library which defines Newton-Cotes open quadrature rules on a triangle.
NINTLIB is a MATLAB library which contains a variety of routines for numerical estimation of integrals in multiple dimensions.
QUADRATURE_RULES_TET is a dataset directory of triples of files defining various quadrature rules on tetrahedrons.
QUADRULE is a MATLAB library which defines quadrature rules on a variety of intervals with different weight functions.
STROUD is a MATLAB library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TET_MESH is a MATLAB library which is useful for work with tetrahedral meshes in 3D;
TETRAHEDRON_MONTE_CARLO, a MATLAB program which uses the Monte Carlo method to estimate integrals over a tetrahedron.
TETRAHEDRONS, a dataset directory which contains examplesof tetrahedrons;
A GZIP'ed TAR file of the contents of this directory is available.
You can go up one level to the MATLAB source codes.