NCO_TETRAHEDERON is a MATLAB library of routines, using double precision arithmetic, 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.
CLENSHAW_CURTIS is a MATLAB library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.
DUNAVANT is a MATLAB library of routines for defining Dunavant rules for quadrature on a triangle.
FEKETE is a MATLAB library of routines for defining Fekete rules for quadrature or interpolation on a triangle.
GM_RULES is a MATLAB library of routines for defining 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 defining Newton-Cotes closed quadrature rules on a tetrahedron.
NCC_TRIANGLE is a MATLAB library defining Newton-Cotes closed quadrature rules on a triangle.
NCO_TETRAHEDRON is also available in a C++ version and a FORTRAN version
NCO_TRIANGLE is a MATLAB library defining Newton-Cotes open quadrature rules on a triangle.
NINTLIB is a MATLAB library containing 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 for defining quadrature rules on a variety of intervals with different weight functions.
STROUD is a MATLAB library containing quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TET_MESH is a MATLAB library of routines useful for work with tetrahedral meshes in 3D;
WANDZURA is a MATLAB library of routines for defining Dunavant rules for quadrature on a triangle.
A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.
You can go up one level to the MATLAB source codes.