NCC_TRIANGLE is a C++ library of routines, using double precision arithmetic, which defines the weights and abscisass for a sequence of 9 Newton-Cotes closed quadrature rules for the triangle.
Newton-Cotes rules have the characteristic that the abscissas are equally spaced. For a triangle, this refers to spacing in the unit reference triangle, or in the barycentric coordinate system. These rules may be mapped to an arbitrary triangle, and will still be valid.
The rules are said to be "closed" when they include points on the boundary of the triangle.
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.
(Note that the first rule included in the set is not, strictly speaking, a Newton-Cotes closed rule; it's just the rule that uses a single point at the centroid. However, by including this rule as the first in the set, we have a rule with each polynomial degree of exactness from 0 to 8.)
CLENSHAW_CURTIS is a C++ library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.
DUNAVANT is a C++ library of routines for defining Dunavant rules for quadrature on a triangle.
FEKETE is a C++ library of routines for defining Fekete rules for quadrature or interpolation on a triangle.
FEM_SAMPLE is a C++ library of routines for evaluating a finite element function defined on an order 3 or order 6 triangulation.
FEMPACK is a C++ library of routines for finite element calculations.
GM_RULES is a C++ library of routines for defining a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.
NCC_TETRAHEDRON is a C++ library defining Newton-Cotes closed quadrature rules on a tetrahedron.
NCC_TRIANGLE is also available in a FORTRAN90 version and a MATLAB version
NCO_TETRAHEDRON is a C++ library defining Newton-Cotes open quadrature rules on a tetrahedron.
NCO_TRIANGLE is a C++ library defining Newton-Cotes open quadrature rules on a triangle.
NINT_EXACTNESS_TRI is an executable C++ program which investigates the polynomial exactness of a quadrature rule for the triangle.
NINTLIB is a FORTRAN90 library containing a variety of routines for numerical estimation of integrals in multiple dimensions.
QUADRULE is a C++ library for defining quadrature rules on a variety of intervals with different weight functions.
STROUD is a C++ library containing quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TEST_TRI_INT is a FORTRAN90 library of functions that can be used to test algorithms for quadrature over a triangle.
TOMS612 is a FORTRAN77 library of routines which can estimate the integral of a function over a triangle.
TOMS706 is a FORTRAN77 library which estimates the integral of a function over a triangulated region.
WANDZURA is a C++ library of routines for defining Wandzura rules for quadrature on a triangle.
One of the tests in the sample calling program creates EPS files of the abscissas in the unit triangle. These have been converted to PNG files for display here.
You can go up one level to the C++ source codes.
