TRIANGLE_LYNESS_RULE is a C++ library which produces the Lyness-Jespersen family of quadrature rules over the interior of a triangle in 2D.
The rules have the following orders (number of points) and precisions (maximum degree of polynomials whose integrals they can compute exactly):
Rule | Order | Precision |
---|---|---|
0 | 1 | 1 |
1 | 3 | 2 |
2 | 4 | 2 |
3 | 4 | 3 |
4 | 7 | 3 |
5 | 6 | 4 |
6 | 10 | 4 |
7 | 9 | 4 |
8 | 7 | 5 |
9 | 10 | 5 |
10 | 12 | 6 |
11 | 16 | 6 |
12 | 13 | 6 |
13 | 13 | 7 |
14 | 16 | 7 |
15 | 16 | 8 |
16 | 21 | 8 |
17 | 16 | 8 |
18 | 19 | 9 |
19 | 22 | 9 |
20 | 27 | 11 |
21 | 28 | 11 |
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
TRIANGLE_LYNESS_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
ANNULUS_RULE, a C++ library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
CUBE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
PYRAMID_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
SIMPLEX_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.
SQUARE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a C++ library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.
TETRAHEDRON_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_ANALYZE, a C++ program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
TRIANGLE_DUNAVANT_RULE, a C++ library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.
TRIANGLE_EXACTNESS, a C++ program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
TRIANGLE_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
TRIANGLE_NCC_RULE, a C++ library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_NCO_RULE, a C++ library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_SYMQ_RULE, a C++ library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
TRIANGLE_WANDZURA_RULE, a C++ library which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a C++ library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.
You can go up one level to the FORTRAN90 source codes.