# triangle_symq_rule

triangle_symq_rule, a C++ code which returns symmetric quadrature rules, with exactness up to total degree 50, over the interior of a triangle, by Hong Xiao and Zydrunas Gimbutas.

The original source code, from which this library was developed, is available from the Courant Mathematics and Computing Laboratory, at https://www.cims.nyu.edu/cmcl/quadratures/quadratures.html ,

### Languages:

triangle_symq_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

simplex_gm_rule, a C++ code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

triangle_analyze, a C++ code 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++ code which defines a Dunavant rule for quadrature over the interior of a triangle in 2D.

triangle_fekete_rule, a C++ code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.

triangle_felippa_rule, a C++ code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.

triangle_integrals, a C++ code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

triangle_lyness_rule, a C++ code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2D.

triangle_monte_carlo, a C++ code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit triangle in 2D.

triangle_ncc_rule, a C++ code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

triangle_nco_rule, a C++ code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

triangle_wandzura_rule, a C++ code which returns a Wandzura quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of the triangle in 2D.

triangle_witherden_rule, a C++ code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.

### Reference:

1. Hong Xiao, Zydrunas Gimbutas,
A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions,
Computers and Mathematics with Applications,
Volume 59, 2010, pages 663-676.

### Source Code:

Last revised on 11 June 2023.