**triangle01_integrals**,
a FORTRAN90 code which
returns the exact value of the integral of any monomial
over the interior of the unit triangle in 2D.

The interior of the unit triangle in 2D is defined by

0 <= x 0 <= y x + y <= 1

The integrands are all of the form

f(x,y) = x^e1 * y^e2where the exponents are nonnegative integers.

The computer code and data files described and made available on this web page are distributed under the MIT license

**triangle01_integrals** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

BALL_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2D.

CUBE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

DISK01_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.

HYPERCUBE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

HYPERSPHERE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

LINE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

POLYGON_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

SIMPLEX_GM_RULE, a FORTRAN90 code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.

SIMPLEX_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

SPHERE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

SQUARE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

TETRAHEDRON_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a FORTRAN90 code which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_FEKETE, a FORTRAN90 code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a FORTRAN90 code which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_SYMQ_RULE, a FORTRAN90 code 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 FORTRAN90 code which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2D.

TRIANGLE01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

- triangle01_integrals.f90, the source code.
- triangle01_integrals.sh, compiles the source code.