Integrals Inside the Unit Triangle in 2D

**TRIANGLE01_INTEGRALS**
is a MATLAB library 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 GNU LGPL license.

**TRIANGLE01_INTEGRALS** is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

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

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

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

DISK_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

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

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

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

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

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

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

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

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

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

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

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

TRIANGLE_FEKETE_RULE, a MATLAB library which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.

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

TRIANGLE_INTEGRALS, a MATLAB library which returns the exact value of the integral of any polynomial over the interior of an arbitrary triangle in 2D.

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

TRIANGLE_MONTE_CARLO, a MATLAB library 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 MATLAB library which defines Newton-Cotes closed quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a MATLAB library which defines Newton-Cotes open quadrature rules on a triangle.

TRIANGLE_SYMQ_RULE, a MATLAB 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 MATLAB 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_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

- i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
- monomial_value.m, evaluates a monomial.
- r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
- timestamp.m prints the current YMDHMS date as a time stamp.
- triangle01_area.m computes the area of the unit triangle in 2D.
- triangle01_monomial_integral.m, monomial integrals in the interior of the unit triangle in 2D.
- triangle01_sample.m samples points from the interior of the unit triangle in 2D.

- triangle01_integrals_test.m, a sample calling program.
- triangle01_integrals_test01.m, uses TRIANGLE01_SAMPLE to estimate integrals over the interior of the unit triangle in 2D.
- triangle01_integrals_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.