triangle01_integrals

triangle01_integrals, an Octave 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^e2
      

Licensing:

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

Languages:

triangle01_integrals 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:

triangle01_integrals_test

ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2d.

cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk01_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hexagon_integrals, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.

hypersphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.

line_integrals, an Octave code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

polygon_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

square_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.

tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

Source Code:

• i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
• monomial_value.m, evaluates a monomial.
• 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.