triangle01_integrals

triangle01_integrals, a MATLAB 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 information on this web page is 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:

matlab_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

triangle01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit triangle in 2d.

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.