Integrals Inside the Unit Wedge in 3D

**WEDGE_INTEGRALS**
is a MATLAB library which
returns the exact value of the integral of any monomial x^i y^j z^k
over the interior of the unit wedge in 3D.

The interior of the unit wedge in 3D is defined by the constraints:

0 <= X 0 <= Y X + Y <= 1 -1 <= Z <= +1

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

**WEDGE_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 circumference 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 unit line segment 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_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_EXACTNESS, a MATLAB program which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

WEDGE_FELIPPA_RULE, a MATLAB library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

WEDGE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- 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.
- wedge01_monomial_integral.m, returns the integral of a monomial in the unit wedge in 3D.
- wedge01_sample.m, samples points uniformly from the unit wedge in 3D.
- wedge01_volume.m, returns the volume of the unit wedge in 3D.

- wedge_integrals_test.m, a sample calling program.
- wedge_integrals_test01.m, compares exact integrals to Monte Carlo estimates.
- wedge_integrals_test_output.txt, the output file.

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