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WEDGE_INTEGRALS\ Integrals Inside the Unit Wedge in 3D {#wedge_integrals-integrals-inside-the-unit-wedge-in-3d align=”center”} =====================================

WEDGE_INTEGRALS is a C++ 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

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

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.

Related Data and Programs: {#related-data-and-programs align=”center”}

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

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

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

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

HYPERBALL_INTEGRALS, a C++ 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 C++ 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 C++ 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 C++ library which returns the exact value of the integral of any monomial over the unit line segment in 1D.

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

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

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

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

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

TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

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

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

WEDGE_GRID, a C++ library which computes a grid of points over the interior of the unit wedge in 3D.

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

Source Code: {#source-code align=”center”}

• wedge_integrals.cpp, the source code.
• wedge_integrals.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• wedge_integrals_prb.cpp, a sample calling program.
• wedge_integrals_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WEDGE01_INTEGRAL returns the integral of a monomial in the unit wedge in 3D.
• WEDGE01_SAMPLE samples points uniformly from the unit wedge in 3D.
• WEDGE01_VOLUME returns the volume of the unit wedge in 3D.

You can go up one level to the C++ source codes.

Last revised on 21 August 2014.