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SPHERE_INTEGRALS\ Integrals On the Surface of the Unit Sphere in 3D {#sphere_integrals-integrals-on-the-surface-of-the-unit-sphere-in-3d align=”center”} =================================================


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

The surface of the unit sphere in 3D is defined by

        x^2 + y^2 + z^2 = 1

The integrands are all of the form

        f(x,y,z) = x^a y^b z^c

where the exponents are nonnegative integers. If any exponent is an odd integer, the integral will be zero. Thus, the “interesting” results occur when all exponents are even.

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”}

SPHERE_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 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 surface 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 length of the unit line 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_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate the integral of a function 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_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

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

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

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

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


Last revised on 06 January 2014.