Geometry

Volume of General Spherical Wedges

Authors: Richard J. Mathar
Comments: 26 pages, including 13 pages of a C++ listing.

A sphere cap is constructed by slicing a sphere with a plane. Slicing a sphere cap again with a second plane splits it into a pair of spherical wedges.This work evaluates spherical wedge volumes, i.e., the triple integrals over essentially the intersection of the two sphere caps established by the two cut planes. The integrals are closed forms of square roots and inverse sines as a function of sphere radius, heights of the sphere caps, and dihedral angle between the cut planes.
Category: Geometry