Derivations of the Solid Angle Subtended at a Point by First- and Sefcond-Order Surfaces and Volumes as a Function of Elliptic Integrals

摘要

An analytic study of the solid angle subtended at a point by8 objects of first and second algebraic order has been made. It is shown that the drived solid angle for all such objects is in the form of a general elliptic integral, which can be written as a lienar combinaion of elliptic itnegrals of the first and third kind and elementary functions. Many common surfaces and volumes have been investigawted, including the conic sections and their volumes of revolution.