Algorithm 550: Solid Polyhedron Measures [Z]

Surface area, centroid, volume, weight, moments, and products of inertia are computed by numerical integration over the bounding surfaces of solid polyhedra.This routine operates directly on geometric definitions consisting of vertex coordinates and face lists, in a format similar to the f o r m a t employed in graphics and in plotting computer programs [1,3,5].Integration is performed through a quadrature rule t h a t is exact for the equations involved. METHODThe several equations, eqs.(1) through (10), to be integrated over the surface of the polyhedra were derived from volume integral forms through application of the Gauss divergence theorem. Pff[xn~+yny+zn~]dS=M(I) mass = P ff[x%]dS CGx = (2) CGy = -~ [ y2ny] dS (3)