Graphics Gems V (IBM Version)

II.1

Efficient Computation of Polygon Area and Polyhedron Volume

Allen Van Gelder,     University of California Santa Cruz, California

Introduction

This gem describes new methods to obtain the area of a planar polygon and the volume of a polyhedron, in three-dimensional space. They provide substantial speed-ups (factors ranging from two to sixteen) over previously reported methods. In most cases, the new methods are also easier to program.

Implementers should be familiar with basic vector operations, particularly the cross product ( Foley et al. 1990, Appendix). This gem assumes a right-handed coordinate system; for a left-handed coordinate system, define the cross product to be the negative of its usual definition. Some derivations require ...