Efficient Computation of Polygon Area and Polyhedron Volume

Publisher Summary This chapter elaborates efficient computation of polygon area and polyhedron volume. It 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. This chapter assumes a right-handed coordinate system; for a left-handed coordinate system, cross product should be defined to be the negative of its usual definition. The most important observation for the formulas to be obtained is that the area is most productively thought of as a vector, particularly if further calculations are to be done with it. This point of view is well known in vector calculus. The chapter also describes two optimization techniques for volume calculations and applies them to obtain further improvements on all polyhedra with four to six faces.