Face traverses and a volume algorithm for polyhedra

Abstract

Face traverses for triangular polyhedra arise in computing the volume of a polyhedron with given vertices. More general volume problems can often be reduced to such a calculation. For triangular polyhedra the expression for volume can be considerably simplified if a face traverse is known. We provide an example which shows that not every triangular polyhedron has a face traverse. In many applications however, a face traverse is readily available. We give an algorithm for computation of the volume of a triangular polyhedron in terms of the vertices, utilizing a traverse of the faces.