Abstract

We study several known volume computation algorithms for convex d-polytopes by classifying them into two classes, triangulation methods and signed-decomposition methods. By incorporating the detection of simplicial faces and a storing/reusing scheme for face volumes we propose practical and theoretical improvements for two of the algorithms. Finally we present a hybrid method combining advantages from the two algorithmic classes. The behaviour of the algorithms is theoretically analysed for hypercubes and practically tested on a wide range of polytopes, where the new hybrid method proves to be superior. 1 Introduction A convex polytope P is the convex hull conv(V ) of a finite set V = fv 1 ; v 2 ; : : : ; vn g of points in R d . Equivalently, it is a bounded subset of R d which is the intersection of a finite set of half spaces. We shall omit `convex' since we only deal with such polytopes, and use d-polytope to mean a d-dimensional polytope. When P = conv(V ), V is called ...

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