Faster ASV Decomposition for Orthogonal Polyhedra, Using the Extreme Vertices Model (EVM)

Abstract

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a b-rep into a CSG model, with all its implicit uses and advantages -like form feature recognition, among others. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set - union and set-difference operators. This paper first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T , regardless the structure and internal nodes of T . The importance of this result becomes apparent, for example, with those solid modeling schemes, for which the Exclusive-OR operation can be performed much faster than both the set union and set difference operators. This is the case for the Extreme Vertices Model (EVM) for orthogonal polyhedra. Therefore, this paper is then devoted for applying this result to orthogonal polyhedra, using the Extreme Vertices Model. It also includes a comparision of using this result vs. not-using it when finding the ASV decomposition of orthogonal polyhedra, as well as some practical uses for the ASV decomposition of orthogonal polyhedra.