Visibility, occlusion, and the aspect graph

Abstract

This chapter studies the ways in which the topology of the image of a polyhedron changes with changing viewpoint. We catalog the ways that the topological appearance, or aspect, can change. This enables us to find maximal regions of viewpoints of the same aspect. We use these techniques to construct the viewpoint space partition (VSP), a partition of viewpoint space into maximal regions of constant aspect, and its dual, the aspect graph. Here, we present tight bounds on the maximum size of the VSP and the aspect graph and give algorithms for their construction, first in the convex case and then in the general case. In particular, we give bounds on the maximum size of θ(n 2) and θ(n 6) under an orthographic projection viewing model and of θ(n 3) and θ(n 9) under a perspective viewing model. The algorithms make use of a new representation of the appearance of polyhedra from all viewpoints, called the aspect representation or asp. We believe that this representation is one of the significant contributions of this paper.