On minimal orthographic view covers for polyhedra

Abstract

In this paper, we consider the external visibility coverage for polyhedra under the orthographic viewing model. The problem is to compute whether the whole boundary of a polyhedron is visible from a finite set of view directions, and if so, how to compute a minimal set of such view directions. A global visibility map based method is developed to calculate an optimal or near-optimal solution using object space segmentation and viewpoint space sampling. Our method subdivides the concave regions of a polyhedron into a ground set containing two types of segments: concave regions with nonempty global visibility maps and convex polygons in the concave regions whose global visibility maps are empty. The viewpoint space is sampled using a generate-as-required heuristic. The corresponding visibility matrix is computed based on global visibility calculation. Our problem is then modeled as an instance of the classical set-cover problem and solved using a minimal visible set based branch-and-bound algorithm.