On minimal orthographic view covers for polyhedra
Min Liu, Karthik Ramani · 2009
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.