Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
On incremental rendering of silhouette maps of polyhedral scene
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the number of views of translates of a cube and related problems
Computational Geometry: Theory and Applications
On incremental rendering of silhouette maps of a polyhedral scene
Computational Geometry: Theory and Applications
On the complexity of umbra and penumbra
Computational Geometry: Theory and Applications
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It is known that a scene consiing of k convex polyhedra of total complexity n has at most O(n4 k2) distinct orthographic views, and that the number of such views is 驴((nk2 + n2)2) in the worst case. The coresponding bounds for perspective views are O(n6 k3) and 驴((nk2 + n2)3), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with 驴(n6 k2) orthographic views, and another with 驴(n6 k3) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of ditinct views from a viewpoint moving along a staight line.