On the Number of Views of Polyhedral Scenes
It is known that a scene consisting of k convex polyhedra of total complexity n has at most O(n 4 k 2) distinct orthographic views, and that the number of such views is Ω((nk 2+n 2)2) in the most case. The corresponding bounds for perspective views are O(n 6 k 3) and Ω((nk 2+n 2)3), respectively. In this papers, we close these gaps by improving the lower bounds. We construct an example of a scene θ(n 4 k 2) orthographic views, and another with θ(n 6 k 3) 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 distinct views from a viewpoint moving along a straight line.
KeywordsLower Bound Problem Complexity Computer Graphic Algorithm Analysis Discrete Mathematic
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