An Efficient Adaptive Algorithm for Constructing the Convex Differences Tree of a Simple Polygon |
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Authors: | Ari Rappoport |
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Affiliation: | Computer Science Department, The Hebrew University, Jerusalem 91904, Israel. Email: . |
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Abstract: | The convex differences tree (CDT) representation of a simple polygon is useful in computer graphics, computer vision, computer aided design and robotics. The root of the tree contains the convex hull of the polygon and there is a child node recursively representing every connectivity component of the set difference between the convex hull and the polygon. We give an O(n log K + K log2 n) time algorithm for constructing the CDT, where n is the number of polygon vertices and K is the number of nodes in the CDT. The algorithm is adaptive to a complexity measure defined on its output while still being worst case efficient. For simply shaped polygons, where K is a constant, the algorithm is linear. In the worst case K = O(n) and the complexity is O(n log2 n). We also give an O(n log n) algorithm which is an application of the recently introduced compact interval tree data structure. |
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Keywords: | Computational geometry adaptive algorithms polygon convexity convex differences tree (CDT) |
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