An Efficient Adaptive Algorithm for Constructing the Convex Differences Tree of a Simple Polygon

Ari Rappoport*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageAmerican English
Pages (from-to)235-240
Number of pages6
JournalComputer Graphics Forum
Volume11
Issue number4
DOIs
StatePublished - Aug 1992

Keywords

  • Computational geometry
  • adaptive algorithms
  • convex differences tree (CDT)
  • convexity
  • polygon

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