## 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 log^{2} 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 log^{2} n). We also give an O(n log n) algorithm which is an application of the recently introduced compact interval tree data structure.

Original language | American English |
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Pages (from-to) | 235-240 |

Number of pages | 6 |

Journal | Computer Graphics Forum |

Volume | 11 |

Issue number | 4 |

DOIs | |

State | Published - Aug 1992 |

## Keywords

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