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Algorithmica

, Volume 27, Issue 1, pp 5–20 | Cite as

Topology-Oriented Implementation—An Approach to Robust Geometric Algorithms

  • K. Sugihara
  • M. Iri
  • H. Inagaki
  • T. Imai

Abstract.

This paper presents an approach, called the ``topology-oriented approach,'' to numerically robust geometric algorithms. In this approach, the basic part of the algorithm is described in terms of combinatorial and topological computation primarily; this description guarantees robustness of the algorithm because combinatorial and topological computation is never contaminated with numerical errors. However, this part of the algorithm is usually nondeterministic, the flow of processing containing many alternative branches. Hence, numerical computation is used in order to choose the branch that seems the most promising to lead to the correct answer. The algorithm designed in this way is robust and simple. The basic idea of this approach as well as the basic properties of the resulting algorithms is shown with examples.

Key words. Clipping a convex polyhedron, Line-segment Voronoi diagram, Robust implementation, Topological consistency. 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • K. Sugihara
    • 1
  • M. Iri
    • 2
  • H. Inagaki
    • 3
  • T. Imai
    • 4
  1. 1.Department of Mathematical Engineering and Information Physics, Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.JP
  2. 2.Department of Information and System Engineering, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.JP
  3. 3.Department of Information and Computer Engineering, Toyota National College of Technology, 2-1 Eisei-cho, Toyota-shi, Aichi 471-8525, Japan.JP
  4. 4.Department of Design and Information Sciences, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan.JP

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