Discrete & Computational Geometry

, Volume 6, Issue 3, pp 485–524 | Cite as

Triangulating a simple polygon in linear time

  • Bernard Chazelle


We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.


Linear Time Tree Decomposition Dual Graph Simple Polygon Polygonal Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • Bernard Chazelle
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA

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