Discrete & Computational Geometry

, Volume 6, Issue 3, pp 485–524

Triangulating a simple polygon in linear time

  • Bernard Chazelle

DOI: 10.1007/BF02574703

Cite this article as:
Chazelle, B. Discrete Comput Geom (1991) 6: 485. doi:10.1007/BF02574703


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.

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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