, Volume 15, Issue 3, pp 223–241 | Cite as

Incremental topological flipping works for regular triangulations

  • H. Edelsbrunner
  • N. R. Shah


A set ofn weighted points in general position in ℝ d defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at mostO(nlogn+n[d/2]). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor logn more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm.

Key words

Geometric algorithms Grid generation Regular and Delaunay triangulations Flipping Topological order Point location Incremental Randomized 


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Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • H. Edelsbrunner
    • 1
  • N. R. Shah
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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