Vertex Deletion for 3D Delaunay Triangulations

  • Kevin Buchin
  • Olivier Devillers
  • Wolfgang Mulzer
  • Okke Schrijvers
  • Jonathan Shewchuk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


We show how to delete a vertex q from a three-dimensional Delaunay triangulation DT(S) in expected O(C  ⊗ (P)) time, where P is the set of vertices neighboring q in DT(S) and C  ⊗ (P) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created during the randomized incremental construction of DT(P). Experiments show that our approach is significantly faster than existing implementations if q has high degree, and competitive if q has low degree.


Point Location Voronoi Diagram Delaunay Triangulation Binary Search Tree Incremental Construction 
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 Berlin Heidelberg 2013

Authors and Affiliations

  • Kevin Buchin
    • 1
  • Olivier Devillers
    • 2
  • Wolfgang Mulzer
    • 3
  • Okke Schrijvers
    • 4
  • Jonathan Shewchuk
    • 5
  1. 1.Technical University EindhovenThe Netherlands
  2. 2.INRIA Sophia Antipolis - MéditerranéeFrance
  3. 3.Freie Universität BerlinGermany
  4. 4.Stanford UniversityUSA
  5. 5.University of California at BerkeleyUSA

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