Tetrahedrizing point sets in three dimensions

  • H. Edelsbrunner
  • F. P. Preparata
  • D. B. West
Computational Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)


This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in O(nlog n) time constructs a tetrahedrization of a set of n points consisting of at most 3n–11 tetrahedra.


Computational geometry tetrahedrization Delaunay tetrahedrization time-optimal algorithms combinatorial geometry extremum problems Euler's formula 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • H. Edelsbrunner
    • 1
  • F. P. Preparata
    • 2
  • D. B. West
    • 3
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Coordinated Science Lab. and Departments of Electrical & Computer Engineering and of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Coordinated Science Lab. and Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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