Computing the union of 3-colored triangles

  • Jean-Daniel Boissonnat
  • Olivier Devillers
  • Franco P. Preparata
II Mathematical Programming II.1 Computational Geometry
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


Given is a set S of n points, each colored with one of k≥3 colours. We say that a triangle defined by three points of S is 3-colored if its vertices have distinct colours. We prove in this paper that the problem of constructing the boundary of the union T(S) of all such 3-colored triangles can be done in optimal O(n log n) time.


Convex hull Legged robot Motion planning Stability 


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  1. [1]
    J.D. Boissonnat and O. Devillers. Motion Planning of Legged Robots. Technical Report, Institut National de Recherche en Informatique et Automatique, (France), 1991. In preparation.Google Scholar
  2. [2]
    F.P. Preparata and M.I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, 1985.Google Scholar
  3. [3]
    R. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1:132–133, 1972.zbMATHCrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Jean-Daniel Boissonnat
    • 1
  • Olivier Devillers
    • 1
  • Franco P. Preparata
    • 2
  1. 1.INRIAValbonne cedexFrance
  2. 2.Department of Computer ScienceBrown UniversityProvidenceUSA

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