Flip Algorithm for Segment Triangulations

  • Mathieu Brévilliers
  • Nicolas Chevallier
  • Dominique Schmitt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5162)


Given a set S of disjoint line segments in the plane, which we call sites, a segment triangulation of S is a partition of the convex hull of S into sites, edges, and faces. The set of faces is a maximal set of disjoint triangles such that the vertices of each triangle are on three distinct sites. The segment Delaunay triangulation of S is the segment triangulation of S whose faces are inscribable in circles whose interiors do not intersect S. It is dual to the segment Voronoi diagram. The aim of this paper is to show that any given segment triangulation can be transformed by a finite sequence of local improvements in a segment triangulation that has the same topology as the segment Delaunay triangulation. The main difference with the classical flip algorithm for point set triangulations is that local improvements have to be computed on non convex regions. We overcome this difficulty by using locally convex functions.


Convex Hull Voronoi Diagram Delaunay Triangulation Local Improvement Polyhedral Surface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mathieu Brévilliers
    • 1
  • Nicolas Chevallier
    • 1
  • Dominique Schmitt
    • 1
  1. 1.Laboratoire LMIAUniversité de Haute-AlsaceMulhouse CedexFrance

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