Pseudotriangulations from surfaces and a novel type of edge flip

Oswin Aichholzer*, Franz Aurenhammer, Hannes Krasser, Peter Brass

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

Original languageEnglish
Pages (from-to)1621-1653
Number of pages33
JournalSIAM Journal on Computing
Issue number6
Publication statusPublished - Sep 2003


  • Constrained regular complex
  • Flip distance
  • Locally convex function
  • Polytope representation
  • Pseudotriangulation
  • Surface realization

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)


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