Abstract
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 language | English |
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Pages (from-to) | 1621-1653 |
Number of pages | 33 |
Journal | SIAM Journal on Computing |
Volume | 32 |
Issue number | 6 |
DOIs | |
Publication status | Published - Sept 2003 |
Keywords
- Constrained regular complex
- Flip distance
- Locally convex function
- Polytope representation
- Pseudotriangulation
- Surface realization
ASJC Scopus subject areas
- Computer Science(all)
- Mathematics(all)