Abstract
We introduce the concept of pre-triangulations, a relaxation of triangulations that goes beyond the frequently used concept of pseudo-triangulations. Pre-triangulations turn out to be more natural than pseudo-triangulations in certain cases. We show that pre-triangulations arise in three different contexts: In the characterization of polygonal complexes that are liftable to three-space in a strong sense, in flip sequences for general polygonal complexes, and as graphs of maximal locally convex functions.
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Research supported by the FWF Joint Research Project ‘Industrial Geometry’ S9205-N12.
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Aichholzer, O., Aurenhammer, F. & Hackl, T. Pre-Triangulations and Liftable Complexes. Discrete Comput Geom 38, 701–725 (2007). https://doi.org/10.1007/s00454-007-9032-z
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DOI: https://doi.org/10.1007/s00454-007-9032-z