Happy endings for flip graphs

Authors:
David Eppstein
Affiliations:
University of California - Irvine, Irvine, CA
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

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Abstract

We show that the triangulations of a finite point set form a flip graph that can be embedded isometrically into a hypercube, if and only if the point set has no empty convex pentagon. Point sets of this type include intersections of lattices with convex sets, points on two lines, and several other infinite families. As a consequence, flip distance in such point sets can be computed efficiently.