Regular Labelings and Geometric Structures
2016
Three types of geometric structure—grid triangulations, rectangular subdivisions, and orthogonal polyhedra— can each be described combinatorially by a regular la-beling: an assignment of colors and orientations to the edges of an associated maximal or near-maximal planar graph. We briefly survey the connections and analogies between these three kinds of labelings, and their uses in designing efficient geometric algorithms. 1