Refolding Planar Polygons

Iben, Hayley N.; O’Brien, James F.; Demaine, Erik D.

doi:10.1007/s00454-009-9145-7

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Cited by 11 publications

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Convexity-Increasing Morphs of Planar Graphs

Kleist

Klemz

Lubiw

et al. 2018

Graph-Theoretic Concepts in Computer Science

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We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal.To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms. * A preliminary version of this paper appeared in the proceedings of WG 2018 [26].

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