A deated polygon is a polygon with no visibility cross- ings. We answer a question posed by Devadoss et al. (2012) by presenting a polygon that cannot be deformed via continuous visibility-decreasing motion into a deated polygon. In order to demonstrate non- deatability, we use a new combinatorial structure for polygons, the directed dual, which encodes the visibility properties of deated polygons. We also show that any two deated polygons with the same directed dual can be deformed, one into the other, through a visibility- preserving deformation.

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Conference 24th Canadian Conference on Computational Geometry, CCCG 2012
Citation
Bose, P, Dujmović, V, Hoda, N. (Nima), & Morin, P. (2012). Visibility-monotonic polygon deation. Presented at the 24th Canadian Conference on Computational Geometry, CCCG 2012.