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arXiv · 1105.3435

Visibility-preserving convexifications using single-vertex moves

Bernardo M. Abrego·Mario Cetina·Jesus Leanos·Gelasio Salazar
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Abstract

Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one vertex is moved at a time (that is, using {\em single-vertex moves})? We prove the redundancy of the "single-vertex moves" condition: an affirmative answer to (1) implies an affirmative answer to (2). Since Aichholzer et al. recently proved (1), this settles (2).

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Bernardo M. Abrego, Mario Cetina, Jesus Leanos, Gelasio Salazar. 2011-05-17. Visibility-preserving convexifications using single-vertex moves. https://arxiv.org/abs/1105.3435

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