English

Visibility-preserving convexifications using single-vertex moves

Computational Geometry 2011-05-18 v1 Robotics Combinatorics

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).

Keywords

Cite

@article{arxiv.1105.3435,
  title  = {Visibility-preserving convexifications using single-vertex moves},
  author = {Bernardo M. Abrego and Mario Cetina and Jesus Leanos and Gelasio Salazar},
  journal= {arXiv preprint arXiv:1105.3435},
  year   = {2011}
}
R2 v1 2026-06-21T18:08:40.448Z