On the Topology of Walkable Environments
Benjamin Burton, Arne Hillebrand, Maarten Löffler, Saul Schleimer, Dylan Thurston, Stephan Tillmann, Wouter van Toll
In 34th European Workshop on Computational Geometry (EuroCG), pp. 66:1-6, 2018.
Motivated by motion planning applications, we study 2-dimensional surfaces embedded in 3-dimensional space with the property that their vertical projection is an immersion. We provide bounds on the complexity of a triangulation of such a surface, given that the projection of the boundary is a polygon with m segments. We then show how these bounds lead to efficient algorithm to compute such a triangulation. Finally, we relate our result to concrete motion planning setting and review related open questions.
@inproceedings{Burton2018-TopologyWalkableEnvironments,
author = {Burton, B. and Hillebrand, A. and L\"offler, M. and Schleimer, S. and Thurston, D. and Tillmann, S. and {van Toll}, W.},
title = {On the Topology of Walkable Environments},
booktitle = {Proceedings of the 34th European Workshop on Computational Geometry (EuroCG)},
year = {2018},
pages = {66:1-6}
}