On the Topology of Walkable Environments

Benjamin Burton; Arne Hillebrand; Maarten Löffler; Saul Schleimer; Dylan Thurston; Stephan Tillmann; Wouter van Toll

On the Topology of Walkable Environments

Benjamin Burton, Arne Hillebrand, Maarten Löffler, Saul Schleimer, Dylan Thurston, Stephan Tillmann, Wouter van Toll

Research output: Contribution to conference › Paper › Other research output

Abstract

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.

Original language	English
Pages	66:1-6
Publication status	Published - 2018
Event	34th European Workshop on Computational Geometry - Berlin, Germany Duration: 21 Mar 2018 → 23 Mar 2018

Conference

Conference	34th European Workshop on Computational Geometry
Abbreviated title	EuroCG 2018
Country/Territory	Germany
City	Berlin
Period	21/03/18 → 23/03/18

Cite this

@conference{6395a8804df8411b9849586b44cd9e53,

title = "On the Topology of Walkable Environments",

abstract = "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.",

author = "Benjamin Burton and Arne Hillebrand and Maarten L{\"o}ffler and Saul Schleimer and Dylan Thurston and Stephan Tillmann and {van Toll}, Wouter",

year = "2018",

language = "English",

pages = "66:1--6",

note = "34th European Workshop on Computational Geometry, EuroCG 2018 ; Conference date: 21-03-2018 Through 23-03-2018",

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TY - CONF

T1 - On the Topology of Walkable Environments

AU - Burton, Benjamin

AU - Hillebrand, Arne

AU - Löffler, Maarten

AU - Schleimer, Saul

AU - Thurston, Dylan

AU - Tillmann, Stephan

AU - van Toll, Wouter

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

M3 - Paper

SP - 66:1-6

T2 - 34th European Workshop on Computational Geometry

Y2 - 21 March 2018 through 23 March 2018

ER -

On the Topology of Walkable Environments

Abstract

Conference

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