Spiderman graph: Visibility in urban regions

Paz Carmi; Eran Friedman; Matthew J. Katz

doi:10.1016/j.comgeo.2014.10.004

Spiderman graph: Visibility in urban regions

Paz Carmi, Eran Friedman, Matthew J. Katz

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Motivated by the inaccuracy of GPS devices in urban regions, we study the problem of computing the visibility graph of an urban region. Given a scene of buildings, where a building is represented by the set of its walls, the vertices of the graph correspond to the buildings' walls, and there is an edge between two walls if and only if they are weakly visible to each other. We present efficient algorithms for several scenes, including a sophisticated O(ⁿ²^log2n)-time algorithm for a scene consisting of n walls of varying heights parallel to the yz-plane, where visibility is restricted to directions whose projections on the xy-plane are horizontal. This algorithm uses persistent search trees.

Original language	English
Pages (from-to)	251-259
Number of pages	9
Journal	Computational Geometry: Theory and Applications
Volume	48
Issue number	3
DOIs	https://doi.org/10.1016/j.comgeo.2014.10.004
State	Published - 1 Jan 2015

Keywords

Persistent search trees
Visibility graphs
Weak visibility

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2014.10.004

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title = "Spiderman graph: Visibility in urban regions",

abstract = "Motivated by the inaccuracy of GPS devices in urban regions, we study the problem of computing the visibility graph of an urban region. Given a scene of buildings, where a building is represented by the set of its walls, the vertices of the graph correspond to the buildings' walls, and there is an edge between two walls if and only if they are weakly visible to each other. We present efficient algorithms for several scenes, including a sophisticated O(n2log2n)-time algorithm for a scene consisting of n walls of varying heights parallel to the yz-plane, where visibility is restricted to directions whose projections on the xy-plane are horizontal. This algorithm uses persistent search trees.",

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AU - Friedman, Eran

AU - Katz, Matthew J.

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N2 - Motivated by the inaccuracy of GPS devices in urban regions, we study the problem of computing the visibility graph of an urban region. Given a scene of buildings, where a building is represented by the set of its walls, the vertices of the graph correspond to the buildings' walls, and there is an edge between two walls if and only if they are weakly visible to each other. We present efficient algorithms for several scenes, including a sophisticated O(n2log2n)-time algorithm for a scene consisting of n walls of varying heights parallel to the yz-plane, where visibility is restricted to directions whose projections on the xy-plane are horizontal. This algorithm uses persistent search trees.

AB - Motivated by the inaccuracy of GPS devices in urban regions, we study the problem of computing the visibility graph of an urban region. Given a scene of buildings, where a building is represented by the set of its walls, the vertices of the graph correspond to the buildings' walls, and there is an edge between two walls if and only if they are weakly visible to each other. We present efficient algorithms for several scenes, including a sophisticated O(n2log2n)-time algorithm for a scene consisting of n walls of varying heights parallel to the yz-plane, where visibility is restricted to directions whose projections on the xy-plane are horizontal. This algorithm uses persistent search trees.

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JO - Computational Geometry: Theory and Applications

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IS - 3

ER -

Spiderman graph: Visibility in urban regions

Abstract

Keywords

ASJC Scopus subject areas

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