TY - JOUR
T1 - Spiderman graph
T2 - Visibility in urban regions
AU - Carmi, Paz
AU - Friedman, Eran
AU - Katz, Matthew J.
N1 - Funding Information:
Work by P. Carmi was partially supported by grant 680/11 from the Israel Science Foundation . Work by E. Friedman was partially supported by the Lynn and William Frankel Center for Computer Sciences . Work by M. Katz was partially supported by grant 1045/10 from the Israel Science Foundation . Work by M. Katz and P. Carmi was partially supported by grant 2010074 from the United States–Israel Binational Science Foundation .
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/1/1
Y1 - 2015/1/1
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.
KW - Persistent search trees
KW - Visibility graphs
KW - Weak visibility
UR - http://www.scopus.com/inward/record.url?scp=84908402101&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2014.10.004
DO - 10.1016/j.comgeo.2014.10.004
M3 - Article
AN - SCOPUS:84908402101
SN - 0925-7721
VL - 48
SP - 251
EP - 259
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3
ER -