Optimal shortest path queries in a simple polygon

Authors:
L. J. Guibas;J. Hershberger
Affiliations:
Computer Science Department, Stanford University, Stanford, CA and DEC Systems Research Center, Palo Alto, CA;Computer Science Department, Stanford University, Stanford, CA and DEC Systems Research Center, Palo Alto, CA
Venue:
SCG '87 Proceedings of the third annual symposium on Computational geometry
Year:
1987

Citing 8
Cited 26

Computational geometry: an introduction

Computational geometry: an introduction
Visibility of disjoint polygons

Algorithmica
Linear time algorithms for visibility and shortest path problems inside simple polygons

SCG '86 Proceedings of the second annual symposium on Computational geometry
Geometric applications of a matrix searching algorithm

SCG '86 Proceedings of the second annual symposium on Computational geometry
Optimal point location in a monotone subdivision

SIAM Journal on Computing
The all-geodesic furthest neighbor problem for simple polygons

SCG '87 Proceedings of the third annual symposium on Computational geometry
Shortest paths in the plane with polygonal obstacles

Journal of the ACM (JACM)
Visibility and intersectin problems in plane geometry

SCG '85 Proceedings of the first annual symposium on Computational geometry

The all-geodesic furthest neighbor problem for simple polygons

SCG '87 Proceedings of the third annual symposium on Computational geometry
Implicitly representing arrangements of lines or segments

SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles

SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An efficient algorithm for link-distance problems

SCG '89 Proceedings of the fifth annual symposium on Computational geometry
On geometric matching

SCG '89 Proceedings of the fifth annual symposium on Computational geometry
On monotone paths among obstacles with applications to planning assemblies

SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Shortest rectilinear paths among weighted obstacles

SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximation algorithms for planar traveling salesman tours and minimum-length triangulations

SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Optimal link path queries in a simple polygon

SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Shortest path queries among weighted obstacles in the rectilinear plane

Proceedings of the eleventh annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces

SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A unified approach to dynamic point location, ray shooting, and shortest paths in planar maps

SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On the all-pairs Euclidean short path problem

Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model

IEEE Transactions on Computers
Efficient multi-agent path planning

Proceedings of the Eurographic workshop on Computer animation and simulation
Separating point sets in polygonal environments

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
k-Server Optimal Task Scheduling Problem with Convex Cost Function

WIOPT '05 Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Power-efficient rate scheduling in wireless links using computational geometric algorithms

Proceedings of the 2006 international conference on Wireless communications and mobile computing
Mutually visible agents in a discrete environment

ACSC '07 Proceedings of the thirtieth Australasian conference on Computer science - Volume 62
On the Complexity of Finding Paths in a Two-Dimensional Domain II: Piecewise Straight-Line Paths

Electronic Notes in Theoretical Computer Science (ENTCS)
Shortest path queries in a simple polygon for 3D virtual museum

ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Two linear-time algorithms for computing the minimum length polygon of a digital contour

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Digital deformable model simulating active contours

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Organization of data in non-convex spatial domains

SSDBM'10 Proceedings of the 22nd international conference on Scientific and statistical database management
Two linear-time algorithms for computing the minimum length polygon of a digital contour

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let P be a simple polygon with n sides. This paper shows how to preprocess the polygon so that, given two query points p and q inside P, the length of the shortest path inside the polygon from p to q can be found in time &Ogr;(log n). The path itself must be polygonal and can be extracted in additional time proportional to the number of turns it makes. The preprocessing consists of triangulation plus a linear amount of additional work.