Fréchet Distance Problems in Weighted Regions

Details Fréchet Distance Problems in Weighted Regions Fréchet Distance Problems in Weighted Regions

2010-04-27

arxiv.org/abs/1004.4901v1

Computer Science

Computational Geometry

24 pages 6 figures

Scientific paper

We discuss two versions of the Fr\'echet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1+epsilon)-factor approximation of the Fr\'echet distance between two polygonal curves. We also consider the Fr\'echet distance between two polygonal curves among polyhedral obstacles in R^3 and present a (1+epsilon)-factor approximation algorithm.

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