Article ID Journal Published Year Pages File Type
414839 Computational Geometry 2011 11 Pages PDF
Abstract

In this paper, we introduce a new generalization of the well-known Fréchet distance between two polygonal curves, and provide an efficient algorithm for computing it. The classical Fréchet distance between two polygonal curves corresponds to the maximum distance between two point objects that traverse the curves with arbitrary non-negative speeds. Here, we consider a problem instance in which the speed of traversal along each segment of the curves is restricted to be within a specified range. We provide an efficient algorithm that decides in time whether the Fréchet distance with speed limits between two polygonal curves is at most ε, where n is the number of segments in the curves, and ε⩾0 is an input parameter. We then use our solution to this decision problem to find the exact Fréchet distance with speed limits in O(n2log2n) time.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics