Go with the flow: the direction-based fréchet distance of polygonal curves

Authors:
Mark de Berg;Atlas F. Cook, IV
Affiliations:
Department of Computing Science, TU Eindhoven, The Netherlands;Department of Computing Science, TU Eindhoven, The Netherlands
Venue:
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Year:
2011

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Abstract

We introduce a new distance measure for directed curves in Rd, called the direction-based Fréchet distance. Like the standard Fréchet distance, this measure optimizes over all parameterizations for a pair of curves. Unlike the Fréchet distance, it is based on differences between the directions of movement along the curves, rather than on positional differences. Hence, the direction-based Fréchet distance is invariant under translations and scalings. We describe efficient algorithms to compute several variants of the direction-based Fréchet distance, and we present an applet that can be used to compare the direction-based Fréchet distance with the traditional Fréchet distance.