Computing the Fréchet distance between simple polygons

Authors:
Kevin Buchin;Maike Buchin;Carola Wenk
Affiliations:
Institute of Computer Science, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany;Institute of Computer Science, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany;Department of Computer Science, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249-0667, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

We present the first polynomial-time algorithm for computing the Frechet distance for a non-trivial class of surfaces: simple polygons, i.e., the area enclosed by closed simple polygonal curves, which may lie in different planes. For this, we show that we can restrict the set of maps realizing the Frechet distance, and develop an algorithm for computing the Frechet distance using the algorithm for curves, techniques for computing shortest paths in a simple polygon, and dynamic programming.