WADS 2011: Algorithms and Data Structures pp 267-278

# Computing the Fréchet Distance between Folded Polygons

• Atlas F. CookIV
• Anne Driemel
• Sariel Har-Peled
• Jessica Sherette
• Carola Wenk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

## Abstract

Computing the Fréchet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fréchet distance for a class of non-flat surfaces which we call folded polygons. Unfortunately, the original algorithm cannot be extended directly. We present three different methods to adapt it. The first of which is a fixed-parameter tractable algorithm. The second is a polynomial-time approximation algorithm. Finally, we present a restricted class of folded polygons for which we can compute the Fréchet distance in polynomial time.

## Keywords

Computational Geometry Shape Matching Fréchet Distance

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## Authors and Affiliations

• Atlas F. CookIV
• 1
• Anne Driemel
• 1
• Sariel Har-Peled
• 2
• Jessica Sherette
• 3
• Carola Wenk
• 3
1. 1.Department of Information and Computing SciencesUniversity of UtrechtNetherlands
2. 2.Department of Computer ScienceUniversity of IllinoisUSA
3. 3.Department of Computer ScienceUniversity of TexasSan AntonioUSA