Computing the Fréchet Distance between Folded Polygons
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.
KeywordsComputational Geometry Shape Matching Fréchet Distance
Unable to display preview. Download preview PDF.
- 2.Godau, M.: On the complexity of measuring the similarity between geometric objects in higher dimensions. PhD thesis. Freie Universität Berlin, Germany (1998)Google Scholar
- 5.Buchin, K., Buchin, M., Wenk, C.: Computing the Fréchet distance between simple polygons in polynomial time. In: 22nd Symposium on Computational Geometry (SoCG), pp. 80–87 (2006)Google Scholar
- 6.Basu, S., Pollack, R., Roy, M.F.: Algorithms in real algebraic geometry. Algorithms and Computation in Mathematics (2006)Google Scholar