Partial Matching between Surfaces Using Fréchet Distance
نویسندگان
چکیده
Computing the Fréchet distance for surfaces is a surprisingly hard problem. It has been shown that it is NP-hard to compute the Fréchet distance between many nice classes of surfaces [God98], [Buc10]. On the other hand, a polynomial time algorithm exists for computing the Fréchet distance between simple polygons [Buc06]. This was the first paper to give an algorithm for computing the Fréchet distance for a nontrivial class of surfaces and remains the only known approach. We consider a partial variant of the Fréchet distance problem, which for given polygons P and Q asks to compute a sub-polygon R ⊆ Q with smallest Fréchet distance to P . This poses various new challenges as the boundary curve of R is not given. We present a polynomial-time algorithm to compute the partial Fréchet distance of two coplanar polygons which is based on the one for simple polygons. We show that the sub-polygon can be computed in polynomial time as well. This is the first algorithm to address a partial Fréchet distance problem for surfaces.
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