Simplifying 3D Polygonal Chains Under the Discrete Fréchet Distance

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Abstract

A well-known measure to characterize the similarity of two polygonal chains is the famous Fréchet distance. In this paper, for the first time, we consider the problem of simplifying 3D polygonal chains under the discrete Fréchet distance. We present efficient polynomial time algorithms for simplifying a single chain, including the first near-linear O(nlogn) time exact algorithm for the continuous min-# fitting problem. Our algorithms generalize to any fixed dimension d > 3. Motivated by the ridge-based model simplification we also consider simplifying a pair of chains simultaneously and we show that one version of the general problem is NP-complete.