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- W1882189295 abstract "Given a curve f and a surface S, how hard is it to find a simple curve f' in S that is the most similar to f? We introduce and study this simple curve embedding problem for piecewise linear curves and surfaces in R^2 and R^3, under Hausdorff distance, weak Frechet distance, and Frechet distance as similarity measures for curves. Surprisingly, while several variants of the problem turn out to have polynomial-time solutions, we show that in R^3 the simple curve embedding problem is NP-hard under Frechet distance even if S is a plane, as well as under weak Frechet distance if S is a terrain. Additionally, these results give insight into the difficulty of computing the Frechet distance between surfaces, and they imply that the partial Frechet distance between non-planar surfaces is NP-hard as well." @default.
- W1882189295 created "2016-06-24" @default.
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- W1882189295 date "2013-03-04" @default.
- W1882189295 modified "2023-09-27" @default.
- W1882189295 title "Simple Curve Embedding" @default.
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