Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Near-Linear Time Approximation Algorithms for Curve Simplification
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Triangulating a convex polygon with small number of non-standard bars
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Polyline fitting of planar points under min-sum criteria
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
PACE: polygonal approximation of thick digital curves using cellular envelope
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
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For a given x-monotone polygonal curve each of whose edge lengths is between $\underline{l}$ and $2\underline{l}$, we consider the problem of approximating it by another x-monotone polygonal curve using points of a square grid so that there exists a small number of different edge lengths and every edge length is between $\underline{l}$ and $\beta \underline{l}$, where β is a given parameter satisfying 1≤β≤2. Our first algorithm computes an approximate polygonal curve using fixed square grid points in O((n/α4)log(n/α)) time. Based on this, our second algorithm finds an approximate polygonal curve as well as an optimal grid placement simultaneously in O((n3/α12)log2(n/α)) time, where α is a parameter that controls the closeness of approximation. Based on the approximate polygonal curve, we shall give an algorithm for finding a uniform triangular mesh for an x-monotone polygon with a constant number of different edge lengths.