Polygonal Curve Approximation Using Grid Points with Application to a Triangular Mesh Generation with Small Number of Different Edge Lengths

  • Shin-ichi Tanigawa
  • Naoki Katoh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)


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/α 4)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((n 3/α 12)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.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shin-ichi Tanigawa
    • 1
  • Naoki Katoh
    • 1
  1. 1.Department of Architecture and Architectural EngineeringKyoto UniversityKyotoJapan

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