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Approximate implicitization of planar curves by piecewise rational approximation of the distance function

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Abstract

We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve.

The proposed method consists of four main steps: quadratic B-spline approximation of the given parametric curve, data reduction, segments-wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global C r spline function which approximates the distance function, for r = 0, 1.

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Authors and Affiliations

  1. Institute of Applied Geometry, Johannes Kepler University, Linz, Austria

    Mohamed Shalaby & Bert Jüttler

  2. Johannes Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria

    Josef Schicho

Authors
  1. Mohamed Shalaby
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  2. Bert Jüttler
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  3. Josef Schicho
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Correspondence to Josef Schicho.

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Shalaby, M., Jüttler, B. & Schicho, J. Approximate implicitization of planar curves by piecewise rational approximation of the distance function. AAECC 18, 71–89 (2007). https://doi.org/10.1007/s00200-006-0025-6

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  • DOI: https://doi.org/10.1007/s00200-006-0025-6

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