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

Mohamed Shalaby, Bert Jüttler, Josef Schicho*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)71-89
Number of pages19
JournalApplicable Algebra in Engineering, Communications and Computing
Volume18
Issue number1-2
DOIs
StatePublished - Feb 2007
Externally publishedYes

Keywords

  • Approximate implicitization
  • Distance function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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