The best quintic chebyshev approximation of circular arcs of order ten

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4 Citations (Scopus)


Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree 10 rather than 6; the Chebyshev error function equioscillates 11 times rather than 7; the approximation order is 10 rather than 6. The method approximates more than the full circle with Chebyshev uniform error of 1/29. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.

Original languageEnglish
Pages (from-to)3779-3785
Number of pages7
JournalInternational Journal of Electrical and Computer Engineering
Issue number5
Publication statusPublished - Oct 2019
Externally publishedYes


  • Approximation order
  • Bézier curves
  • CAD
  • Circular arc
  • High accuracy
  • High performance computing
  • Quintic approximation

ASJC Scopus subject areas

  • General Computer Science
  • Electrical and Electronic Engineering


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