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Abedallah M. Rababah
United Arab Emirates University
Computer Science & IT Electrical & Electronics Engineering

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The best quintic Chebyshev approximation of circular arcs of order ten Abedallah M. Rababah
International Journal of Electrical and Computer Engineering (IJECE) Vol 9, No 5: October 2019
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (352.223 KB) | DOI: 10.11591/ijece.v9i5.pp3779-3785

Abstract

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  $1/2^{9}$. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.
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