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Licensed Unlicensed Requires Authentication Published by De Gruyter June 8, 2016

Curvature approximation of circular arcs by low-degree parametric polynomials

  • Boštjan Kovač EMAIL logo and Emil Žagar


In this paper some new methods for curvature approximation of circular arcs by low-degree Bézier curves are presented. Interpolation by geometrically continuous (G1) parametric polynomials is considered. All derived approximants are given explicitly and are therefore practically applicable. Moreover, obtained results indicate that G1 biarcs with at least G1 continuity at the junction have smaller curvature error as parametric polynomial counterparts of the same degree. It is also shown that all considered methods provide optimal asymptotic approximation order.


The authors are very grateful to the anonymous referees for their valuable suggestions which improved the paper.


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Received: 2014-7-2
Revised: 2015-2-24
Accepted: 2015-4-15
Published Online: 2016-6-8
Published in Print: 2016-6-1

© 2016 by Walter de Gruyter Berlin/Boston

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