A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves
Applied and Computational Mathematics
Volume 5, Issue 2, April 2016, Pages: 40-45
Received: Feb. 18, 2016; Accepted: Feb. 26, 2016; Published: Mar. 9, 2016
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Authors
Zhi Liu, School of Mathematics, Hefei University of Technology, Hefei, China
Na Wei, School of Mathematics, Hefei University of Technology, Hefei, China
Jieqing Tan, School of Mathematics, Hefei University of Technology, Hefei, China
Xiaoyan Liu, Department of Mathematics, University of La Verne, La Verne, USA
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Abstract
A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous quartic Bézier approximation methods. A quartic G2-continuous spline approximation of conic sections is obtained by using the subdivision scheme at the shoulder point of the conic section.
Keywords
Conic Section, Quartic Bézier Curve, Hausdorff Distance, Approximation, G2-Continuous, Subdivision Scheme
To cite this article
Zhi Liu, Na Wei, Jieqing Tan, Xiaoyan Liu, A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves, Applied and Computational Mathematics. Vol. 5, No. 2, 2016, pp. 40-45. doi: 10.11648/j.acm.20160502.11
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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