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Proceedings of the American Mathematical Society

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Taylor theorem for planar curves

Author: Abedallah Rababah
Journal: Proc. Amer. Math. Soc. 119 (1993), 803-810
MSC: Primary 41A58; Secondary 41A10
MathSciNet review: 1151815
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Abstract: We describe an approximation method for planar curves that significantly improves the standard rate obtained by local Taylor approximations. The method exploits the freedom in the choice of the parametrization and achieves the order $ 4m/3$ where $ m$ is the degree of the approximating polynomial parametrization. Moreover, we show for a particular set of curves that the optimal rate $ 2m$ is possible.

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Keywords: Taylor polynomial, planar curves, approximation order, computer aided geometric design
Article copyright: © Copyright 1993 American Mathematical Society