A recursive Taylor method for algebraic curves and surfaces

Shou, Huahao, Martin, Ralph Robert, Wang, Guojin, Bowyer, Adrian and Voiculescu, Irina 2005. A recursive Taylor method for algebraic curves and surfaces. Dokken, Tor and Juttler, Bert, eds. Computational Methods for Algebraic Spline Surfaces, Berlin Heidelberg: Springer Verlag, pp. 135-154. (10.1007/3-540-27157-0_10)

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Abstract

This paper examines recursive Taylor methods for multivariate polynomial evaluation over an interval, in the context of algebraic curve and surface plotting as a particular application representative of similar problems in CAGD. The modified affine arithmetic method (MAA), previously shown to be one of the best methods for polynomial evaluation over an interval, is used as a benchmark; experimental results show that a second order recursive Taylor method (i) achieves the same or better graphical quality compared to MAA when used for plotting, and (ii) needs fewer arithmetic operations in many cases. Furthermore, this method is simple and very easy to implement. We also consider which order of Taylor method is best to use, and propose that second order Taylor expansion is generally best. Finally, we briefly examine theoretically the relation between the Taylor method and the MAA method.

Item Type:	Book Section
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Additional Information:	PDF uploaded in accordance with publisher's policy http://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124 [accessed 27/01/2015] The final publication is available at Springer via http://dx.doi.org/10.1007/3-540-27157-0_10
Publisher:	Springer Verlag
ISBN:	3540232745
Last Modified:	29 Nov 2024 09:00
URI:	https://orca.cardiff.ac.uk/id/eprint/31774

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