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Reviewed by José-Javier Martínez

By Mr (review D (q and Sánchez-reyes J. (e-clmin-mae


Simple determination via complex arithmetic of geometric characteristics of Bézier conics. (English summary) Comput. Aided Geom. Design 28 (2011), no. 6, 345–348. This short paper is devoted to showing how to compute in a simple way the geometric characteristics of conics expressed in rational Bézier form. A useful introduction presents the approach being used, including references to previous approaches to the problem. The successful idea is to represent conics in the complex plane, where points can be not only added, but also multiplied and divided, and square roots are meaningful. Using this idea, in Section 2 the author characterizes the focus of a conic in a simple form by using complex products. The result of Section 2 leads in Section 3 to the computation of the foci, the center and the linear eccentricity of a Bézier conic. As stated in Section 4 (devoted to conclusions), this work is an example of how “[c]omplex analysis is a powerful and elegant tool that, although restricted to the planar case, facilitates the construction and analysis of curves in CAGD”. To make the advantages of this approach mor

Year: 2013
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