Geodesic
Construction of optimal B\'ezier splines
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 57-72.

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We consider a construction of a smooth curve by a set of interpolation nodes. The curve is constructed as a spline consisting of cubic Bézier curves. We show that if we require the continuity of the first and second derivatives, then such a spline is uniquely defined for any fixed parameterization of Bézier curves. The control points of Bézier curves are calculated as a solution of a system of linear equations with a four-diagonal band matrix. We consider various ways of parameterization of Bézier curves that make up a spline and their influence on its shape. The best spline is computed as a solution of an optimization problem: minimize the integral of the square of the second derivative with a fixed total transit time of a spline. 
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     title = {Construction of optimal {B\'ezier} splines},
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V. V. Borisenko. Construction of optimal B\'ezier splines. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 57-72. http://geodesic.mathdoc.fr/item/FPM_2016_21_3_a3/

[1] A primer on Bézier curves: A free, online book for when you really need to know how to do Bézier things, http://pomax.github.io/bezierinfo/

[2] Bartels R. H., Beatty J. C., Barsky B. A., “Bézier Curves”, An Introduction to Splines for Use in Computer Graphics and Geometric Modelling, Morgan Kaufmann, San Francisco, 1998, 211–245 | MR

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