Geodesic
Construction of optimal Bézier splines
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 57-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{FPM_2016_21_3_a3,
     author = {V. V. Borisenko},
     title = {Construction of optimal {B\'ezier} splines},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {57--72},
     year = {2016},
     volume = {21},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_3_a3/}
}
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V. V. Borisenko. Construction of optimal Bézier splines. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 57-72. http://geodesic.mathdoc.fr/item/FPM_2016_21_3_a3/

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