Construction of optimal Bézier splines
V. V. Borisenko
Lomonosov Moscow State University
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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Journal of Mathematical Sciences (New York), 2019, 237:3, 375–386
V. V. Borisenko, “Construction of optimal Bézier splines”, Fundam. Prikl. Mat., 21:3 (2016), 57–72; J. Math. Sci., 237:3 (2019), 375–386
Citation in format AMSBIB
\paper Construction of optimal B\'ezier splines
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
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