Construction of Optimal Bézier Splines
- Authors: Borisenko V.V.1
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Affiliations:
- Moscow State University
- Issue: Vol 237, No 3 (2019)
- Pages: 375-386
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/242350
- DOI: https://doi.org/10.1007/s10958-019-04164-6
- ID: 242350
Cite item
Abstract
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.
About the authors
V. V. Borisenko
Moscow State University
Author for correspondence.
Email: vladimir_borisen@mail.ru
Russian Federation, Moscow
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