RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2016, Volume 21, Issue 3, Pages 57–72 (Mi fpm1734)

Construction of optimal Bézier splines

V. V. Borisenko

Lomonosov Moscow State University

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.

Full text: PDF file (260 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2019, 237:3, 375–386

UDC: 004.925.86

Citation: 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
\Bibitem{Bor16} \by V.~V.~Borisenko \paper Construction of optimal B\'ezier splines \jour Fundam. Prikl. Mat. \yr 2016 \vol 21 \issue 3 \pages 57--72 \mathnet{http://mi.mathnet.ru/fpm1734} \transl \jour J. Math. Sci. \yr 2019 \vol 237 \issue 3 \pages 375--386 \crossref{https://doi.org/10.1007/s10958-019-04164-6}