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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1734
  • http://mi.mathnet.ru/eng/fpm/v21/i3/p57

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Фундаментальная и прикладная математика
    Number of views:
    This page:173
    Full text:71
    References:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020