Numerical Algorithms

, Volume 59, Issue 4, pp 607–622 | Cite as

Polynomial approximation of rational Bézier curves with constraints

  • Stanisław Lewanowicz
  • Paweł Woźny
  • Paweł Keller
Original Paper


We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.


Rational Bézier curve Polynomial approximation Constrained dual Bernstein basis 

AMS 2000 Subject Classifications

Primary 41A10; Secondary 65D17 33D45 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Stanisław Lewanowicz
    • 1
  • Paweł Woźny
    • 1
  • Paweł Keller
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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