Mediterranean Journal of Mathematics

, Volume 8, Issue 3, pp 369–381

Approximation of a Continuous Curve by its Bernstein-Bézier Operator


DOI: 10.1007/s00009-010-0094-4

Cite this article as:
Tachev, G.T. Mediterr. J. Math. (2011) 8: 369. doi:10.1007/s00009-010-0094-4


In this paper we consider integer and rational parametric Bézier curves and study the distance between the curve and its control polygon. To measure the distance we use first and second order moduli of smoothness of vector-valued function. We consider also NURBS curves with equidistant knots. Some direct approximation theorems will be presented.

Mathematics Subject Classification (2010)

Primary 65D07 65D17 Secondary 41A15 41A25 41A28 41A36 41A63 


Integer and rational Bézier curves NURBS curves control polygon approximation degree moduli of continuity 

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Architecture, Civil Engineering and GeodesySofiaBulgaria

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