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Approximation of a Continuous Curve by its Bernstein-Bézier Operator

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, BG-1426, Sofia, Bulgaria

    Gancho T. Tachev

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  1. Gancho T. Tachev
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Correspondence to Gancho T. Tachev.

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Tachev, G.T. Approximation of a Continuous Curve by its Bernstein-Bézier Operator. Mediterr. J. Math. 8, 369–381 (2011). https://doi.org/10.1007/s00009-010-0094-4

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  • DOI: https://doi.org/10.1007/s00009-010-0094-4

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