creative_2010_19_2_191_198_001

Bezier type curves generated by some class of positive linear operators


Ovidiu T. PopDan BărbosuLaurian Pișcoran


Abstract

creative_2010_19_2_191_198_abstract

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creative_2010_19_2_191_198

In this paper, we will consider the Bezier type curves in which the fundamental Bernstein basis will be replaced with other function sequences. For ´ all the applications the graphic representation will be done for the same ordinates of the control points. In the first example, we consider Bezier type ´ curves generated by fundamental Bernstein polynomials and ”classical” nodes xm,k = k m and also with ”changed ” nodes ym,k = p k(k + 1) m , where m = 3 and k ∈ {0, 1, 2, 3}. In the second example, we consider Bezier type curves generated by fundamental Bleimann-Butzer-Hahn ´ polynomials and ”classical ” nodes xm,k = k m + 1 − k and also with ”changed ” nodes ym,k = p (m2 − 1)k m2(m + 1 − k) , where m = 3 and k ∈ {0, 1, 2, 3}. In each example, the ”classical ” and ”changed ” points are ”close”. The obtained curves in each example are plotted in the same figure.

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Author(s)

Bărbosu, Dan, Pișcoran, Laurian, Pop, Ovidiu T