3 research outputs found
Bezier curves and surfaces based on modified Bernstein polynomials
In this paper, we use the blending functions of Bernstein polynomials with
shifted knots for construction of Bezier curves and surfaces. We study the
nature of degree elevation and degree reduction for Bezier Bernstein functions
with shifted knots.
Parametric curves are represented using these modified Bernstein basis and
the concept of total positivity is applied to investigate the shape properties
of the curve. We get Bezier curve defined on [0, 1] when we set the parameter
\alpha=\beta to the value 0. We also present a de Casteljau algorithm to
compute Bernstein Bezier curves and surfaces with shifted knots. The new curves
have some properties similar to Bezier curves. Furthermore, some fundamental
properties for Bernstein Bezier curves and surfaces are discussed.Comment: 11 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1507.0411
Approximation by a Kantorovich type q-Bernstein-Stancu operators
In this paper, we introduce a Kantorovich type generalization of
q-Bernstein-Stancu operators. We study the convergence of the introduced
operators and also obtain the rate of convergence by these operators in terms
of the modulus of continuity. Further, we study local approximation property
and Voronovskaja type theorem for the said operators. We show comparisons and
some illustrative graphics for the convergence of operators to a certain
function.Comment: 14 pages, submitte
Approximation Of Function By Baskakov Durrmeyer Type Operators
In the present note, we give the generalization of Baskakov
Durrmeyer operators depending on a real parameter > 0. We present the
approximation results in Korovkin and weighted Korovkin spaces. We also prove
the order of approximation, rate of approximation for these operators. In the
end, we verify our results with the help of numerical examples by using
Mathematica.Comment: 12 pages, 6 figure