Abstract
In this paper, we use the blending functions of Bernstein-Stancu-Chlodowsky type operators with shifted knots for construction of modified Chlodowsky B\'{e}zier curves. We study the nature of degree elevation and degree reduction for B\'{e}zier Bernstein-Stancu-Chlodowsky functions with shifted knots for $t \in [\frac{\gamma}{n+\delta},\frac{n+\gamma}{n+\delta}]$. We also present a de Casteljau algorithm to compute Bernstein B\'{e}zier curves with shifted knots. The new curves have some properties similar to B\'{e}zier curves. Furthermore, some fundamental properties for Bernstein B\'{e}zier curves are discussed. Our generalizations show more flexibility in taking the value of $\gamma$ and $\delta$ and advantage in shape control of curves. The shape parameters give more convenience for the curve modelling.
Highlights
Kejal Khatri∗ and Vishnu Narayan Mishra abstract: In this paper, we use the blending functions of Bernstein-Stancu-Chlodowsky type operators with shifted knots for construction of modified Chlodowsky Bezier curves
We present a de Casteljau algorithm to compute Bernstein Bezier curves with shifted knots
In computer aided geometric design (CAGD), Bernstein polynomials and its variants are used in order to preserve the shape of the curves or surfaces
Summary
1, if k = n, 0, k = n, clearly both side end point property holds. 4. Reducibility: when γ = δ = 0, bn = 1 formula (2.1) reduces to the classical Bernstein bases on [0, 1]. Proof: All these property can be proved from equation (2.1). We can see that sum of blending fuctions is always unity and satisfies end point interpolation property. Apart from the basic properties above, Bernstein-Stancu-Chlodowsky functions satisfy the following recurrence relations, as for the classical Bernstein basis
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