Generalized B\'{e}zier curves based on Bernstein-Stancu-Chlodowsky type operators

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.