Generalized Bezier Curves Based on Bernstein-Stancu-Chlodowsky Type Operators

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 study the nature of degree elevation and degree reduction for Bezier Bernstein-Stancu-Chlodowsky functions with shifted knots for t is an element of [gamma/n+delta, n+gamma/n+delta]. We also present a de Casteljau algorithm to compute Bernstein Bezier curves with shifted knots. The new curves have some properties similar to Bezier curves. Furthermore, some fundamental properties for Bernstein Bezier 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.