Bezier curves and surfaces based on modified Bernstein polynomials

. 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 Bézier curve defined on [0, 1] when we set the parameter α, β to the value 0. We also present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properties similar to Bézier curves. Furthermore, some fundamental properties for Bernstein Bézier curves and surfaces are discussed.