  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.
