Through heightening the degree of polynomial function

a class of polynomial function of(n+1)degree that containing an adjustable constantparameterλis presented in this paper. They are an extension ofndegree Bernstein basis functions. Properties of this new basis are analyzed

which have symmetry

linear independence

weighting property and nonnegative property when the parameter λis between -2 and 1

based onwhich a(n+1)degree polynomial curvewith a shape parameter λis defined. The curve

to be called λ Bézier curve not only inherits the most properties of n degree Bézier curve

such as endpoints’properties

symmetry

convex hull property

geometric invariability

affine invariance

convex preserving property

variation diminishing property and so on

but also can be adjusted in shape by changing the value of λ without changement of control points. Whenλ=0

the curve degenerates ton2degree BézierCurve. Using tensor product approach

a surfacewith parameterλis constructed

whose properties are similar to the curve’s. At last

examples illustrate themethod of constructing curve is very useful for curve/surface design.