In order to develop the theory of B-spline curve

the representation of cubic uniform B-spline curve is extended to a general form based on linear combination of curves. Moreover

some properties of the extended curve are discussed in details. The research shows that the basis of the generalized curve is relative simple

and the extended curve includes the original B-spline curve and shows much better shape-control capability than the original curve. Meanwhile

the extended curve keeps the same degree of original one. It is easy to find that the curve can be reshape by adjusting the shape factor. Also

a new method of the representation of closed curve is given.