Extension of the cubic uniform B-spline curve based on the linear combination of curves
基于曲线线性组合的3次均匀B样条曲线的拓展

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.