基于曲线线性组合的3次均匀B样条曲线的拓展

摘要

为了丰富和发展B样条曲线理论,利用曲线线性组合的思想,将3次均匀B样条曲线进行了拓展,并讨论了拓展曲线的性质.研究表明,拓展曲线的基具有较简单的表达式;拓展曲线包含了原曲线的基本形式,比原曲线具有更强的描述能力,且保持曲线次数不变.利用曲线的形状因子可以调整曲线的局部形状;同时得到了一种闭曲线表示的新途径.%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.