多形状参数的指数均匀B样条曲线曲面

Exponential Uniform B-Spline Curves and Surfaces with Multiple Shape Parameters

论文构造了一类带多个形状参数的指数均匀B样条曲线曲面,它保持了指数均匀B样条曲线曲面的主要性质(如连续性、凸包性等)。此类曲线在不改变控制顶点的情况下,通过改变其形状参数的取值,可以生成多条逼近于控制多边形的曲线,进而实现对曲线的整体或局部调控。此外,它还可以精确表示双曲线、悬链线等超越曲线。此类曲面是通过张量积的方法生成的,所以具有与曲线类似的性质。论文结尾给出了大量数值实例。

A class of exponential uniform B-spline curves and surfaces with multiple shape parameters is provided.They preserve the main properties of the exponential uniform B-spline curves and surfaces,such as positive property,convexity-preserving property and so on.The curves can be adjusted by changing the values of shape parameters without moving their control points.So we can realize the entire or local adjustment of the curves.What’s more,the exponential uniform B-spline curves can represent hyperbola,catenary and other transcendental curves precisely.The corresponding surfaces can be constructed by using tensor product,so their properties are similar to that of the curves.Plenty of numerical tests are given to show the effectiveness of our method.