中文摘要：

为了使曲线曲面可以在相对简单的条件下实现较高阶的光滑拼接,同时使曲线曲面的形状在不改变控制顶点的情况下自由调整,构造了一组带5个参数的有理多项式函数.基于该组函数,分别采用与3次Bezier曲线、曲面相同的定义方式,定义了由4个控制顶点确定的新曲线、16个控制顶点确定的新曲面,并讨论了曲线、曲面的光滑拼接条件.根据拼接条件,采用与B样条方法相同的组合思想,但是不同的组合方式,分别定义了由新曲线、新曲面构成的分段组合曲线、分片组合曲面,定义方式自动保证了组合曲线、曲面的连续性.数值实例结果显示了该方法的有效性.

英文摘要：

In this paper, a set of rational polynomial functions with five parameters are proposed to achieve the following two goals; 1） make curve and surface achieve higher order smoothness by joining under relatively simple conditions, and 2） adjust their shape freely without changing the positions of control points. Based on the proposed polynomial functions, we define a new curve determined by four control points and a new surface determined by sixteen control points. The smooth join conditions of the new curve and surface are discussed. According to the continuity conditions, we define a piecewise combination curve and surface consisting of the new curve and surface. Our method automatically ensures the continuity of the resulting curve and surface. Experimental results show the effectiveness of the method.