构造两个曲面的拼接曲面

Constructing Blending Surface for Two Arbitrary Surfaces

给出了当两个待拼接曲面的拼接线具有参数化形式或者可以参数化时,它们之间 G1光滑拼接曲面的构造方法。所得的拼接曲面是由一个空间曲线集定义的,每一条空间曲线由拼接线上的点对确定。并且拼接曲面都是参数曲面,它们的形状可以通过预设的参数很好地调整和控制。作为实例,讨论了两个截口是平面的或非平面的(由两个二次曲面定义)的二次曲面之间的拼接曲面的构造和一般的参数曲面的拼接曲面的构造。

In this paper, we present a method, which can be used to solve the blending problem of two arbitrary surfaces as long as they have regular blending boundaries. The blending surface is defined as a collection of space curves which are defined by point pairs on the blending boundaries and the corresponding information of the given surfaces on the blending boundaries. The blending surface has a parametric form and its shape is easy to be controlled by adjusting the parameters left for the user. As examples of our method, we show how to construct blending surfaces between two quadratic surfaces with boundaries to be the intersection of this surface and a plane or another quadratic surface. Based on this method, a dynamic software package is implemented.