【摘要】 本文利用u-w参数平面与xyz空间的对应关系,把以双参数形式给定的自由曲面 P(u,w)=[X(u,w),Y(u,w),Z(u,w)] Umin≤u≤UmaxWmin≤W≤Wmax 与以隐函数给定的函数曲面 g(x,y,z)=O 求交这一空间问题,转化为u-w参数平面上曲线flu,w,=O的求解这一平面问题。通过曲线的导数信息和曲线上的一个初始点,又将后者转化为一个一阶常微分方程组的初值问题。从而导出了双参数自由曲面与函数曲面求交的数值解法,并在此基础上,具体讨论了计算机辅助几何设计中常用的Bezier曲面、Coons曲面,B-Spline曲面这三种不同类型的自由曲面与函数曲面求交问题,分别给出了相应的求交迭代格式。更多还原

【Abstract】 In surface modelling, biparametric free-form surfaces, which are defined by P(u,w)= [X(u,w) Y(u,w)Z(u, w)],are very conenient. However,cylinder,paraboloid, hyperboloid, and so on, which may be represented as a function g(x,y,z)-0 , are often used in engineering. It is difficult to find the intersection between two surfaces which are described by the different mathematical model.In this paper, according to the correspondence between xyz space and u-w parametric space, the intersection between a free-form surface and a funcion surface, which is in three-dimensional space, is turned into a parametric curve f(u, w) = 0 which is on two-dimensional plane. By means of the differential informatin and the initial point, the parameter curve f(u, w)=0 is turned into a initial value problem of ordinary differential equations. Thus, numerical solution of finding the intersection between a free-form surface and a function surface is derived. In addtion, authors put emphasis on discussing how to find the intersection between a function surface and a BEZIER/ COONS/ B-SPLINE surface which are often used in computer aided geometry design, the relevant algorithm forfinding the intersection between two surfaces are obtained.更多还原