直线与参数曲面求交的一种有效算法

参数曲面求交是曲面造型中的最基本、最重要的问题之一。针对该问题，提出了一种计算直线与参数曲面的交点的有效方法。该方法基于参数曲面的几何不变性，通过对其进行几何变换，将直线转换成投影面垂直线；利用过直线的假想平面对曲面片进行反得分割，直到新的曲面片边界参数值之差满足给定的精度要求为止，以其平均值为交点的参数值。并以双三次参数B样条曲面为例，给出了具体的实现算法。

A Novel Algorithm for Solving Intersections of Line and Parametric Surface

Intersection between two geometric entities is one of the most basic operations that forms the core of surface modeling systems. An efficient approach for solving intersections of line and parametric surface is presented based on the property of geometric invariance of parametric surfaces. The line is transformed into a particular one which is perpendicular to the projection plane, and imaginary planes passing through the line are used to divide the surface patches into new ones until the patches are small enough to meet the needs of precision demands. Intersections are obtained thus by means of the average of boundary curves' parameters of the patches. An algorithm for implementing the proposed approach based on the bicubic B-spline surface is described in detail.