一种高效的自由曲面求交算法

针对目前常用的Ｂｅｚｉｅｒ曲面分割法求交难同时满足高精度和高速度要求的问题，提出了一种快速跟踪求交的算法。着重论述卫确定跟踪起点的方法，并对所求交线的完备性作了充分的考虑。算法利用一曲面参数曲线和另一面的快速求交算法，找到两曲面交线上的某一点，解决了确定跟踪起点的问题，兼顾了快速和高精度两方面的要求；同时，利用求曲面间的极值距离获取控制网格间小交线上的跟踪起点，再用跟踪法求得小交线，从而保证了小交

Algorithm for Intersecting Line of Free-Form Surfaces

The dividing surface method with Bezier can not meet the needs of high precision and high speed. A fast tracing algorithm is proposed. It searches for the initial tracing point on intersecting lines and considers completeness of intersecting lines. The algorithm seeks on intersecting point between a parameter curve on a surface and another to define certain initial points. It utilizes the extremum of distance between two surface patches to obtain initial point of intersecting lines located within a grid. This guarantees completeness of the intersecting lines. The algorithm makes full use of geometric information of intersecting lines to speed up the calculation according to the arc height tolerance. In this way, the requirements of high precision and efficiency can be met at the same time. Application has been made in home developed CAM system.