复合三角Bezier曲面和平面的求交及其应用

Intersection of Composite Triangular Bezier Surface and Plane and its Application

本文提出了一种根据组成复合三角Bezier曲面的各三角Bezier曲面片与平面的相交类型,采用不同方法求取初始交点;通过迭代求精、求近曲面点和边界点计算,由一个初始交点顺序跟踪出整条交线的方法。这种包括各曲面片边界点的交线计算方法可处理复合曲面与平面间形成多条交线、交线环的情况,所得到的交点记录了坐标值和相应曲面片的参数值。测试显示这种交线计算方法简单可靠,精度高,在自由曲面数控加工编程中具有广泛的应用场合,对提高汽车等领域的自由曲面NC加工精度具有重要的工程价值。

An algorithm for calculating the intersection curves between composite triangular Bezier surface and a plane is presented. According to the type of intersection curve of plane and triangular Bezier patches that constitute composite triangular Bezier surface point deriving and border point calculating, the whole intersection curve can be traced starting from only one initial intersection point. The method by which certain intersection points are on the patch borderlines is successful in finding multiple intersection curves and intersection loops. The coordinates and relative parametric values have been recorded for each intersection point. Experiments show that the method is simple, reliable, precise and applicable in NC automatic programming. It is significant in improving the precision of NC machining for free surface of motor vehicles.