摘要
求空间两条曲线的交点是CAD/CAM重要内容之一,它的准确性与效率直接影响系统的可靠性与实用性。通常是将两条曲线的方程联立求解,或者是对曲线建立包围盒。但上述两种方法计算量较大,甚至求解困难。这里提出一种快速实用的曲线求交算法,具有较高的稳定性和可靠性。该算法分两步进行,首先根据B样条曲线的控制多边形判断两条曲线是否相交,并求出两条曲线存在交点的可能参数区间,然后在此区间内,利用控制顶点算出所对应的曲线段,进行精确求交计算。与常用的包围盒方法相比,该算法效率高、精度易于控制,并通过实例验证算法的有效性。
The algorithm for finding the intersection point of two free-form curves is one of crucial steps in CAD/CAM system. Its accuracy and efficiency influence the reliability and practicability of the system. Generally, the intersection point of two free-form curves may be calculated by resolving simultaneously two set of curve equations, or establishing an envelope-bounding box. But the calculating procedure is very complex, even difficult in practice. This paper puts forward a quick and practical algorithm and discusses the calculating procedure of the intersection point in detail, and proves the algorithm robust and reliable. It is carried out in two steps. First step is to determine whether two curves intersect based on the characteristic polygon of B-spline curves, and to find the parametric domain where the two curves may intersect. Second step is to calculate the curve pieces corresponding the parametric domain based on control vertexes, and then the intersection point is computed accurately. Comparing with the common method of container box, the efficiency of this algorithm is higher, and the calculating precision is more tractable. The effectiveness of algorithm is verified by some examples.
出处
《机械设计与制造》
2004年第5期55-56,共2页
Machinery Design & Manufacture
关键词
曲线求交
算法
B样条曲线
自由曲线
Intersection of curves
Algorithm
B-spline curve
Free-form curve
