一种快速求取空间点到曲面最短距离的算法

求空间点到曲面的最短距离是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.通常可以采用穷举法或目标优化的方法,但对于复杂曲面数据量较大,计算工作量较大,不能满足快速高精度的要求.文章提出一种快速实用的算法,具有较高的稳定性和可靠性.该算法首先将曲面划分网格,求空间点到网格节点的距离,距离最短者作为迭代初始曲面点,然后再进行迭代精确计算.与常规方法相比,该算法计算效率高、精度易于控制,并通过实例验证了算法的有效性.

An algorithm for quickly calculating the minimum distance between a space point and a surface

It is an important step to calculate the minimum distance between a space point and a surface in CAD/CAM system. Its accuracy and efficiency influence the reliability and practicability of the system. Generally, the minimum distance may be calculated by an enumerating method or an optimizing method. But for a free form surface, the data amount is large, and the calculating procedure of the two methods is very complex. Therefore it can't meet the needs of high precision and high efficiency. In this paper, a quick and practical algorithm for calculating the minimum distance between a space point and a surface is put forward, and it is proved to be robust and reliable. The algorithm contains three steps. The first step is to plot out the mesh of surface, and calculate the distance between the space point and the net node of surface mesh. Second step is to choose the minimum value as the initial point of iterative procedure in the surface. Finally iterative computations are carried out. Therefore the computing speed of this algorithm is high, and the calculating precision is tractable. The effectiveness of algorithm is verified by some examples.