Abstract: To improve the accuracy, efficiency, and reliability of calculating the shortest distance, a dynamic grid algorithm for calculating the shortest distance from a spatial point to a freeform surface was presented. First of all, four grid areas were created in the vicinity of a proper initial point on the surface under the given step length. The distances from a spatial point to the initial point and the centers of four grid areas were then calculated, the minimum value among which was selected as the shortest distance, and the corresponding surface point was obtained. Then, this point was selected as the next initial point, and the step length became a half. The above process was iterated until the accuracy of the shortest distance reached the given value. The proposed algorithm was compared to some existing algorithms under two example surfaces. Results showed that the effectiveness of this method.

Key words: the shortest distance, surface, grid, five-axis, machining, interference checking

摘要： 为提高最短距离计算的精度、效率和稳定性，提出了一种计算点到曲面最短距离的网格法。该方法首先利用曲面上给定的一点作为初始点，以该点为中心按给定步长将曲面划分为四个网格区域;然后分别计算空间点与初始点以及四个网格中心的距离，选取其中最小的距离作为最短距离，并得到相应网格中心;最后以该中心作为初始点，步长减半，重复以上步骤，从而获得满足一定精度的最短距离。分别以两个复杂曲面为计算实例，通过对所提方法与其他方法的计算结果进行比较，验证了该方法的有效性。

关键词: 最短距离, 曲面, 网格, 五坐标, 加工, 干涉检查