点到隐式曲线曲面的最小距离

The Minimum Distance from a Point to an Implicit Curve or Surface

求解给定点到隐式曲线曲面的最小距离通常都是应用一般的搜索算法,但搜索算法的稳定性和有效性通常不高。文章基于隐式曲线曲面的几何特性,将这个求最小值问题转化为方程组求解的问题。对于方程组的求解,则应用了计算复杂度较低的离散牛顿法。将其迭代区间进行细分并在各个细分区间中应用离散牛顿迭代算法,增强了算法的稳定性。

The general way of solving the problem how to compute the minimum distance from a point to a implicit curve or surface is by the searching algorithm, like the optinization algorithm in mathematic programming. The searching algorithm is always poor in stability and efficiency. Based on the geometric characteristics of the implicit curve or surface, we change the problem of finding the minimum value to the problem of finding roots of an equation group. In order to solve the equation group, we adopt the Discrete Newton Method. In order to increase the stability of our algorithm, we divide the parametric surface into lots of smaller area and apply the Discrete Newton Mehod in each smaller area.