基于曲面精确表示的距离极值点的计算及在刀具干涉检测中的应用

摘要

针对基于曲面精确表示的刚体碰撞检测中裁剪曲面距离极值点的求解问题，提出了利用平面向量场估计初始曲面距离极值点的方法，避免了曲面过度细分，讨论了距离极值点满足的微分几何条件，给出了解析曲面/参数曲面、参数曲面/参数曲面、点/参数曲面和曲线/参数曲面的距离极值点迭代算法。实例验证分析了该算法的高效性和可靠性。%Aiming at the problem of solving distance extreme points on trimmed surfaces in collision detection of rigid bodies which are represented by exact surface, a method is presented to obtain the initial distance extreme points using the plane vector field, which can avoid the excessive subdivision of the surface. The differential geometry conditions of the distance extreme points are discussed, and iterative formulas for obtaining distance extreme points of the analytic surface/parametric surface and parametric surface/parametric surface are given in this paper. The efficiency and reliability of the algorithm are verified by an example.