点到三维隐式曲线的正交投影算法

Algorithm for Orthogonal Projection onto 3D Implicit Curves

针对点到三维(3D)隐式曲线的正交投影问题,提出了一种稳定的几何迭代算法。算法首先给出了基于二阶泰勒逼近的投影点追踪公式;通过将给定点向初始点处的曲率圆作投影,提出了基于曲率的步长控制策略;考虑到迭代过程中存在的误差,给出了基于梯度的迭代误差矫正方法;最后,给出了计算点到三维隐式曲线的正交投影的完整算法实现步骤。仿真结果表明,算法对初始值的敏感性较低,算法稳定、高效,收敛性良好。

A steady geometric iteration algorithm was proposed for projecting a point onto three-dimensional implicit curves. A tracing formula for projection point based second-order Taylor approximation method was proposed. By projecting the given point onto the curvature circle of the implicit curve at an initial point, a step controlling method based curvature was put forward. Considering the iteration error caused by the Taylor method, a correctional way based gradient was given. Finally, integrated computing method for projecting a point onto 3D implicit curves was summarized. Simulations indicate that sensitivity of the algorithm to the initial values is small and it has good robustness, efficiency and high convergence soeed.