中文摘要：

针对点到二维（2D）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．分析隐式曲线在初始点处的曲率，将给定点向初始点处的切线或曲率圆作投影，并建立了追踪投影点的一阶和二阶泰勒迭代方法；在此基础上提出了基于曲率的步长控制策略；考虑到泰勒迭代方法产生的误差，进一步给出了基于梯度的迭代误差矫正方法．最后，给出了计算给定点到二维隐式曲线正交投影的完整算法．仿真结果表明，算法稳定、高效，收敛性良好．

英文摘要：

A geometric iteration algorithm for projecting a point onto planar implicit curves is presented. A first-order and a second-order Taylorts algorithms for tracing the projections are established by analyzing the curvature of the implicit curve and projecting the given point onto the tangent or curvature circle at the initial point. A curvature based method for controlling iteration step is further proposed. Considering the iteration error brought by the aforementioned Taylor＇s method, a gradient based method for correcting iteration errors is carried out. Complete algorithm for computing the orthogonal proiection of a given point on a two-dimensional implicit curve is summarized ulitimatley. Simulations indicate that the proposed algorithm has good convergence, robustness and efficiency.