基于渐进迭代逼近的矢量地图曲线化简方法

矢量地图化简在地形仿真、制图综合等研究中具有重要应用。针对已有算法难以兼顾化简曲线 的整体形态和局部特征点精度的问题，提出一种基于 B 样条曲线渐进迭代逼近(PIA)的矢量地图曲线化简方法。 首先筛选出能保持曲线轮廓、具有最大信息量的特征点列，将其作为初始控制点列，得到相应的非均匀 3 次 B 样条拟合曲线；然后根据拟合曲线与特征点的误差进行迭代调整控制点，逐步得到一系列逼近曲线，直至最终 满足精度要求。实验表明，PIA 方法不仅保持了化简曲线的整体几何形态，而且能在满足全局误差要求的情况 下，实现特征点处的高精度逼近。

Vector map curve simplification algorithm based on progressive-iterative approximation

Vector map simplification plays an important role in the research on terrain simulation, cartographic generalization, and so on. As it is difficult to balance the overall shape and local feature point accuracy of the simplified curve with the existing algorithms, a vector map simplification method based on progressive iterative approximation (PIA) with B-spline curve was proposed. First, select the feature point sequence that can maintain the contour of the curve with the largest amount of information, and use it as the initial control point sequence to obtain the corresponding nonuniform cubic B-spline curve. Secondly, it obtained a series of curves that were gradually fitting the real one by iteratively adjusting the control points according to the bias between the fitted curve and the feature points until the accuracy requirements were met. The experiments result show that the PIA method can not only keep the overall geometry of the map curve, but also achieve high-precision approximation at feature points while meeting the global bias requirements.