曲线的保面积细分算法

摘要

针对文献(Gordon D.Corner cutting and augmentation:An area preserving method for smoothing polygons and polylines.Computer Aided Geometric Design,2010,27(7):551-562)中给出的CCA1算法做了改进,提出了曲线保面积细分算法——CCA(k)细分算法.该算法将CCA1中的割角由等腰三角形推广至割角两边与特征多边形的相邻两边成比例,从而使极限曲线能更好地契合初始的特征多边形.文中还推导了CCA(k)算法的递推关系式和割比的适定取法,并证明了极限曲线的收敛性和连续性.数值实例表明,对于大多数的封闭多边形,CCA(k)算法都能得到理想的细分结果.%To improve the CCA1 method in reference (Gordon D. Corner cutting and augmentation: An area-preserving method for smoothing polygons and polylines [J]. Computer Aided Geometric Design, 2010, 27(7): 551-562), a new curve subdivision method with area-preserving called CCA1 method .is presented in this paper. This method cuts corners according to the ratio of the adjacent edges while the cutting triangles are isosceles in the CCA1 method, so the limit curve can fit the initial polygon better. The recursive formulas and the well-posed solution of the cutting ratio are obtained in the paper. Meanwhile, the convergence and the continuity of limit curve are proved. For many different kinds of closed polygons, numerical examples show that the good subdivision results can be got by CCA(&) method.