平面简单闭合曲线离散采样与重建算法-科学学研究.PDFVIP

2015 年 8 月 图 学 学 报 August 2015 第 36 卷 第4 期 JOURNAL OF GRAPHICS Vol.36 No.4 平面简单闭合曲线离散采样与重建算法 范丽鹏， 王丽英， 庞明勇 (南京师范大学教育技术系，江苏 南京 210097) 摘 要：提出一种鲁棒的平面简单闭合曲线离散采样与重建算法。算法分为采样过程和重 建过程两部分。采样部分首先对平面闭合曲线均匀取点，然后计算各点到曲线所围平面区域中 轴的最近距离，最后根据所求距离确定采样间隔，获取采样点集；重建部分首先构建采样点集 的Delaunay 三角剖分，然后从得到的三角形中选择边构建初始化图形，最后通过修改该图形获 得重建图形。实验表明算法得到的采样点较少且能反映曲线的局部几何特性，重建图形能够较 好地表示原闭合曲线的形状及走向。 关 键 词：曲线重建；离散采样；无序点集；平面图形 中图分类号：TP 391. 41 文献标识码：A 文 章 编 号：2095-302X(2015)04-0511-05 Discretely Sampling and Reconstructing Simple Planar Closed Curves Fan Lipeng, Wang Liying, Pang Mingyong (Department of Educational Technology, Nanjing Normal University, Nanjing Jiangsu 210097, China) Abstract: A robust algorithm is proposed for discretely sampling continuous planar curves and reconstructing the curves from the sampled point sets. The algorithm covers two processes, sampling and reconstruction. In the sampling part, the points are evenly obtained from a given planar closed curve, and then the distances are calculated between each point and the medial-axis of the planar area surrounded by the closed curve. Subsequently, the sampling intervals are decided by the distances and finds the sampling points. In the reconstruction part, a Delaunay triangulation is first built for the sampled points, and then edges are selected from the triangulation to build the initialize graph. Finally, the reconstructed curve is obtained by modifying the graph to a new version. Experiments show that the point sets sampled by our algorithm are locally adapted to the local geometric characteristics of the curves, and the reconstructed curv