二阶几何连续的闭合全凸曲线的构建  

Construction of Closed, Global Convexity and G^2 Continuity Curve

作　　者：尤磊[1,2,3] 冯岩 郭建伟[2] 叶军涛[2] 唐守正[3] 宋新宇[4] You Lei;Feng Yan;Guo Jianwei;Ye Juntao;Tang Shouzheng;Song Xinyu(College of Computer and Information Technology, Xinyang Normal University, Xinyang 464000;National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190;Institute of Forest Resources and Information Techniques, Chinese Academy of Forestry, Beijing 100091;College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000)

机构地区：[1]信阳师范学院计算机与信息技术学院,信阳464000 [2]中国科学院自动化研究所模式识别国家重点实验室,北京100190 [3]中国林业科学研究院资源信息研究所,北京100091 [4]信阳师范学院数学与统计学院,信阳464000

出　　处：《计算机辅助设计与图形学学报》2017年第12期2216-2224,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家"八六三"高技术研究发展计划(2012AA102002);国家自然科学基金(31470641;11501489;61379096;61761003);国家自然科学基金重点项目(61331018);河南省科技计划项目(152102210129;172102210454);河南省科技开放合作项目(172106000071);河南省高等学校重点科研项目资助计划(18A520009);信阳师范学院"南湖学者奖励计划"青年项目

摘　　要：针对现有保凸曲线插值算法不能解决过平面凸包点集构建闭合全凸光滑曲线的实际应用问题,提出一种二阶几何连续的闭合全凸曲线的插值算法.该算法以一个平面凸包点集为插值点,以相邻的2个凸包点作为1条3次Bézier曲线的第1个与第4个控制点,根据相邻3次Bézier曲线间的二阶几何连续性条件求解每条3次Bézier曲线的第2个与第3个控制点;然后从理论上证明了曲线的闭合性、全凸性及二阶几何连续性,并提出一种简易有效的曲线构建算法.实验结果表明,该插值曲线具备明确的物理学意义上的解释;将该算法应用于模拟卷尺测量轨迹以提取树干直径的实际场景中,进一步验证了其精确性与实用性.existing methods of curve interpolation cannot solve practical application problems of constructing a closed smooth curve with global convexity for planar convex hull point set.For this purpose,a curve interpolation algorithm for constructing a closed G2continuity curve with global convexity is proposed.A planar convex hull point set was used as interpolating points.The two adjacent convex hull points were used as the first and the fourth control points of a cubic Bézier curve,and the second and the third control points were resolved by the relationship of geometric continuity between the two adjacent Bézier curves.The closed,G2continuity and global convexity properties of the constructed curve were proved theoretically.A simple and effective curve constructing algorithm was presented.The experiment showed that the constructed curve has an explicit physical explanation.The practical application of simulating the measurement path of tape to retrieve stem diameter by the constructed curves verifies the accuracy and practicability of the proposed curve interpolation algorithm.

关 键 词：曲线插值 凸包 凸曲线 几何连续性 模拟测量 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]