二阶几何连续的闭合全凸曲线的构建

发布时间：2019-04-22 12:25

【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.
[Abstract]:In view of the fact that the existing interpolation algorithms for convex preserving curves can not solve the practical problem of constructing closed fully convex smooth curves by convex hull point sets, an interpolation algorithm for closed fully convex curves with second order geometric continuity is proposed. The algorithm takes a set of plane convex hull points as interpolation points, and takes two adjacent convex hull points as the first and fourth control points of a cubic B 茅 zier curve. The second and third control points of each cubic B 茅 zier curve are solved according to the second order geometric continuity condition between adjacent cubic B 茅 zier curves. Then the closed, completely convex and second-order geometric continuity of the curve are proved theoretically, and a simple and effective curve construction algorithm is proposed. The experimental results show that the interpolation curve has a clear physical interpretation, and the algorithm is applied to the actual scene of simulating the measuring track of the tape to extract the diameter of the trunk, and the accuracy and practicability of the interpolation curve are further verified.
【作者单位】：信阳师范学院计算机与信息技术学院;中国科学院自动化研究所模式识别国家重点实验室;中国林业科学研究院资源信息研究所;信阳师范学院数学与统计学院;
【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
【分类号】：TP391.7

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