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 二阶几何连续的闭合全凸曲线的构建 尤磊1,2,3; 冯岩1; 郭建伟2; 叶军涛2; 唐守正3; 宋新宇4 Source Publication 计算机辅助设计与图形学学报 2017-12 Volume 29Issue:12Pages:2216-2224 Abstract 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. Other Abstract The 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 closedG2 continuity 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,G2 continuity 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. Keyword 曲线插值 凸包 凸曲线 几何连续性 模拟测量 Document Type 期刊论文 Identifier http://ir.ia.ac.cn/handle/173211/15682 Collection 模式识别国家重点实验室_多媒体计算与图形学 Corresponding Author 宋新宇 Affiliation 1.信阳师范学院计算机与信息技术学院2.中国科学院自动化研究所模式识别国家重点实验室3.中国林业科学研究院资源信息研究所4.信阳师范学院数学与统计学院 Recommended CitationGB/T 7714 尤磊,冯岩,郭建伟,等. 二阶几何连续的闭合全凸曲线的构建[J]. 计算机辅助设计与图形学学报,2017,29(12):2216-2224. APA 尤磊,冯岩,郭建伟,叶军涛,唐守正,&宋新宇.(2017).二阶几何连续的闭合全凸曲线的构建.计算机辅助设计与图形学学报,29(12),2216-2224. MLA 尤磊,et al."二阶几何连续的闭合全凸曲线的构建".计算机辅助设计与图形学学报 29.12(2017):2216-2224.
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