摘要
文章针对非均匀采样点拟合光滑B样条曲线构造问题,提出一种基于已知控制点和相邻控制点之间弦长求解控制点方程组系数矩阵来构造光滑B样条曲线的方法。该方法通过控制顶点所在曲线的光顺性提高最终生成曲线的连续性和光滑性。在此基础上,设计了闭合B样条曲线控制点的快速求解算法。首先利用所有控制顶点和相邻点间弦长建立求解系数的参数矩阵,再提出一种基于LU矩阵分解的优化算法。根据方程组系数矩阵的特点,参照追赶法的LU分解,构造了分解后的L、U矩阵结构。最后通过实例说明,采用文中方法所构造的B样条曲线具有较好的光滑性,也证明了该算法的可靠性和有效性。
In order to overcome the problem resulted from none-uniform sampled dataset, this paper presents a method to calculate unknown control points using adjacent vertices＇ chord length parameters to generate a smooth B-spline curve. This method improves the continuity and the smoothness of the generated B-spline curve by controlling the feasibility of the curve including the vertices. On the basis of it, a quick solving algorithm is designed for closed B-spline curve .This method first establishes parameter matrix group based on all control points and adjacent vertices＇ chord length parameters to calculate coefficient, then an optimization algorithm based on LU matrix decomposition is presented. Based on the characteristic of the control points equations, decomposed matrix structures are constructed according to the LU decomposition of pursuit method. The examples in the last section illustrate the feasibility of this method, and the reliability and efficiency of the algorithm are also proved.
出处
《信息网络安全》
2013年第4期39-42,共4页
Netinfo Security
关键词
弦长参数
光滑
B样条曲线
插值
chord length parameters
smooth
B-spline curve
interpolation
