用封闭周期域对称B样条基实现均匀样条逼近  

Uniform Spline Approach Using Symmetric B-Spline Basis on Closed Periodic Zone

作　　者：周凯汀[1] 郑力新[1] 林福泳[2] 

机构地区：[1]华侨大学信息科学与工程学院,泉州362021 [2]华侨大学机电及自动化学院,泉州362021

出　　处：《计算机辅助设计与图形学学报》2009年第10期1406-1411,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：教育部科学技术研究重点项目(207145);福建省高等学校新世纪优秀人才支持计划(07FJRC01);福建省自然科学基金(A0610019);国务院侨办科研基金(07QZR02)

摘　　要：针对现有求解均匀样条曲线控制顶点方法中使用较为复杂的迭代算法的不足,提出均匀样条曲线控制顶点的快速并行算法.首先将基本B样条基平移建立对称B样条基(参数定义域为单位区间);然后利用复函数组{ξk(v)=eikv}的正交性构造封闭周期区域的正交B样条基,得出正交B样条基系数的显式并行计算公式;进一步,利用正交基系数与对称B样条基系数(样条曲线控制顶点)的关系,得出控制顶点的显式并行计算公式.最后以四阶与三阶样条逼近为例分析并行公式的快速算法,用从封闭及任意给定点列构造B样条曲线的2个例子证明了该算法的有效性.实验结果表明,文中算法为简单的B样条基增加了对称性,能够容易地实现快速并行计算,可提高构造大规模样条曲面的效率.To overcome the weakness of using complicated iterative algorithms in the existing methods of solving for control points of uniform B-spline curve, this paper presents fast parallel algorithms to compute control points of uniform B-spline curves. First we shift naive B-spline basis and establish symmetric B-spline basis （parametric variable is defined on unit interval）. Next we use orthogonal properties of complex functions {ξk（v）=e^ikv} to establish orthogonal B-spline basis on closed periodic zone, and derive explicit parallel computing formulas for coefficients of orthogonal B-spline basis. We further use relations among coefficients of orthogonal B-spline basis and coefficients of symmetric B-spline basis （control points of B-spline curve） to achieve explicit parallel computing formulas for control points of B-spline curve. At last, fourth order and third order B-spline approaches are taken as examples to analyze the proposed fast algorithms of the parallel computing formulas. Two examples of constructing B-spline curves from closed and non-closed given points are provided to verify the presented method. Experimental results show that, the method presented in this paper adds symmetric property to simple B-spline basis. It can easily carry out parallel computation for control points of B-spline curves and can improve efficiency of building large-scale B-spline curves.

关 键 词：样条函数 正交样条 参数曲线 并行计算 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]