一种任意次非均匀B样条的细分算法  

A Subdivision Algorithm for Non-uniform B-Splines of Arbitrary Degree

作　　者：韩力文[1,2] 杨玉婷 邱志宇[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024 [2]河北省计算数学与应用重点实验室,河北石家庄050024 [3]沙城中学,河北张家口075400

出　　处：《图学学报》2013年第5期56-61,共6页Journal of Graphics

基　　金：国家自然科学基金资助项目(61170107);河北省教育厅自然科学研究项目(Q2012041)

摘　　要：类似于经典的、应用于任意次均匀B样条的Lane-Riesenfeld细分算法,提出了一种任意次非均匀B样条的细分算法,算法包含加细和光滑两个步骤,可生成任意次非均匀B样条曲线。算法是基于于开花方法提出的,不同于以均匀B样条基函数的卷积公式为基础的Lane-Riesenfeld细分算法。通过引入两个开花多项式,给出了算法正确性的详细证明。算法的时间复杂度优于经典的任意次均匀B样条细分算法,与已有的任意次非均匀B样条细分算法的计算量相当。A subdivision algorithm is presented for non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform B-splines of arbitrary degree.The algorithm contains two steps：refining and smoothing,and achieves non-uniform B-Splines curve of arbitrary degree.The algorithm is based on blossoming rather than the continuous convolution formula for the uniform B-spline basis functions.Two blossoming polynomials are introduced to verify the correctness of the subdivision algorithm.The subdivision algorithm is more efficient than the classical uniform subdivision algorithm for B-splines of arbitrary degree,and as efficient as those currently available non-uniform subdivision algorithms for B-splines of arbitrary degree.

关 键 词：计算机辅助几何设计 细分 开花 B样条 非均匀 节点插入 

分 类 号：O241.5[理学—计算数学]