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.
出处
《图学学报》
CSCD
北大核心
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)
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
computer aided geometric design
subdivision
blossoming
B-splines
non-uniform
knot insertion
