一种任意次非均匀B 样条的细分算法

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 for Non-uniform B-Splines of Arbitrary Degree

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.