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

Abstract: 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.

Key words: computer aided geometric design, subdivision, blossoming, B-splines;
non-uniform, knot insertion