具有任意自由度的B样条非均匀细分

Non-uniform subdivision for B-splines of arbitrary degree

为了便于工程实际应用,非均匀细分方法现在已经成为计算机图形学和几何建模中的热点问题。提出一种具有任意自由度的B样条非均匀细分算法,其实现与B样条均匀细分即Lane-Riesenfeld细分方法相似。该算法包含了非均匀d环结构生成的双重控制点,其中d环相似于d度均匀B样条曲线的Lane-Riesenfeld算法中均匀的d环结构。Lane-Riesenfeld算法是由B样条曲线基函数的连续卷积公式直接得出的,而本算法是blosso-ming方法的一个扩展。对于非均匀B样条曲线来说,该节点插入方法比之前的方法更简单有效。

Though Chinese engineers engaged in CAGD,this paper presented an efficient algorithm for subdividing 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 discussed consists of the doubling control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane-Riesenfeld algorithm for uniform B-splines of degree d.However,unlike the Lane-Riesenfeld algorithm which followed most directly from the continuous convolution formula for the uniform B-spline basis functions,the algorithm followed naturally from blossoming.For non-uniform B-splines,the result shows that the knot insertion method is simpler and more efficient than previous knot insertion algorithms.