任意控制顶点曲线多分辨光顺中的快速小波构造

Rapid Wavelet Construction of Multi-resolution Fairing for Curves With Arbitrary Number of Control Vertexes

在曲线曲面光顺领域,任意分辨率小波光顺将小波光顺技术推广到了一般领域,大大提高了其应用范围,但是多分辨分析小波光顺的重构算法至今没有完善。文章着重研究了任意控制顶点曲线多分辨光顺过程中,重构矩阵的具体算法。该算法将小波重构归纳为零空间的求解问题,并通过系数矩阵E构造m-n个矩阵Ei,对其进行分解与简化,保证了得到的解为对角占优的带状矩阵,实现了重构矩阵的快速求解,从而快速地实现了紧支集小波构造。文章最后通过光顺一条叶片截面线,对算法进行了验证,说明了该算法的准确性与稳定性。

In the field of curves and surfaces fairing, arbitrary resolution wavelet fairing algorithm make wavelet fairing technology be widely extended to general curves, but for reconstruction algorithm of the multi-resolution for the wavelet fairing, it still has not been perfect. The paper mainly studies a concrete algorithm of reconstruction matrix in the process of multi-resolution fairing for curves with arbitrary number of control vertexes. In this algorithm, wavelet reconstruction is concluded to the solution of null space. Reconstruction matrix could be solved rapidly and steadily by the division and simplification of the m-n matrix Ei which are constructed by the coefficient matrix E. And it guarantee the solution be a sparse and diagonally dominant matrix. Then, this algorithm could be used to construct the compactly supported wavelet rapidly. In the last part of the paper, the algorithm is verified by a blade section line, and the results show that the accuracy and stability of the algorithm.