Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

Abstract

In the field of curves and surfaces fairing, arbitrary resolution wavelet fairing algorithm made wavelet fairing technology widely extended to general curves and surfaces, which are determined by any number of control vertices. Unfortunately, accurate wavelet construction algorithm for general curves and surfaces still has not been perfect now. In this article, a concrete algorithm for reconstruction matrix and wavelet construction was emphatically studied, which would be used in the multi-resolution fairing process for curves and surfaces with any number of control vertices. The essence of this algorithm is to generalize wavelet construction into the solution of null space, which could be solved gradually and rapidly by the procedures of decomposition and simplification of coefficient matrix. Certainly, the related compactly supported wavelets could be constructed efficiently and accurately, too. In the last of the article, a complex curve and a complex surface case were provided to verify the stability, high performance, and robustness of this algorithm.