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.

在曲线和曲面光顺领域，任意分辨率的小波光顺算法使小波光顺技术广泛地扩展到由任意数量的控制顶点确定的一般曲线和曲面。不幸的是，用于一般曲线和曲面的精确小波构造算法现在仍不完善。本文着重研究了一种用于重建矩阵和小波构造的具体算法，该算法将用于具有任意数量控制顶点的曲线和曲面的多分辨率光顺过程。该算法的本质是将小波构造推广到零空间解中，可以通过分解和简化系数矩阵的过程来逐步，快速地解决。当然，相关的紧支撑小波也可以高效，准确地构造。在本文的最后，提供了复杂的曲线和复杂的表面情况以验证该算法的稳定性，高性能和鲁棒性。