Abstract: In the process of free-form surface fairing, the number of control vertices of surface on u and v directions is usually arbitrary. On the basis of arbitrary resolution wavelet fairing algorithm (ARWFA) for curves with any amount of control vertices, the ARWFA is extended to two-dimensional space by the tensor product operation. By this tensor product operation, the construction of 2D B-spline wavelets and corresponding decomposition-reconstruction algorithm were realized with rigorous mathematical derivation. As a result, original control vertices were decomposed into one low frequency part, which is the new control vertices of the faired surface, and three high frequency parts, which are the filtered noises. Because the multi-resolution analysis principle is followed strictly in the whole calculation process, the original surface still can be reconstructed accurately with low frequency part and three high frequency parts by reconstruction algorithm. On this basis, a complicated fairing case is given to verify the correctness and precision of this algorithm.

Key words: any resolution, computer graphics, multi-resolution analysis(MRA), reverse engineering, surface fairing