基于多分辨技术的任意控制顶点曲面光顺

Multi-resolution Analysis Based Fairing Algorithm to Surfaces with Any Amount of Control Vertices

在自由曲面的光顺过程中,针对曲面u、v方向控制顶点数任意的情况,以任意控制顶点曲线的多分辨光顺算法为基础,通过张量积的方法,把任意分辨率下的多分辨光顺技术推广到了二维空间。该算法基于张量积运算,用严格的数学推导实现了二维B样条小波的构造及其分解重构算法,由此把原始曲面的控制顶点分解成了低频部分和三个细节部分,其中,低频部分即为光顺曲面的控制顶点,细节部分即为过滤掉的噪声。由于整个计算过程严格遵循多分辨分析思想,原始曲面仍然可以通过重构算法由低频部分和细节部分进行精确重构。在此基础上,通过一个复杂的实例,验证了本多分辨光顺算法的正确性和准确性。

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.