基于小波的准均匀B样条曲线曲面变分造型

变分造型是自由曲线曲面交互设计中常用的技术之一，在传统的变分造型技术中，一般将此类问题转化为对控制顶点的优化求解问题，但当基函数多进，B样条的局部性常会导致待求解系统的性态不好，求解效率降低，对此，文中应用小波方法解决准均匀B样条曲线曲面变分造型中的优化求解问题，由于小波基具有多分辨特性，该方法可以大大提高迭代速度。

Variational Modeling of Quasi-Uniform B-Spline Curve and Surface with Wavelets

Easy and quick manipulation of geometry is the key requirement of an interactive CAD system. One of the most widely used approaches is variational technology. Traditionally, a variational problem can be transformed to the optimization of control points. Unfortunately as the number of basis functions in the set grows, the local support property of B spline often makes an optimization system poorly conditioned, which results in low efficiency. To solve this problem, a wavelet based method is presented for the variational modeling of quasi uniform B spline curves and surfaces. With the multiresolution property of wavelets basis, the iteration speed can be greatly improved.