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.