Multi-resolution Smoothing of Nurbs Curves Based on Non-uniform B-spline Wavelets

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aimed at uniform or quasi-uniform b-spline curves. Uniform and quasi-uniform b-spline curves are just exceptional cases of NURBS curves. Multi-resolution smoothing for these types of curves mostly depend on uniform b-spline wavelets, so this smoothing method can’t be directly applied to NURBS curves. In this paper, firstly, new non-uniform b-spline wavelets are created based on discrete b-spline basis functions in the light of the particularities of NURBS curves, the wavelet reconstruction and decomposition algorithms are provided. The wavelets, obviously, have greater flexibility and applicability than uniform b-spline wavelets because of their distance-independence of neighbor nodes in knot vectors. Then, this paper presents the multi-resolution smoothing method for NURBS curves based on the newly built wavelets. Lastly, an example is presented to confirm effectiveness of this multi-resolution smoothing method. Furthermore, the method can also be applied to NURBS surfaces if extended properly.