Wavelet-Based Multiresolution NURBS Curve Fairing

Abstract

A multiresolution approach is presented for NURBS curve fairing based on nonuniform semiorthogonal B-spline wavelets built. This method provides greater flexibility and applicability than uniform B-spline wavelets for multiresolution curve fairing. An example is presented to validate effectiveness of this multiresolution fairing method. Furthermore, the algorithm can be easily applied to NURBS curves in three dimensions as well as in two.

Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

“…By means of decomposition and simplification of coefficient matrix E, an expected highquality reconstruction matrix Q mn could be solved directly without modification of knot vector, different from literature. [18][19][20][21] The advantage is that there is no approximate calculation in the process of MRF. Certainly, the related compactly supported wavelets C n could be constructed efficiently and accurately, too.…”

“…An interactive tool was developed that allows editing of NUR surfaces, which can reflect the effects of different strength of the multi-resolution decomposition. Based on the available non-uniform semi-orthogonal B-spline wavelet algorithm, Li et al 18 and Li and Tian 19 proposed a new curve multi-resolution representation method without the limitation of wavelet multi-resolution representation. This algorithm can be applied to the MRA for any uniform or non-uniform B-spline curves, and reduces the computational cost of construction of non-uniform B-spline wavelets in the process of MRF.…”