A Multiresolution Fairing Approach for NURBS Curves

Abstract

Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.

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.…”