A multi-level filtering approach for fairing planar cubic B-spline curves

Abstract

In this paper a new approach to the problem of fairing planar B-spline curves is introduced. We propose an algorithm based on a multi-level representation of cubic B-spline curves, which enables the identification of bad control points that need to be faired. The multi-level representation allows splitting a curve into its low resolution and details function parts. The details function permits the formulation of a different approach to the selection of bad control points, differing from others methods that are based on the evaluation of curve and curvature derivatives. Moreover, this new technique leads to an increased interaction with designers that can identify faster the set of bad control points and then operate on them through their level-of-detail (LOD) representation in manner to obtain the expected shape. Hence, designers have more control over the entire slope by thresholding details in several manners fully described in the following chapters. Several numerical examples are presented to validate the effectiveness of this algorithm compared with another technique in (Farin, G., Sapidis, N., 1989. Curvature and the fairness of curves and surfaces. IEEE Computer Graphics and Applications 9 (2), 52–57).