B-spline curve fairing with constraints.

In industry design and reverse engineering, the B-spline curve is an important tool for shape design and data fitting. The quality of final product shape is determined by the fairness of the B-spline curve directly. In this paper, a new method for fairing a B-spline curve is presented. The shape of a B-spline curve can be modified by adjusting its control points. The adjusting range of the control points is restricted by the β constraint, while the shape of the whole curve can be restricted by the α constraint. Finally, the fairing curve can be obtained by solving a linear system of equations. The method can be applied for global or local curve fairing. Examples of B-spline curve fairing from simulated and real data are presented to show the efficiency of the method.