  The fairing curves and surfaces are used extensively in geometric design,
modeling, and industrial manufacturing. However, the majority of conventional
fairing approaches, which lack sufficient parameters to improve fairness, are
based on energy minimization problems. In this study, we develop a novel
progressive-iterative approximation method for fairing curve and surface
generation (fairing-PIA). Fairing-PIA is an iteration method that can generate
a series of curves (surfaces) by adjusting the control points of B-spline
curves (surfaces). In fairing-PIA, each control point is endowed with an
individual weight. Thus, the fairing-PIA has many parameters to optimize the
shapes of curves and surfaces. Not only a fairing curve (surface) can be
generated globally through fairing-PIA, but also the curve (surface) can be
improved locally. Moreover, we prove the convergence of the developed
fairing-PIA and show that the conventional energy minimization fairing model is
a special case of fairing-PIA. Finally, numerical examples indicate that the
proposed method is effective and efficient.
