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The fairing curves and surfaces are used extensively in geometric design,modeling, and industrial manufacturing. However, the majority of conventionalfairing approaches, which lack sufficient parameters to improve fairness, arebased on energy minimization problems. In this study, we develop a novelprogressive-iterative approximation method for fairing curve and surfacegeneration (fairing-PIA). Fairing-PIA is an iteration method that can generatea series of curves (surfaces) by adjusting the control points of B-splinecurves (surfaces). In fairing-PIA, each control point is endowed with anindividual weight. Thus, the fairing-PIA has many parameters to optimize theshapes of curves and surfaces. Not only a fairing curve (surface) can begenerated globally through fairing-PIA, but also the curve (surface) can beimproved locally. Moreover, we prove the convergence of the developedfairing-PIA and show that the conventional energy minimization fairing model isa special case of fairing-PIA. Finally, numerical examples indicate that theproposed method is effective and efficient.

Fairing-PIA: Progressive iterative approximation for fairing curve and surface generation