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

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