Variational Progressive-iterative Approximation for Fairing Curve and Surface Generation

Fairing curve and surface generation is an important topic in geometric design. However, the conventional method for generating the fairing curve and surface, which fit the giving data points, is hard to control the fitting precision, because it is a minimization problem where the objective function is the weighted sum of a fitting term and a fairness term. In this paper, we develop the variational progressive-iterative approximation (abbr. variational PIA) method for fitting a data point sequence. While the variational PIA is easy to control the fitting precision, the generated fitting curve or surface is the most fairing one in some scope. Lots of comparisons show that the fairness results of the variational PIA are comparable to that of the conventional method.