Variational Design and Fairing of Spline Surfaces

Variational principles have become quite popular in the design of free form surfaces. Among others they are used for fairing purposes. The choice of the ‘right’ fairness functional is a crucial step. There is always a tradeoff between high quality and computational effort. In this paper we present fairness functionals that allow fairing efficiently, i.e., produce high quality surfaces in a reasonable amount of time. These functionals can be considered as simplified thin plate energy functionals for parametric surfaces or as simplified MVC functionals.