In mathematics, Surface fairing is an aspect of mesh smoothing. The goal of surface fairing is to compute shapes that are as smooth as possible.
f:S → \Rd
f
How to actually measure smoothness or fairness obviously depends on the application, but in general fair surfaces should follow the principle of simplest shape: the surface should be free of any unnecessary details or oscillations.[2] This can be modeled by a suitable energy that penalizes unaesthetic behavior of the surface. A minimization of this fairness energy—subject to user-defined constraints—eventually yields the desired shape. Example applications include the construction of smooth blend surfaces and hole filling by smooth patches.