Constructing fair curves and surfaces with a Sobolev gradient method Original Research Article

We have devised a new method for constructing discrete approximations to fair curves and surfaces by directly minimizing an arbitrarily selected fairness functional subject to geometric constraints. The nonlinear optimization problem is solved efficiently by a Sobolev gradient method. We first describe the method in general terms and then present results which demonstrate its effectiveness for constructing minimum variation curves which interpolate specified control points, tangent vectors, and/or curvature vectors.