Recent methods for surface shape optimization Original Research Article

This paper extends to C1 quintic Bézier triangular patches the recent results obtained by Greiner using C2 bicubic B-spline surfaces. Tensor notation is used to elucidate the invariance properties of Greinerʹs fairness functional and of his blending-surface functional based on the Laplace-Beltrami operator. The notation shows how to construct additional invariant functionals. A functional that minimizes the square of Gaussian curvature is introduced following the guidelines of Greiner. The paper also discusses a few test results obtained using the Laplace-Beltrami and Gaussian functionals, comparing them with a simple quadratic functional based on a special choice of parametric coordinates.