Mesh optimisation based on Willmore energy

An algorithm for improving the quality of an initial triangulation on a fixed set of vertices is suggested. The edge flip operation is performed consecutively, aiming to minimise the discrete Willmore energy over a triangulated surface (or mesh). The Will- more energy of a surface is a function of Gaussian and mean curvature, and measures local deviation from a sphere. Virtual points are introduced in the triangulation to overcome the local invariance of Willmore energy under edge flips. Some experimental results are given.