Mesh smoothing using the Geometric Element Transformation Method

A novel method for smoothing triangular surface meshes is presented. It is based on the Geometric Element Transformation Method (GETMe) representing a simple geometric operation. In contrast to existing smoothing techniques, GETMe transforms single elements thus resulting in a simultaneous movement of all nodes of an element. The effect of this transformation, if applied iteratively, is the asymptotical but rapid regularization of the initial element. Mesh smoothing is achieved by applying this transformation to every poor quality element until overall mesh quality reaches a user defined level. Thereby, a lower bound for the minimal element angle and an upper bound for the maximal element angle serve as natural control variables in order to freely adjust mesh quality with respect to subsequent applications. Descriptions of the basic smoothing algorithm as well as modifications to preserve shape and to incorporate constraints on nodes are given. Numerical experiments on both artificial and real world meshes demonstrate the method’s potential and flexibility.