ABSTRACT
The transformations and smoothing methods presented in the previous chapters are based on a geometric approach, and focus on computational efficiency, implementational simplicity, and controllability. Furthermore, the regularizing effect of polygon transformations has been proven. However, there is yet no proof of regularization for the polyhedral element transformations given in Section 5.2 and the aspects of GETMe smoothing. Therefore, this chapter provides definitions of alternative element transformations facilitating the mathematical analysis of element regularization and mesh improvement. Furthermore, an overview of recent research results regarding the theoretical background of geometric element transformation-based smoothing methods is given.
