Among a variety of grid deformation methods, the method proposed by Liao
seems to be one of the most favourables. In this article, we introduce a generalisation
of Liao`s method which allows for generating a desired mesh size distribution for quite
arbitrary grids without giving rise to mesh tangling. Furthermore, we tackle the efficient
implementation of the underlying steps and we discuss accuracy aspects like convergence
behaviour as well as the robustness of the presented technique. The benefits of our new
method are demonstrated for several applications and examples.