An Analytical Framework for Quadrilateral Surface Mesh Improvement with an Underlying Triangulated Surface Definition

Surface mesh quality plays a very important role in the solution accuracy and in the quality of the ensuing volumetric mesh. Amongst the techniques available, optimization based methods are commonly used for mesh quality improvement. Optimization methods for volumetric and planar surface mesh quality improvement are very well researched. However, this is not true for non-planar meshes. In this manuscript, we focus on quadrilateral non-planar surface meshes obtained during hexahedral mesh generation of anatomic structures. A modified untangling function based on node normals for quadrilateral elements is proposed. A parameterization-based method available is enhanced by giving it an analytical framework. A new projectionbased method is proposed and its performance is comparable to the parametric method. The results of the enhanced/proposed methods are superior to the results obtained from Laplacian smoothing.