Local Surface Approximation and its Application to Smoothing in Three-dimensional Indirect Mesh Generation

Smoothing techniques are of major importance for the generation of surface meshes. For this reason a considerable amount of research has been spent on developing a large variety of sophisticated smoothing approaches. However, these methods either require direct access to the analytic surface description or are restricted to flat meshes in two dimensions. In particular, if no analytic surface data is available as in the case of indirect mesh generation, it is not possible to reposition nodes on a three-dimensional geometry. To cope with this problem, this paper presents an approach based on the local approximation of an analytic surface which is used for repositioning nodes when smoothing is performed. Furthermore, the paper shows how established two-dimensional smoothing techniques such as length smoothing, angle smoothing and isoparametric smoothing are adapted to three dimensions by combining them with the local surface approximation. A quadrilateral mesh generator that implements the presented techniques finally demonstrates the benefits of this approach.