An Approach to Improving Triangular Surface Mesh

Our method is based on an implementation of quasi-statistical modeling for improving meshes by producing mesh elements with modeled values of different mesh quality parameters. In this paper we implement this approach to triangular surface mesh. Considering the initial distribution of the mesh quality parameter values, we assume that after improvement the distribution of elements of the mesh varies from a rather random distribution to a smoother one, such as a normal distribution. The preliminary choice of the desirable distribution affects the new parameter values modeled by the formula presented here. Uncertainty of the smoothed vertex positions of the mesh element affords to use a statistical approach in sense of random variable modeling to connect quasi-statistical modeling and mesh improvement techniques. The so-called “kernel” method allows creating different applicable to a mesh processing algorithms, which can be interpreted as a kind of smoothing technique to determine vertex direction movement with the distribution control of the shape of mesh elements. An aspect ratio is mainly used in present research as a mesh quality parameter. The geometry of the initial mesh surface is preserved by local mesh improving such that the new positions of the interior nodes of the mesh remain on the original discrete surface. Our method can be interpreted as a kind of smoothing technique with using the distribution control of the mesh quality parameter values. This method is comparable with optimization-based approach for avoiding the invalid elements of the mesh by producing a mesh with a rather homogeneous distribution of the mesh elements. Experimental results are included to demonstrate the functionality of our method. This method can be used at a pre-process stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing the better-input parameters for these processes.