Olga Egorova

Mesh quality improvement: radial basis functions approach

In this paper, we present a novel simple method, based on an implementation of space mapping technique, for improvement of the quality of tetrahedral and hexahedral meshes. The same approach is used for surface meshes where geometry of the initial surface mesh is preserved by a local mesh improvement such that new positions of the interior nodes of the mesh remain on the original discrete surface. The proposed method can be used in the pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.

Mesh generation and refinement of polygonal data sets

This paper presents work in progress and continues a project devoted to developing shape modeling system based on implementation of radial based function (RBF) technology. In this paper, we study the opportunities offered by this technology to computer-aided design and computer graphics communities by looking at the problems of surface generation and enhancement. Experimental results are included to demonstrate the functionality of our mesh-modeling tool.

Modeling of Quality Parameter Values for Improving Meshes

A novel quasi-statistical approach to improve the quality of triangular meshes is presented. The present method is based on modeling of an event of the mesh improvement. This event is modeled via modeling of a discrete random variable. The random variable is modeled in a tangent plane of each local domain of the mesh. One domain collects several elements with a common point. Values of random variable are calculated by modeling formula according to the initial sampling data of the projected elements with respect to all neighbors of the domain. Geometrical equivalent called potential form is constructed for each element of the domain with a mesh quality parameter value equal to the modeled numerical value. Such potential forms create potential centers of the domain. Averaging the coordinates of potential centers of the domain gives a new central point position. After geometrical realization over the entire mesh, the shapes of triangular elements are changed according to the normal distribution. It is shown experimentally that the mean of the final mesh is better than the initial one in most cases, so the event of the mesh improvement is likely occurred. Moreover, projection onto a local tangent plane included in the algorithm allows preservation of the model volume enclosed by the surface mesh. The implementation results are presented to demonstrate the functionality of the method. Our approach can provide a flexible tool for the development of mesh improvement algorithms, creating better-input parameters for the triangular meshes and other kinds of meshes intended to be applied in finite element analysis or computer graphics.

Characteristic Topology Method for Quadrilateral Mesh Without Self-Intersection of Dual Cycles

The Dual Cycle Elimination method was proposed by Muller-Hannemann for hexahedral mesh generation. The method begins with a surface quadrilateral mesh whose dual cycles have no self-intersections and, after the elimination of dual cycles, a hexahedral mesh is generated while tracing back the reverse order of eliminations and supplementing hexahedrons inside the object step by step. This paper presents the Characteristic Topology Method as a means to prescribe a quadrilateral surface mesh that can be initial data for further hexahedral mesh generation. The goal of this method is to stress the topology of the given surface and thus use construction of the loops within the algorithm. The surface is given in a nodal polygonal model and then decomposed into a triangle-quadrilateral model. Templates are used to determine the loops. Then due to some rules every loop is implemented by special additional Dual Cycles. The total mesh is the dual graph to the graph of dual cycles. The problem of self-intersections that may appear comes from Muller-Hannemann’s approach stated above and that is also implemented in this work as a sketch.Copyright

On the selection of a platonic solid for mesh segmentation

In present paper we propose a method for optimization of the choice of the platonic solid which is used for triangular mesh segmentation. Our approach is based on the idea to apply the platonic solids for surface mesh segmentation. The main contribution of this paper is the selection of the best platonic solid for a given model by finding the optimum value of a cost function with many local minima. Two functions are proposed for the selection of the best platonic solid to be used in a real application. Thanks to the proposed functions, the selection of the best model is done automatically. Experimental results show that method can be applied as guidance for shape modeling in reverse engineering.