Maria Savchenko

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.

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.

Finite element simulation of robotic origami folding

Abstract In this paper, we focus on some aspects of the finite element simulations of robotic paper folding and the reconstruction of models from the origami crease patterns by the robot arms. The paper highlights the simulation problems, which should be solved in developing our recent study in mechanical and geometrical design of the origami-performing robot. The basic premise underlying the study is that folding operations with the origami crease patterns are considered as the functions of the mechanical systems such as a robot. Manipulations with the foldable objects, such as a sheet of paper (the origami crease pattern), by the robot arms in the simulation environment lead to understanding the design of the origami-performing robot without testing physical prototypes at each design stage. In this case, dynamic and kinematic behavior of the robot arms in forming the 3D origami objects is modelled by using the finite element method (FEM) in LS-DYNA solver. For simulating, two forms of origami are considered: flexible, if bending is used for paper folding, and rigid, if origami patterns are considered as the kinematic systems. Results of the simulation are presented and provided by the illustrations.

A Color Mapping Method for Decimated Model

In this paper we present a method for coloring the surface of the decimated mesh with an original texture without reparametrization. This approach combines the generation of the dense triangle mesh on each mesh element with the vertex color interpolation across the planes of the new generated triangles. The proposed method minimizes the texture distortion that is obtained by the displacement of points on the mesh during the decimation processing. The suggested approach provides transformation of an original model with texture at-tributes to the model with the decreased size and color-mapped surface.

Polygonal Mesh Partitioning for NURBS Surface Generation

Surface reconstruction and NURBS surface generation based on 3D surface mesh partitioning are more essential today. In this paper, we present a new method of automatic partitioning complex surface meshes into the bounded regions with four corner points (quadrilateral regions) based on using control points (notches) for NURBS surface generation. The procedure of this method consists of 4 major steps: (1) the 3D polygons mapping into 2D polygons; (2) convex decomposition of the polygons in the 2D space; (3) subdivision of each polygons into quadrilateral regions; (4) mapping the received 2D regions onto the 3D original surface mesh. Main contribution in this paper is automatic partitioning of the 3D segmented parts of complex surfaces into quadrilateral regions based on combination of segmentation, mapping, and subdivision techniques. Automatic partitioning allows us to create not rectangular but quadrilateral regions without using any user-dependent parameters for further NURBS surface generation.

A Novel Tetrahedral Mesh Generation Algorithm for Finite Element Analysis

In this paper, a robust tetrahedral mesh generation method based on Advancing Front technique is proposed. The proposed method inherits advantages of Delaunay method and Advancing Front method, such as efficiency of Delaunay method and maintaining the given boundary triangle mesh exactly of advancing front method. Tetrahedral mesh is generated from the given triangle surface mesh. This method mainly includes three stages. Firstly, the minimum container box of the triangular surface mesh is calculated and points are inserted into the box. Then the proper point is selected out to generate tetrahedron’s layers from surface to the interior volume of the model, so g the surface mesh can be maintained. The operation is simplified, and calculation efficiency is also higher than common Advancing Front method. At last, triangle intersection is examined. This technique allows generating the tetrahedral mesh with high quality elements with surface mesh preservation. A shoes model with both convex and concave surface is chosen for the experiment. The result clarified the robust and high efficiency of the proposed algorithm.

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.