There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Photoplethysmography and its application in clinical physiological measurement

Computer-Aided Geometric Design

Mesh smoothing using the Geometric Element Transformation Method

The geometric element transformation method for tetrahedral mesh smoothing

Finite element simulation of robotic origami folding

Flexible mesh morphing in sustainable design using data mining and mesh subdivision

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 quality improvement: radial basis functions approach

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.

An Approach to Improving Triangular Surface Mesh

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.

Maria Savchenko

Papers

Finite element simulation of robotic origami folding

Flexible mesh morphing in sustainable design using data mining and mesh subdivision

Mesh quality improvement: radial basis functions approach

An Approach to Improving Triangular Surface Mesh

On the selection of a platonic solid for mesh segmentation