Development of Mesh Modification System for
Finite Element Simulations Using CAVE Environments
Satoshi Tanaka1, Kazuo Kashiyama1, Akira Kageyama2 and Nobuaki Ohno3
11

Graduate School of Science and Engineering, Chuo University, Japan
2
Graduate School of System Informatics, Kobe University, Japan
3
Graduate School of Simulation Studies, University of Hyogo, Japan

Introduction

The three dimensional finite element simulations arebecoming more powerful and popular tool for various CAE(Computational Aided Engineering) problems in accordancewith the development of hard- and software of computers.
However, the following problem is pointed out in pre-process
for practical computations as: it is difficult to check and modify
the quality of mesh for the complicated spatial domain, since themesh normally express on the 2D screen or display.
This paper presents an interactive mesh modification system
based on the virtual reality technology for large scale three
dimensional finite element simulations in order to overcome theproblem.
The present authors have been presented a prototype system
for the mesh modification [1]. Users can check the details of
three dimensional mesh structures and can modify the shape ofmesh idealization in VR space interactively by using thecontroller. However, as the node relocation method was onlyemployed for the mesh modification method, the improvementof mesh quality was not sufficient. In order to improve the mesh
quality sufficiently, the mesh refinement method is introduced
as a new mesh modification method in this paper.
23Mesh Modification System

Users can investigates the details of three dimensional meshstructures and to improve the mesh quality interactively in VR
space by the present system. For the finite element mesh, thefour nodes linear tetrahedral element is employed. The presentsystems are developed by the VR programming languages,
Open GL and CAVE library.
3.1

Flow Chart
FIG. 2 shows the flow chart of the present system. First, themesh quality is computed, and then the mesh quality isimproved by the mesh modification by both mesh relocation andmesh refinement methods. Users can select the modification
method from the menu which is displayed in the VR space.
Users can change the nodal position of the bad quality elementin the node relocation method, and can refine the bad quality
element in the mesh refinement method. The modification
method by mesh refinement is added as a new modification
method to the conventional system [1].

CAVE Environments

The present systems are designed for the use of virtual
reality system based on IPT (Immersive Projection Technology)
such as CAVE [2]. The stereoscopic view is realized in VR
space by creating the images that corresponds to binocularretinal images. Fig. 1 shows the exterior view of the VR system“Holostage” of Chuo University, which consists of a PC cluster(one master-PC and four-slave-PC), three projectors, three large
screens and a position tracking system. The stereoscopic image
from the arbitrary viewpoint of observer is displayed in VRspace by the position tracking system.

Fig.2 Flow Chart
3.2

Fig.1 CAVE system

Input data and mesh quality
The mesh data is prepared for the input data for preprocessing system. The four nodes tetrahedral element isemployed for the finite element. The Delaunay triangulation
method [3] is employed for the mesh generator.
The mesh quality Qm can be evaluated by the followingequation [4].

3

 1 6 2 2
  Li 6Qm   i1 
8.4796V(1)

where Li denotes the length of the edge of the element, V is thevolume of the element. The mesh quality is to be 1 if theelement is to be a regular tetrahedron and the value is to be bigvalue if the element becomes a bent element. In this system, theelements which exceed the setting value for mesh quality aredisplayed by the red color in VR space.
Modification by mesh refinement method
In the modification by mesh refinement, the elements which
exceed the setting value for mesh quality are refined. Users canspecify the element by using the controller. If users move the tipof beam generated from the controller to the inside of theelement and click the button, then the element can be specified.
In order to investigate the judgment that the element includes
the tip of beam or not, the mapping method using a generalized
coordinate system is employed. Fig. 3 shows two patterns ofmesh refinement methods. The new node is generated at thecentroid of the element and the element is subdivided into four
smaller elements in case (a). The new nodes are generated on
the edge of the element and the element is subdivided into eightsmaller elements in case (b). In case (b), the effect of meshrefinement is influenced to the neighbouring elements.

introduced for the nodes on the boundary. The condition isprepared by the geographical information, which is obtained by
the mesh data. Fig. 4 shows the example for the mesh around a
cubic structure. The nodes at the apex (gray nodes in Fig. 4) are
assumed to be fixed point. The nodes on the edge-line of thestructure (red nodes) can move on the edge-line only. The nodes
on the surface of the structure (green nodes) can move on thesurface of the boundary only. The nodes in the computational
domain (blue nodes) can move to any direction. In this system,
if the element violates the geometrical shape by the noderelocation, the element is displayed by the green color in VRspace.

3.3

4Application Example

The present method is applied to the three dimensional finite
element analysis of over-dentures using dental implants. Fig. 5shows the scene the user modifies the mesh idealization
manually using the controller. The mesh quality is improved andthe high quality computation is realized by the application of thepresent system. More detail discussion will be shown in the fullpaper.

Fig. 5 Mesh modification using controller in VR space
5Fig. 3 Mesh refinement methods

Conclusion

The interactive mesh modification systems based on thevirtual reality technology for three dimensional finite element
simulations have been developed. Users can improve thenumerical accuracy and stability by using the mesh modification
system based on node relocation and mesh refinement. From
this, it can be concluded that the present system provides auseful tool to realize the high quality computing for three
dimensional finite element simulations.
References
[1]

[2]

Fig. 4 Node movement condition
Modification by node relocation method
The modification method by node relocation is alsoavailable in order to improve the mesh quality. However, therestriction condition for the mesh movement is required to not
violate the geometrical shape by the node relocation. In order toavoid this problem, the node movement condition must be

[3]

3.4

[4]

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