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The Algorithm Research on Sphere Approximation and Tetrahedralization of3D Mesh Models

Author: WangJunLiang
Tutor: LiZhong
School: Zhejiang University of Technology
Course: Basic mathematics
Keywords: Model approximation Inner sphere Sphere clustering Tetrahedralization Laplaciancoordinates Tetrahedron optimization
CLC: TP391.41
Type: Master's thesis
Year: 2014
Downloads: 4
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Abstract

The algorithm of sphere approximation and tetrahedralization is the basis algorithm ofcomputer graphics. It can provide a good solution method as pretreatment for the technology ofvirtual reality simulation such as model approximation, collision detection, model segmentation,finite element analysis. And it has important applications in computer animation, computergames, medical visualization and other fields.At the current study, the most existing methods of sphere approximation are commonly havesome problems such as more number of units, poor quality of tightness in sphere units. At thesame time, the methods of tetrahedralization have some problems such as poor quality ofapproximation and undesirable units in tetrahedral meshes. In order to achieve a fast collisiondetection and finite element analysis between objects, this paper proposes improved algorithmsabout sphere approximation and tetrahedralization of3D mesh model. Details are as follows:(1) Provide an overview of the research background and research status about sphereapproximation algorithm and tetrahedralization method of3D mesh model, and the summary ofsome basis technologies of the algorithm.(2) The algorithm about sphere approximation of3D mesh model is proposed. It firstlypresents a novel3D model approximation method with inner spheres based on three-dimensionalmodel voxelization. It also reduces the number of inner spheres and enhances the sphereconnectivity. And the boundary voxels were subdivided to improve the effect of approximationwhen at lower voxel resolution. Then this approach improves the inner sphere clustering basedon the geodesic distance. It obtains meaningful clustering results which can be applied in manyapplications such as the structure construction of hierarchical inner sphere-trees and the semanticsegmentation of3D models.(3) The algorithm about tetrahedralization of3D mesh model is proposed. It firstly uses the principal component analysis of3D model as pre-processing to optimize the initial position ofthe model, and then builds the initial tetrahedron based on body-centered cubic. It computes thecutting point through comparing the intersection between the edge of the original tetrahedron andthe model after getting the node’s symbol of body-centered cubic. It also improved the movablemanner of cut point on the boundary to keep the local characteristics of the model. At last, theerror function of energy with density based on the quality of meshes was used to optimize thequality of the tetrahedral mesh.(4) This paper combines the use of VC++, MFC and OpenGL graphics library to realize thealgorithm. Experimental results demonstrate the feasibility and effectiveness of these methods.Finally, this paper summarizes the work of this project and its research results, and furtherpoints out that the main problems even existed and discusses the research directions of the futurework.

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