A new characterization of simple elements in a tetrahedral mesh

This paper deals with topological analysis of sets of tetrahedra (“tetrahedral meshes” of three-dimensional objects). We introduce a definition of simple elements for any normal tetrahedral representation. Then we prove a local characterization of simple tetrahedra in the case of a scene composed of...

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Bibliographic Details
Published in:Graphical models 2005-07, Vol.67 (4), p.260-284
Main Authors: Bloch, Isabelle, Pescatore, Jérémie, Garnero, Line
Format: Article
Language:English
Subjects:
3D topology
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Finite element meshes
Homology
Local topological characterization
Pattern recognition. Digital image processing. Computational geometry
Simple tetrahedron
Tetrahedral mesh
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Summary:This paper deals with topological analysis of sets of tetrahedra (“tetrahedral meshes” of three-dimensional objects). We introduce a definition of simple elements for any normal tetrahedral representation. Then we prove a local characterization of simple tetrahedra in the case of a scene composed of one object and its background, based on homology groups and on relative homology. This allows us to define homotopic deformations of a tetrahedral representation. Using this characterization, we illustrate the problem of generating three-dimensional finite element meshes from medical voxel datasets.
ISSN:1524-0703
1524-0711
DOI:10.1016/j.gmod.2004.12.001