Substructure Topology Preserving Simplification of Tetrahedral Meshes
| Autor: | Fabien Vivodtzev, Georges-Pierre Bonneau, Stefanie Hahmann, Hans Hagen |
|---|---|
| Přispěvatelé: | Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), Valerio Pascucci and Xavier Tricoche and Hans Hagen and Julien Tierny |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Collapse (topology)
Shape 020207 software engineering 02 engineering and technology Volume mesh Combinatorial topology Topology [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] Domain (software engineering) Simplicial complex 0202 electrical engineering electronic engineering information engineering Substructure 020201 artificial intelligence & image processing Topology (chemistry) Geometry and topology Mathematics ComputingMethodologies_COMPUTERGRAPHICS |
| Zdroj: | Topological Methods in Data Analysis and Visualization Valerio Pascucci and Xavier Tricoche and Hans Hagen and Julien Tierny. Topological Methods in Data Analysis and Visualization, Springer, pp.55-66, 2011, Mathematics and Visualization, 978-3-642-15013-5. ⟨10.1007/978-3-642-15014-2_5⟩ Mathematics and Visualization ISBN: 9783642150135 |
| DOI: | 10.1007/978-3-642-15014-2_5⟩ |
| Popis: | International audience; Interdisciplinary efforts in modeling and simulating phenomena have led to complex multi-physics models involving different physical properties and materials in the same system. Within a 3d domain, substructures of lower dimensions appear at the interface between different materials. Correspondingly, an unstructured tetrahedral mesh used for such a simulation includes 2d and 1d substructures embedded in the vertices, edges and faces of the mesh. The simplification of such tetrahedral meshes must preserve (1) the geometry and the topology of the 3d domain, (2) the simulated data and (3) the geometry and topology of the embedded substructures. Although intensive research has been conducted on the first two goals, the third objective has received little attention. This paper focuses on the preservation of the topology of 1d and 2d substructures embedded in an unstructured tetrahedral mesh, during edge collapse simplification. We define these substructures as simplicial sub-complexes of the mesh, which is modeled as an extended simplicial complex. We derive a robust algorithm, based on combinatorial topology results, in order to determine if an edge can be collapsed without changing the topology of both the mesh and all embedded substructures. Based on this algorithm we have developed a system for simplifying scientific datasets defined on irregular tetrahedral meshes with substructures. The implementation of our system is discussed in detail. We demonstrate the power of our system with real world scientific datasets from electromagnetism simulations. |
| Databáze: | OpenAIRE |
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