A surface mesh smoothing and untangling method independent of the CAD parameterization

A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar ele...

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Veröffentlicht in:	Computational mechanics Jg. 53; H. 4; S. 587 - 609
Hauptverfasser:	Gargallo-Peiró, Abel, Roca, Xevi, Sarrate, Josep
Format:	Journal Article Verlag
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014 Springer Springer Nature B.V
Schlagworte:	90B Operations research and management science 90C Mathematical programming Analysis Business relocation CAD surfaces Classical and Continuum Physics Computation Computational Science and Engineering Computer aided design Computer graphics Distortion Engineering IMPROVEMENT INITIAL MESHES Investigació operativa Matemàtiques i estadística Mathematical models Mesh optimization Mesh quality Methods Nodes Operations research Optimització Optimització i investigació operativa OPTIMIZATION Original Paper Parameterization Parametrization Programació (Matemàtica) Programming (Mathematics) Quadrilaterals QUALITY METRICS Smoothing Smoothing and untangling Theoretical and Applied Mechanics TRIANGULATIONS Àrees temàtiques de la UPC Mesh optimization CAD surfaces Mesh quality Smoothing and untangling
ISSN:	0178-7675, 1432-0924
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Abstract	A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces.
AbstractList	A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces. A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces. Keywords Mesh quality * Mesh optimization * Smoothing and untangling * CAD surfaces; A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces. Peer Reviewed
Audience	Academic
Author	Gargallo-Peiró, Abel Sarrate, Josep Roca, Xevi
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Contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
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Snippet	A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface...
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SubjectTerms	90B Operations research and management science 90C Mathematical programming Analysis Business relocation CAD surfaces Classical and Continuum Physics Computation Computational Science and Engineering Computer aided design Computer graphics Distortion Engineering IMPROVEMENT INITIAL MESHES Investigació operativa Matemàtiques i estadística Mathematical models Mesh optimization Mesh quality Methods Nodes Operations research Optimització Optimització i investigació operativa OPTIMIZATION Original Paper Parameterization Parametrization Programació (Matemàtica) Programming (Mathematics) Quadrilaterals QUALITY METRICS Smoothing Smoothing and untangling Theoretical and Applied Mechanics TRIANGULATIONS Àrees temàtiques de la UPC
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Title	A surface mesh smoothing and untangling method independent of the CAD parameterization
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