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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Vydáno v:Computational mechanics Ročník 53; číslo 4; s. 587 - 609
Hlavní autoři: Gargallo-Peiró, Abel, Roca, Xevi, Sarrate, Josep
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014
Springer
Springer Nature B.V
Témata:
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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Shrnutí: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.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-013-0920-1