Chapter 10: Variational tetrahedral meshing

Pierre Alliez; David Cohen-Steiner; Mariette Yvinec; Mathieu Desbrun

doi:10.1145/1198555.1198669

Chapter 10: Variational tetrahedral meshing

Pierre Alliez
, David Cohen-Steiner
, Mariette Yvinec
, Mathieu Desbrun

Research output: Contribution to conference › Paper › peer-review

Abstract

In this chapter, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the L1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.

Original language	English
DOIs	https://doi.org/10.1145/1198555.1198669
Publication status	Published - 31 Jul 2005
Externally published	Yes
Event	ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005 - Los Angeles, United States Duration: 31 Jul 2005 → 4 Aug 2005

Conference

Conference	ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005
Country/Territory	United States
City	Los Angeles
Period	31/07/05 → 4/08/05

Keywords

Delaunay mesh
Isotropic meshing
Sizing field
Slivers

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10.1145/1198555.1198669

Cite this

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title = "Chapter 10: Variational tetrahedral meshing",

abstract = "In this chapter, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the L1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.",

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day = "31",

doi = "10.1145/1198555.1198669",

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TY - CONF

T1 - Chapter 10

T2 - ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005

AU - Alliez, Pierre

AU - Cohen-Steiner, David

AU - Yvinec, Mariette

AU - Desbrun, Mathieu

PY - 2005/7/31

Y1 - 2005/7/31

N2 - In this chapter, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the L1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.

AB - In this chapter, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the L1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.

KW - Delaunay mesh

KW - Isotropic meshing

KW - Sizing field

KW - Slivers

U2 - 10.1145/1198555.1198669

DO - 10.1145/1198555.1198669

M3 - Paper

AN - SCOPUS:84929567289

Y2 - 31 July 2005 through 4 August 2005

ER -

Chapter 10: Variational tetrahedral meshing

Abstract

Conference

Keywords

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