Dihedral angle-based maps of tetrahedral meshes
Identifieur interne : 000408 ( Main/Exploration ); précédent : 000407; suivant : 000409Dihedral angle-based maps of tetrahedral meshes
Auteurs : Gilles-Philippe Paillé [Canada] ; Nicolas Ray [France] ; Pierre Poulin [Canada] ; Alla Sheffer [Canada] ; Bruno Lévy [France]Source :
Abstract
We present a geometric representation of a tetrahedral mesh that is solely based on dihedral angles. We first show that the shape of a tetrahedral mesh is completely defined by its dihedral angles. This proof leads to a set of angular constraints that must be satisfied for an immersion to exist in R3. This formulation lets us easily specify conditions to avoid inverted tetrahedra and multiply-covered vertices, thus leading to locally injective maps. We then present a constrained optimization method that modifies input angles when they do not satisfy constraints. Additionally, we develop a fast spectral reconstruction method to robustly recover positions from dihedral angles. We demonstrate the applicability of our representation with examples of volume parameterization, shape interpolation, mesh optimization, connectivity shapes, and mesh compression.
Url:
DOI: 10.1145/2766900
Affiliations:
- Canada, France
- Grand Est, Lorraine (région)
- Metz, Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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<front><div type="abstract" xml:lang="en">We present a geometric representation of a tetrahedral mesh that is solely based on dihedral angles. We first show that the shape of a tetrahedral mesh is completely defined by its dihedral angles. This proof leads to a set of angular constraints that must be satisfied for an immersion to exist in R3. This formulation lets us easily specify conditions to avoid inverted tetrahedra and multiply-covered vertices, thus leading to locally injective maps. We then present a constrained optimization method that modifies input angles when they do not satisfy constraints. Additionally, we develop a fast spectral reconstruction method to robustly recover positions from dihedral angles. We demonstrate the applicability of our representation with examples of volume parameterization, shape interpolation, mesh optimization, connectivity shapes, and mesh compression.</div>
</front>
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<affiliations><list><country><li>Canada</li>
<li>France</li>
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<region><li>Grand Est</li>
<li>Lorraine (région)</li>
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<settlement><li>Metz</li>
<li>Nancy</li>
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<orgName><li>Institut national polytechnique de Lorraine</li>
<li>Université Nancy 2</li>
<li>Université de Lorraine</li>
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<tree><country name="Canada"><noRegion><name sortKey="Paille, Gilles Philippe" sort="Paille, Gilles Philippe" uniqKey="Paille G" first="Gilles-Philippe" last="Paillé">Gilles-Philippe Paillé</name>
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<name sortKey="Poulin, Pierre" sort="Poulin, Pierre" uniqKey="Poulin P" first="Pierre" last="Poulin">Pierre Poulin</name>
<name sortKey="Sheffer, Alla" sort="Sheffer, Alla" uniqKey="Sheffer A" first="Alla" last="Sheffer">Alla Sheffer</name>
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<country name="France"><region name="Grand Est"><name sortKey="Ray, Nicolas" sort="Ray, Nicolas" uniqKey="Ray N" first="Nicolas" last="Ray">Nicolas Ray</name>
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