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3 results on '"tolerance volume"'

2. Isotopic approximation within a tolerance volume.

Author

Mandad, Manish, Cohen-Steiner, David, and Alliez, Pierre

Subjects
ALGORITHMS, NUMERICAL grid generation (Numerical analysis), TOPOLOGY, TRIANGULATION, MATHEMATICAL functions, GEOMETRIC surfaces
Abstract

We introduce in this paper an algorithm that generates from an input tolerance volume a surface triangle mesh guaranteed to be within the tolerance, intersection free and topologically correct. A pliant meshing algorithm is used to capture the topology and discover the anisotropy in the input tolerance volume in order to generate a concise output. We first refine a 3D Delaunay triangulation over the tolerance volume while maintaining a piecewise-linear function on this triangulation, until an isosurface of this function matches the topology sought after. We then embed the isosurface into the 3D triangulation via mutual tessellation, and simplify it while preserving the topology. Our approach extends to surfaces with boundaries and to non- manifold surfaces. We demonstrate the versatility and efficacy of our approach on a variety of data sets and tolerance volumes. [ABSTRACT FROM AUTHOR]

Published
2015
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3. Isotopic Approximation within a Tolerance Volume

Author

Manish Mandad, David Cohen-Steiner, Pierre Alliez, Geometric Modeling of 3D Environments (TITANE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Understanding the Shape of Data (DATASHAPE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 257474,EC:FP7:ERC,ERC-2010-StG_20091028,IRON(2011), and European Project: 339025,EC:FP7:ERC,ERC-2013-ADG,GUDHI(2014)

Subjects
Surface (mathematics), 0102 computer and information sciences, 02 engineering and technology, intersection-free, Computer Science::Computational Geometry, Topology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Isosurface, Triangle mesh, 0202 electrical engineering, electronic engineering, information engineering, Isotopic approximation, Topology (chemistry), Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, Tessellation, Delaunay triangulation, Triangulation (social science), 020207 software engineering, Function (mathematics), mesh simplification, Computer Graphics and Computer-Aided Design, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, tolerance volume, mutual tessellation, 010201 computation theory & mathematics, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], mesh refinement
Abstract

International audience; We introduce in this paper an algorithm that generates from an input tolerance volume a surface triangle mesh guaranteed to be within the tolerance, intersection free and topologically correct. A pliant meshing algorithm is used to capture the topology and discover the anisotropy in the input tolerance volume in order to generate a concise output. We first refine a 3D Delaunay triangulation over the tolerance volume while maintaining a piecewise-linear function on this triangulation, until an isosurface of this function matches the topology sought after. We then embed the isosurface into the 3D triangulation via mutual tessellation, and simplify it while preserving the topology. Our approach extends to surfaces with boundaries and to non-manifold surfaces. We demonstrate the versatility and efficacy of our approach on a variety of data sets and tolerance volumes.

Published
2015
Full Text
View/download PDF

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