Learning smooth shapes by probing

Jean Daniel Boissonnat; Leonidas J. Guibas; Steve Oudot

doi:10.1016/j.comgeo.2006.05.008

Learning smooth shapes by probing

Jean Daniel Boissonnat
, Leonidas J. Guibas
, Steve Oudot

INRIA
Stanford University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problem of discovering a smooth unknown surface S bounding an object O in ^R3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated that approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.

Original language	English
Pages (from-to)	38-58
Number of pages	21
Journal	Computational Geometry: Theory and Applications
Volume	37
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.comgeo.2006.05.008
Publication status	Published - 1 Jan 2007
Externally published	Yes

Keywords

Blind surface approximation
Delaunay refinement
Interactive surface reconstruction
Manifold learning
Surface meshing

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10.1016/j.comgeo.2006.05.008

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title = "Learning smooth shapes by probing",

abstract = "We consider the problem of discovering a smooth unknown surface S bounding an object O in R3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated that approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.",

keywords = "Blind surface approximation, Delaunay refinement, Interactive surface reconstruction, Manifold learning, Surface meshing",

author = "Boissonnat, \{Jean Daniel\} and Guibas, \{Leonidas J.\} and Steve Oudot",

year = "2007",

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journal = "Computational Geometry: Theory and Applications",

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T1 - Learning smooth shapes by probing

AU - Boissonnat, Jean Daniel

AU - Guibas, Leonidas J.

AU - Oudot, Steve

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We consider the problem of discovering a smooth unknown surface S bounding an object O in R3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated that approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.

AB - We consider the problem of discovering a smooth unknown surface S bounding an object O in R3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated that approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.

KW - Blind surface approximation

KW - Delaunay refinement

KW - Interactive surface reconstruction

KW - Manifold learning

KW - Surface meshing

UR - https://www.scopus.com/pages/publications/33847092586

U2 - 10.1016/j.comgeo.2006.05.008

DO - 10.1016/j.comgeo.2006.05.008

M3 - Article

AN - SCOPUS:33847092586

SN - 0925-7721

VL - 37

SP - 38

EP - 58

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 1 SPEC. ISS.

ER -

Learning smooth shapes by probing

Abstract

Keywords

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