Learning smooth objects by probing

Jean Daniel Boissonnat; Leonidas J. Guibas; Steve Oudot

doi:10.1145/1064092.1064124

Learning smooth objects by probing

Jean Daniel Boissonnat
, Leonidas J. Guibas
, Steve Oudot

INRIA
Stanford University

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

Abstract

We consider the problem of discovering a smooth unknown surface S bounding an object O in ℝ ³. 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 which 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	198-207
Number of pages	10
DOIs	https://doi.org/10.1145/1064092.1064124
Publication status	Published - 1 Dec 2005
Externally published	Yes
Event	21st Annual Symposium on Computational Geometry, SCG'05 - Pisa, Italy Duration: 6 Jun 2005 → 8 Jun 2005

Conference

Conference	21st Annual Symposium on Computational Geometry, SCG'05
Country/Territory	Italy
City	Pisa
Period	6/06/05 → 8/06/05

Keywords

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

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10.1145/1064092.1064124

Cite this

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title = "Learning smooth objects by probing",

abstract = "We consider the problem of discovering a smooth unknown surface S bounding an object O in ℝ 3. 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 which 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",

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month = dec,

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doi = "10.1145/1064092.1064124",

language = "English",

pages = "198--207",

note = "21st Annual Symposium on Computational Geometry, SCG'05 ; Conference date: 06-06-2005 Through 08-06-2005",

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TY - CONF

T1 - Learning smooth objects by probing

AU - Boissonnat, Jean Daniel

AU - Guibas, Leonidas J.

AU - Oudot, Steve

PY - 2005/12/1

Y1 - 2005/12/1

N2 - We consider the problem of discovering a smooth unknown surface S bounding an object O in ℝ 3. 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 which 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 ℝ 3. 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 which 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/33244476040

U2 - 10.1145/1064092.1064124

DO - 10.1145/1064092.1064124

M3 - Paper

AN - SCOPUS:33244476040

SP - 198

EP - 207

T2 - 21st Annual Symposium on Computational Geometry, SCG'05

Y2 - 6 June 2005 through 8 June 2005

ER -

Learning smooth objects by probing

Abstract

Conference

Keywords

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