Jet fitting 3: A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting
Identifieur interne : 004170 ( Main/Exploration ); précédent : 004169; suivant : 004171Jet fitting 3: A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting
Auteurs : Frédéric Cazals [France] ; Marc Pouget [France]Source :
- ACM Transactions on Mathematical Software [ 0098-3500 ] ; 2008.
Abstract
Surfaces of R3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in Computer Graphics, Computer Aided Design, Computational Geometry, Computer Vision. %% One strategy to perform such an estimation consists of resorting to polynomial fitting, either interpolation or approximation, but this route is difficult for several reasons: choice of the coordinate system, numerical handling of the fitting problem, extraction of the differential properties. This paper presents a generic C++ software package solving these problems. %% On the theoretical side and as established in a companion paper, the interpolation and approximation methods provided achieve the best asymptotic error bounds known to date. %% On the implementation side and following state-of-the-art coding rules in Computational Geometry, genericity of the package is achieved thanks to four template classes accounting for (a) the type of the input points (b) the internal geometric computations (c) a convertion mechanism between these two geometries and (d) the linear algebra operations. An instantiation within the Computational Geometry Algorithms Library (CGAL, version 3.3) and using LAPACK is also provided.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 002D25
- to stream Hal, to step Curation: 002D25
- to stream Hal, to step Checkpoint: 003614
- to stream Main, to step Merge: 004694
- to stream Main, to step Curation: 004170
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Jet fitting 3: A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting</title><author><name sortKey="Cazals, Frederic" sort="Cazals, Frederic" uniqKey="Cazals F" first="Frédéric" last="Cazals">Frédéric Cazals</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-51872" status="VALID"><idno type="RNSR">200818987H</idno><orgName>Algorithms, Biology, Structure</orgName><orgName type="acronym">ABS</orgName><desc><address><addrLine>2004 route des Lucioles, BP 9306902 Sophia-Antipolis</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/abs</ref></desc><listRelation><relation active="#struct-34586" type="direct"></relation><relation active="#struct-300009" type="indirect"></relation></listRelation><tutelles><tutelle active="#struct-34586" type="direct"><org type="laboratory" xml:id="struct-34586" status="VALID"><idno type="RNSR">198318250R</idno><orgName>Inria Sophia Antipolis - Méditerranée </orgName><orgName type="acronym">CRISAM</orgName><desc><address><addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre/sophia/</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2573" status="OLD"><idno type="RNSR">200518305E</idno><orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName><orgName type="acronym">VEGAS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/vegas</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:inria-00329731</idno><idno type="halId">inria-00329731</idno><idno type="halUri">https://hal.inria.fr/inria-00329731</idno><idno type="url">https://hal.inria.fr/inria-00329731</idno><date when="2008">2008</date><idno type="wicri:Area/Hal/Corpus">002D25</idno><idno type="wicri:Area/Hal/Curation">002D25</idno><idno type="wicri:Area/Hal/Checkpoint">003614</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">003614</idno><idno type="wicri:doubleKey">0098-3500:2008:Cazals F:jet:fitting:a</idno><idno type="wicri:Area/Main/Merge">004694</idno><idno type="wicri:Area/Main/Curation">004170</idno><idno type="wicri:Area/Main/Exploration">004170</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Jet fitting 3: A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting</title><author><name sortKey="Cazals, Frederic" sort="Cazals, Frederic" uniqKey="Cazals F" first="Frédéric" last="Cazals">Frédéric Cazals</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-51872" status="VALID"><idno type="RNSR">200818987H</idno><orgName>Algorithms, Biology, Structure</orgName><orgName type="acronym">ABS</orgName><desc><address><addrLine>2004 route des Lucioles, BP 9306902 Sophia-Antipolis</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/abs</ref></desc><listRelation><relation active="#struct-34586" type="direct"></relation><relation active="#struct-300009" type="indirect"></relation></listRelation><tutelles><tutelle active="#struct-34586" type="direct"><org type="laboratory" xml:id="struct-34586" status="VALID"><idno type="RNSR">198318250R</idno><orgName>Inria Sophia Antipolis - Méditerranée </orgName><orgName type="acronym">CRISAM</orgName><desc><address><addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre/sophia/</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author><author><name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2573" status="OLD"><idno type="RNSR">200518305E</idno><orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName><orgName type="acronym">VEGAS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/vegas</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic><series><title level="j">ACM Transactions on Mathematical Software</title><idno type="ISSN">0098-3500</idno><imprint><date type="datePub">2008</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="it"><term>Approximation</term><term>C++ design</term><term>Computational Geometry</term><term>Di</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Surfaces of R3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in Computer Graphics, Computer Aided Design, Computational Geometry, Computer Vision. %% One strategy to perform such an estimation consists of resorting to polynomial fitting, either interpolation or approximation, but this route is difficult for several reasons: choice of the coordinate system, numerical handling of the fitting problem, extraction of the differential properties. This paper presents a generic C++ software package solving these problems. %% On the theoretical side and as established in a companion paper, the interpolation and approximation methods provided achieve the best asymptotic error bounds known to date. %% On the implementation side and following state-of-the-art coding rules in Computational Geometry, genericity of the package is achieved thanks to four template classes accounting for (a) the type of the input points (b) the internal geometric computations (c) a convertion mechanism between these two geometries and (d) the linear algebra operations. An instantiation within the Computational Geometry Algorithms Library (CGAL, version 3.3) and using LAPACK is also provided.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><noRegion><name sortKey="Cazals, Frederic" sort="Cazals, Frederic" uniqKey="Cazals F" first="Frédéric" last="Cazals">Frédéric Cazals</name></noRegion><name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 004170 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 004170 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= Hal:inria-00329731
|texte= Jet fitting 3: A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting
}}
| This area was generated with Dilib version V0.6.33. |  |