An elementary digital plane recognition algorithm
Identifieur interne : 006379 ( Main/Exploration ); précédent : 006378; suivant : 006380An elementary digital plane recognition algorithm
Auteurs : Y. Gerard [France] ; I. Debled-Rennesson [France] ; P. Zimmermann [France]Source :
- Discrete applied mathematics [ 0166-218X ] ; 2005.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
A naive digital plane is a subset of points (x, y, z) ∈ Z3 verifying h ≤ ax + by + cz < h + max{|a|, |b|, |c|}, where (a, b, c, h) ∈ Z4. Given a finite unstructured subset of Z3, the problem of the digital plane recognition is to determine whether there exists a naive digital plane containing it. This question is rather classical in the field of digital geometry (also called discrete geometry). We suggest in this paper a new algorithm to solve it. Its asymptotic complexity is bounded by O(n7) but its behavior seems to be linear in practice. It uses an original strategy of optimization in a set of triangular facets (triangles). The code is short and elementary (less than 300 lines) and available on http://www.loria.fr/∼debled/plane.
Affiliations:
- France
- Auvergne (région administrative), Auvergne-Rhône-Alpes, Grand Est, Lorraine (région)
- Aubière, Villers-lès-Nancy
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Le document en format XML
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Debled-Rennesson</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, INRIA Lorraine, 615 rue du Jardin Botanique, BP 101</s1><s2>54600 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Zimmermann, P" sort="Zimmermann, P" uniqKey="Zimmermann P" first="P." last="Zimmermann">P. Zimmermann</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, INRIA Lorraine, 615 rue du Jardin Botanique, BP 101</s1><s2>54600 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">05-0447898</idno><date when="2005">2005</date><idno type="stanalyst">PASCAL 05-0447898 INIST</idno><idno type="RBID">Pascal:05-0447898</idno><idno type="wicri:Area/PascalFrancis/Corpus">000511</idno><idno type="wicri:Area/PascalFrancis/Curation">000527</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000523</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000523</idno><idno type="wicri:doubleKey">0166-218X:2005:Gerard Y:an:elementary:digital</idno><idno type="wicri:Area/Main/Merge">006660</idno><idno type="wicri:Area/Main/Curation">006379</idno><idno type="wicri:Area/Main/Exploration">006379</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">An elementary digital plane recognition algorithm</title><author><name sortKey="Gerard, Y" sort="Gerard, Y" uniqKey="Gerard Y" first="Y." last="Gerard">Y. Gerard</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>LLAIC, IUT, Ensemble Universitaire des Cézeaux</s1><s2>63172 Aubière</s2><s3>FRA</s3><sZ>1 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Auvergne-Rhône-Alpes</region><region type="old region" nuts="2">Auvergne (région administrative)</region><settlement type="city">Aubière</settlement></placeName></affiliation></author><author><name sortKey="Debled Rennesson, I" sort="Debled Rennesson, I" uniqKey="Debled Rennesson I" first="I." last="Debled-Rennesson">I. Debled-Rennesson</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, INRIA Lorraine, 615 rue du Jardin Botanique, BP 101</s1><s2>54600 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Zimmermann, P" sort="Zimmermann, P" uniqKey="Zimmermann P" first="P." last="Zimmermann">P. Zimmermann</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, INRIA Lorraine, 615 rue du Jardin Botanique, BP 101</s1><s2>54600 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Discrete applied mathematics</title><title level="j" type="abbreviated">Discrete appl. math.</title><idno type="ISSN">0166-218X</idno><imprint><date when="2005">2005</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Discrete applied mathematics</title><title level="j" type="abbreviated">Discrete appl. math.</title><idno type="ISSN">0166-218X</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Chord set</term><term>Complexity</term><term>Computer theory</term><term>Digital plane</term><term>Discrete geometry</term><term>Linear programming</term><term>Optimization method</term><term>Triangular facet</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Géométrie discrète</term><term>Complexité</term><term>Méthode optimisation</term><term>Programmation linéaire</term><term>Informatique théorique</term><term>Algorithme reconnaissance</term><term>Ensemble chordal</term><term>Plan numérique</term><term>Facette triangulaire</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A naive digital plane is a subset of points (x, y, z) ∈ Z<sup>3</sup> verifying h ≤ ax + by + cz < h + max{|a|, |b|, |c|}, where (a, b, c, h) ∈ Z<sup>4</sup>. Given a finite unstructured subset of Z<sup>3</sup>, the problem of the digital plane recognition is to determine whether there exists a naive digital plane containing it. This question is rather classical in the field of digital geometry (also called discrete geometry). We suggest in this paper a new algorithm to solve it. Its asymptotic complexity is bounded by O(n<sup>7</sup>) but its behavior seems to be linear in practice. It uses an original strategy of optimization in a set of triangular facets (triangles). The code is short and elementary (less than 300 lines) and available on http://www.loria.fr/∼debled/plane.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Auvergne (région administrative)</li><li>Auvergne-Rhône-Alpes</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Aubière</li><li>Villers-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Auvergne-Rhône-Alpes"><name sortKey="Gerard, Y" sort="Gerard, Y" uniqKey="Gerard Y" first="Y." last="Gerard">Y. Gerard</name></region><name sortKey="Debled Rennesson, I" sort="Debled Rennesson, I" uniqKey="Debled Rennesson I" first="I." last="Debled-Rennesson">I. Debled-Rennesson</name><name sortKey="Zimmermann, P" sort="Zimmermann, P" uniqKey="Zimmermann P" first="P." last="Zimmermann">P. Zimmermann</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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