Differential Behaviour of Iteratively Generated Curves
Identifieur interne : 001E46 ( Main/Exploration ); précédent : 001E45; suivant : 001E47Differential Behaviour of Iteratively Generated Curves
Auteurs : Dmitry Sokolov [France] ; Christian Gentil [France] ; Hicham Bensoudane [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and right half-tangents, what gives us an additional parameter to characterize shapes.
Url:
DOI: 10.1007/978-3-642-27413-8_44
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 003642
- to stream Istex, to step Curation: 003600
- to stream Istex, to step Checkpoint: 000435
- to stream Main, to step Merge: 001E65
- to stream Main, to step Curation: 001E46
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Differential Behaviour of Iteratively Generated Curves</title><author><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name></author><author><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name></author><author><name sortKey="Bensoudane, Hicham" sort="Bensoudane, Hicham" uniqKey="Bensoudane H" first="Hicham" last="Bensoudane">Hicham Bensoudane</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:E30198DD990280CDBFB0F36A04818F4C0CBD99CB</idno><date when="2012" year="2012">2012</date><idno type="doi">10.1007/978-3-642-27413-8_44</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-5T585GKT-C/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">003642</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003642</idno><idno type="wicri:Area/Istex/Curation">003600</idno><idno type="wicri:Area/Istex/Checkpoint">000435</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000435</idno><idno type="wicri:doubleKey">0302-9743:2012:Sokolov D:differential:behaviour:of</idno><idno type="wicri:Area/Main/Merge">001E65</idno><idno type="wicri:Area/Main/Curation">001E46</idno><idno type="wicri:Area/Main/Exploration">001E46</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Differential Behaviour of Iteratively Generated Curves</title><author><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LORIA - Alice, Campus Scientifique, BP 239, 54506, Vandoeuvre-les-Nancy Cedex</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Faculté des Sciences Mirande, Laboratoire LE2I — UMR CNRS 5158, Aile de l’Ingénieur, 21078, Dijon Cedex</wicri:regionArea><placeName><region type="region" nuts="2">Bourgogne-Franche-Comté</region><region type="old region" nuts="2">Bourgogne</region><settlement type="city">Dijon</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Bensoudane, Hicham" sort="Bensoudane, Hicham" uniqKey="Bensoudane H" first="Hicham" last="Bensoudane">Hicham Bensoudane</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Faculté des Sciences Mirande, Laboratoire LE2I — UMR CNRS 5158, Aile de l’Ingénieur, 21078, Dijon Cedex</wicri:regionArea><placeName><region type="region" nuts="2">Bourgogne-Franche-Comté</region><region type="old region" nuts="2">Bourgogne</region><settlement type="city">Dijon</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and right half-tangents, what gives us an additional parameter to characterize shapes.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Bourgogne</li><li>Bourgogne-Franche-Comté</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Dijon</li><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name></region><name sortKey="Bensoudane, Hicham" sort="Bensoudane, Hicham" uniqKey="Bensoudane H" first="Hicham" last="Bensoudane">Hicham Bensoudane</name><name sortKey="Bensoudane, Hicham" sort="Bensoudane, Hicham" uniqKey="Bensoudane H" first="Hicham" last="Bensoudane">Hicham Bensoudane</name><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</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 001E46 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 001E46 | 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= ISTEX:E30198DD990280CDBFB0F36A04818F4C0CBD99CB
|texte= Differential Behaviour of Iteratively Generated Curves
}}
| This area was generated with Dilib version V0.6.33. |  |