Boundary Controlled Iterated Function Systems
Identifieur interne : 000402 ( Main/Exploration ); précédent : 000401; suivant : 000403Boundary Controlled Iterated Function Systems
Auteurs : Dmitry Sokolov [France] ; Gilles Gouaty [France] ; Christian Gentil [France] ; Anton Mishkinis [France]Source :
English descriptors
Abstract
Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a powerful tool allowing creation of an object with a prescribed topology (e.g. surface patch) independent of its geometrical texture. We also show how to impose constraints on the IFS transformations to guarantee the production of smooth shapes. Objects modeled through Computer Aided Geometric Design (CAGD) systems are often inspired by standard machining processes. However, other types of objects, such as objects with a porous structure or with a rough surface, may be interesting to create: porous structures can be used for their lighter weight while maintaining satisfactory mechanical properties, rough surfaces can be used for acoustic absorption. Fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. Because of their specific physical
Url:
DOI: 10.1007/978-3-319-22804-4_29
Affiliations:
- France
- Grand Est, Lorraine (région), Région Bourgogne
- Dijon, Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Bourgogne, Université de Bourgogne Franche-Comté, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 001287
- to stream Hal, to step Curation: 001287
- to stream Hal, to step Checkpoint: 000379
- to stream Main, to step Merge: 000402
- to stream Main, to step Curation: 000402
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Boundary Controlled Iterated Function Systems</title><author><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-3174" status="OLD"><idno type="RNSR">200618296R</idno><orgName>Geometry and Lighting</orgName><orgName type="acronym">ALICE</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/alice</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><author><name sortKey="Gouaty, Gilles" sort="Gouaty, Gilles" uniqKey="Gouaty G" first="Gilles" last="Gouaty">Gilles Gouaty</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author><author><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author><author><name sortKey="Mishkinis, Anton" sort="Mishkinis, Anton" uniqKey="Mishkinis A" first="Anton" last="Mishkinis">Anton Mishkinis</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:hal-01244612</idno><idno type="halId">hal-01244612</idno><idno type="halUri">https://hal.inria.fr/hal-01244612</idno><idno type="url">https://hal.inria.fr/hal-01244612</idno><idno type="doi">10.1007/978-3-319-22804-4_29</idno><date when="2015-08-14">2015-08-14</date><idno type="wicri:Area/Hal/Corpus">001287</idno><idno type="wicri:Area/Hal/Curation">001287</idno><idno type="wicri:Area/Hal/Checkpoint">000379</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000379</idno><idno type="wicri:Area/Main/Merge">000402</idno><idno type="wicri:Area/Main/Curation">000402</idno><idno type="wicri:Area/Main/Exploration">000402</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Boundary Controlled Iterated Function Systems</title><author><name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-3174" status="OLD"><idno type="RNSR">200618296R</idno><orgName>Geometry and Lighting</orgName><orgName type="acronym">ALICE</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/alice</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><author><name sortKey="Gouaty, Gilles" sort="Gouaty, Gilles" uniqKey="Gouaty G" first="Gilles" last="Gouaty">Gilles Gouaty</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author><author><name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author><author><name sortKey="Mishkinis, Anton" sort="Mishkinis, Anton" uniqKey="Mishkinis A" first="Anton" last="Mishkinis">Anton Mishkinis</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-22594" status="VALID"><orgName>Laboratoire Electronique, Informatique et Image</orgName><orgName type="acronym">Le2i</orgName><desc><address><addrLine>Université de Bourgogne - Laboratoire Le2i - UFR Sciences et Techniques - BP 47870 - 21078 DIJON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://le2i.cnrs.fr</ref></desc><listRelation><relation active="#struct-300062" type="direct"></relation><relation active="#struct-300270" type="direct"></relation><relation name="UMR6306" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300062" type="direct"><org type="institution" xml:id="struct-300062" status="VALID"><orgName>Arts et Métiers ParisTech</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300270" type="direct"><org type="institution" xml:id="struct-300270" status="VALID"><orgName>Université de Bourgogne</orgName><orgName type="acronym">UB</orgName><desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.u-bourgogne.fr/</ref></desc></org></tutelle><tutelle name="UMR6306" active="#struct-441569" type="direct"><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></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Dijon</settlement><region type="region" nuts="2">Région Bourgogne</region></placeName><orgName type="university">Université de Bourgogne</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName></affiliation></author></analytic><idno type="DOI">10.1007/978-3-319-22804-4_29</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>B-splines</term><term>Iterated Function System</term><term>fractals</term><term>subdivision surfaces</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a powerful tool allowing creation of an object with a prescribed topology (e.g. surface patch) independent of its geometrical texture. We also show how to impose constraints on the IFS transformations to guarantee the production of smooth shapes. Objects modeled through Computer Aided Geometric Design (CAGD) systems are often inspired by standard machining processes. However, other types of objects, such as objects with a porous structure or with a rough surface, may be interesting to create: porous structures can be used for their lighter weight while maintaining satisfactory mechanical properties, rough surfaces can be used for acoustic absorption. Fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. Because of their specific physical</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>Région Bourgogne</li></region><settlement><li>Dijon</li><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Bourgogne</li><li>Université de Bourgogne Franche-Comté</li><li>Université de Lorraine</li></orgName></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="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name><name sortKey="Gouaty, Gilles" sort="Gouaty, Gilles" uniqKey="Gouaty G" first="Gilles" last="Gouaty">Gilles Gouaty</name><name sortKey="Mishkinis, Anton" sort="Mishkinis, Anton" uniqKey="Mishkinis A" first="Anton" last="Mishkinis">Anton Mishkinis</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 000402 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000402 | 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:hal-01244612
|texte= Boundary Controlled Iterated Function Systems
}}
| This area was generated with Dilib version V0.6.33. |  |