Geometry control of the junction between two fractal curves
Identifieur interne : 001318 ( Main/Exploration ); précédent : 001317; suivant : 001319Geometry control of the junction between two fractal curves
Auteurs : Sergey Podkorytov [France] ; Christian Gentil [France] ; Dmitry Sokolov [France] ; Sandrine Lanquetin [France]Source :
- Computer-Aided Design [ 0010-4485 ] ; 2013-02-01.
Abstract
The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated Function System model. Then we deduct the conditions that guarantees continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterise the differential behaviour at the connection points between the curves and the intermediate one. This behaviour depends on the nature of the initial curves and coefficients of the subdivision matrices. We also suggest a method to control the differential behaviour by adding intermediate control points.
Url:
DOI: 10.1016/j.cad.2012.10.025
Affiliations:
- France
- Grand Est, Lorraine (région), Région Bourgogne
- Dijon, Metz, Nancy
- Université de Bourgogne, Université de Bourgogne Franche-Comté, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 002625
- to stream Hal, to step Curation: 002625
- to stream Hal, to step Checkpoint: 001246
- to stream Main, to step Merge: 001333
- to stream Main, to step Curation: 001318
Le document en format XML
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<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>
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<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
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</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
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<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">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Lanquetin, Sandrine" sort="Lanquetin, Sandrine" uniqKey="Lanquetin S" first="Sandrine" last="Lanquetin">Sandrine Lanquetin</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>
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</address>
<ref type="url">http://le2i.cnrs.fr</ref>
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</address>
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<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>
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</address>
<ref type="url">http://www.u-bourgogne.fr/</ref>
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<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
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</address>
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</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>
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</author>
</analytic>
<idno type="DOI">10.1016/j.cad.2012.10.025</idno>
<series><title level="j">Computer-Aided Design</title>
<idno type="ISSN">0010-4485</idno>
<imprint><date type="datePub">2013-02-01</date>
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<front><div type="abstract" xml:lang="en">The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated Function System model. Then we deduct the conditions that guarantees continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterise the differential behaviour at the connection points between the curves and the intermediate one. This behaviour depends on the nature of the initial curves and coefficients of the subdivision matrices. We also suggest a method to control the differential behaviour by adding intermediate control points.</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>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><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="Région Bourgogne"><name sortKey="Podkorytov, Sergey" sort="Podkorytov, Sergey" uniqKey="Podkorytov S" first="Sergey" last="Podkorytov">Sergey Podkorytov</name>
</region>
<name sortKey="Gentil, Christian" sort="Gentil, Christian" uniqKey="Gentil C" first="Christian" last="Gentil">Christian Gentil</name>
<name sortKey="Lanquetin, Sandrine" sort="Lanquetin, Sandrine" uniqKey="Lanquetin S" first="Sandrine" last="Lanquetin">Sandrine Lanquetin</name>
<name sortKey="Sokolov, Dmitry" sort="Sokolov, Dmitry" uniqKey="Sokolov D" first="Dmitry" last="Sokolov">Dmitry Sokolov</name>
</country>
</tree>
</affiliations>
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