InforLorV4, Main, Merge, bibRecord, 001907

Geometry control of the junction between two fractal curves

Identifieur interne : 001907 ( Main/Merge ); précédent : 001906; suivant : 001908

Geometry control of the junction between two fractal curves

Auteurs : Sergey Podkorytov [France] ; Christian Gentil [France] ; Dmitry Sokolov [France] ; Sandrine Lanquetin [France]

Source :

RBID : Hal:hal-00755851

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. 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 generalize our approach to surfaces. We formalize the problem with Boundary Controlled Iterated Function System model. Then we deduct the conditions that guaranties continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterize 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.

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Le document en format XML

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<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
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<country>France</country>
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<settlement type="city">Metz</settlement>
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<region type="old region" nuts="2">Lorraine (région)</region>
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<orgName type="university">Université de Lorraine</orgName>
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<author><name sortKey="Lanquetin, Sandrine" sort="Lanquetin, Sandrine" uniqKey="Lanquetin S" first="Sandrine" last="Lanquetin">Sandrine Lanquetin</name>
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<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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<desc><address><addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine>
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<placeName><settlement type="city">Dijon</settlement>
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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. 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 generalize our approach to surfaces. We formalize the problem with Boundary Controlled Iterated Function System model. Then we deduct the conditions that guaranties continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterize 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>
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Geometry control of the junction between two fractal curves

Geometry control of the junction between two fractal curves

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