Boundary Controlled Iterated Function Systems

Dmitry Sokolov 1, 2 Gilles Gouaty 2 Christian Gentil 2 Anton Mishkinis 2
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 Le2i - Laboratoire Electronique, Informatique et Image [UMR6303]
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
Keywords : subdivision surfaces fractals Iterated Function System B-splines
Type de document :
Chapitre d'ouvrage
Curves and Surfaces, Springer, 2015, Lecture Notes in Computer Science - 8th International Conference, Paris, France, June 12-18, 2014, Revised Selected Papers, 978-3-319-22803-7. 〈10.1007/978-3-319-22804-4_29〉
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https://hal.inria.fr/hal-01244612
Contributeur : Sokolov Dmitry <>
Soumis le : mercredi 16 décembre 2015 - 13:58:42
Dernière modification le : mercredi 12 septembre 2018 - 01:27:36
Document(s) archivé(s) le : samedi 29 avril 2017 - 16:04:43

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Dmitry Sokolov, Gilles Gouaty, Christian Gentil, Anton Mishkinis. Boundary Controlled Iterated Function Systems. Curves and Surfaces, Springer, 2015, Lecture Notes in Computer Science - 8th International Conference, Paris, France, June 12-18, 2014, Revised Selected Papers, 978-3-319-22803-7. 〈10.1007/978-3-319-22804-4_29〉. 〈hal-01244612〉

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