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International Conference on Curves and Surfaces

Curves and Surfaces 2014: Curves and Surfaces pp 414–432Cite as

Boundary Controlled Iterated Function Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9213))

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.

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Notes

  1. 1.

    Strictly speaking, we do not need the equality of the halftangents, collinearity suffice, so the adjacency constraint can be written as \(T{}_0^e {B{}_1^e}' \begin{bmatrix}-\alpha \\ \alpha \end{bmatrix} = T{}_1^e {B{}_0^e}' \begin{bmatrix}-1 \\ 1\end{bmatrix}\) for some \(\alpha \ne 0\).

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Author information

Authors and Affiliations

  1. LORIA - Alice, Campus Scientifique, BP 239, 54506, Vandoeuvre-les-Nancy Cedex, France

    Dmitry Sokolov

  2. Laboratoire des Sciences de l’Information et des Systémes – UMR 7296, Polytech Marseille Campus de Luminy, Case postale 925, 13288, Marseille Cedex, France

    Gilles Gouaty

  3. Laboratoire LE2I – UMR CNRS 6306, Faculté des Sciences Mirande, Aile de l’Ingénieur, 21078, Dijon Cedex, France

    Christian Gentil & Anton Mishkinis

Authors
  1. Dmitry Sokolov
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  2. Gilles Gouaty
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  3. Christian Gentil
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  4. Anton Mishkinis
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Corresponding author

Correspondence to Dmitry Sokolov .

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. École Normale Supérieure, Paris, France

    Albert Cohen

  3. Arts Et Metiers ParisTech Lab de Sciences de l'Information, Paris, France

    Olivier Gibaru

  4. INSA de Rouen, LMI, Saint-Étienne-du-Rouvray, France

    Christian Gout

  5. Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche

  6. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Sokolov, D., Gouaty, G., Gentil, C., Mishkinis, A. (2015). Boundary Controlled Iterated Function Systems. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_29

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  • DOI: https://doi.org/10.1007/978-3-319-22804-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22803-7

  • Online ISBN: 978-3-319-22804-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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