IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v45y2012i11p1444-1451.html
   My bibliography  Save this article

Approximate convex hull of affine iterated function system attractors

Author

Listed:
  • Mishkinis, Anton
  • Gentil, Christian
  • Lanquetin, Sandrine
  • Sokolov, Dmitry

Abstract

In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

Suggested Citation

  • Mishkinis, Anton & Gentil, Christian & Lanquetin, Sandrine & Sokolov, Dmitry, 2012. "Approximate convex hull of affine iterated function system attractors," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1444-1451.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1444-1451
    DOI: 10.1016/j.chaos.2012.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077912001713
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2012.07.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pierre-Antoine Arrighi & Pascal Le Masson & Benoit Weil & Akin Kazakçi, 2016. "Uncovering the specificities of CAD tools for industrial design with design theory – style models for generic singularity," Post-Print hal-01389651, HAL.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1444-1451. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.