IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-74238-8_11.html
   My bibliography  Save this book chapter

Smooth Approximation and Rendering of Large Scattered Data Sets

In: From Nano to Space

Author

Listed:
  • Jörg Haber

    (Max-Planck-Institut für Informatik)

  • Frank Zeilfelder

    (Max-Planck-Institut für Informatik)

  • Oleg Davydov

    (Justus-Liebig-Universität Giessen)

  • Hans-Peter Seidel

    (Max-Planck-Institut für Informatik)

Abstract

We present an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a C 1-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and non-uniform distribution of the data are taken into account by using local polynomial least squares approximations of varying degree. Since we only need to solve small linear systems and no triangulation of the scattered data points is required, the overall complexity of the algorithm is linear in the total number of points. Numerical examples dealing with several real world scattered data sets with up to millions of points demonstrate the efficiency of our method. The resulting spline surface is of high visual quality and can be efficiently evaluated for rendering and modeling. In our implementation we achieve real-time frame rates for typical fly-through sequences and interactive frame rates for recomputing and rendering a locally modified spline surface.

Suggested Citation

  • Jörg Haber & Frank Zeilfelder & Oleg Davydov & Hans-Peter Seidel, 2008. "Smooth Approximation and Rendering of Large Scattered Data Sets," Springer Books, in: Michael H. Breitner & Georg Denk & Peter Rentrop (ed.), From Nano to Space, pages 127-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74238-8_11
    DOI: 10.1007/978-3-540-74238-8_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-540-74238-8_11. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.