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Ω-Arithmetization of Ellipses

  • Agathe Chollet
  • Guy Wallet
  • Eric Andres
  • Laurent Fuchs
  • Gaëlle Largeteau-Skapin
  • Aurélie Richard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6026)

Abstract

Multi-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs. Moreover, we give a global condition for the connectivity of the discrete curves generated by the method at every scale.

Keywords

discrete geometry multi-resolution analysis nonstandard analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Agathe Chollet
    • 1
  • Guy Wallet
    • 1
  • Eric Andres
    • 2
  • Laurent Fuchs
    • 2
  • Gaëlle Largeteau-Skapin
    • 2
  • Aurélie Richard
    • 2
  1. 1.Laboratoire MIAUniversité de La RochelleLa Rochelle cedexFrance
  2. 2.Laboratoire XLIM SIC, UMR 6172Université de PoitiersFrance

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