Subdivision as a Sequence of Sampled Cp Surfaces

  • Cédric Gérot
  • Loïc Barthe
  • Neil A. Dodgson
  • Malcolm Sabin
Part of the Mathematics and Visualization book series (MATHVISUAL)


This article deals with practical conditions for tuning a subdivision scheme in order to control its artifacts in the vicinity of a mark point. To do so, we look for good behaviour of the limit vertices rather than good mathematical properties of the limit surface. The good behaviour of the limit vertices is characterised with the definition of C2-convergence of a scheme. We propose necessary explicit conditions for C2-convergence of a scheme in the vicinity of any mark point being a vertex of valency greater or equal to three.


Limit Surface Mark Point Subdivision Scheme Polygonal Mesh Subdivision Surface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cédric Gérot
    • 1
  • Loïc Barthe
    • 2
  • Neil A. Dodgson
    • 3
  • Malcolm Sabin
    • 4
  1. 1.Laboratoire des Images et des SignauxDomaine UniversitaireGrenobleFrance
  2. 2.Computer Graphics Group, IRIT/UPSToulouseFrance
  3. 3.Computer LaboratoryUniversity of CambridgeUK
  4. 4.Numerical Geometry Ltd.CambridgeUK

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