Subdivision as a sequence of sampled Cp surfaces

Cédric Gérot (1) , Loïc Barthe (2, 3, 4) , Neil A. Dodgson (5) , Malcolm A. Sabin (6)

1 LIS - Laboratoire des images et des signaux
2 IRIT - Institut de recherche en informatique de Toulouse
3 IRIT-STORM - Structural Models and Tools in Computer Graphics
4 UT3 - Université Toulouse III - Paul Sabatier
5 CAM - University of Cambridge [UK]
6 Numerical Geometry

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.

Mots clés: subdivision; artifacts; tuning; convergence

Domaines: Informatique [cs]

Cédric Gérot, Loïc Barthe, Neil A. Dodgson, Malcolm A. Sabin. Subdivision as a sequence of sampled Cp surfaces. Neil A. Dodgson; Malcolm A. Sabin. Advances in Multiresolution for Geometric Modelling, Springer-Verlag, pp.259-270, 2004, Part of the book series: Mathematics and Visualization (MATHVISUAL), 978-3-540-21462-5. ⟨10.1007/3-540-26808-1_14⟩. ⟨hal-00097551⟩