Smoothing the Antagonism between Extraordinary Vertex and Ordinary Neighbourhood on Subdivision Surfaces
- Cédric GérotAffiliated withGIPSA-lab
- , François DestelleAffiliated withGIPSA-lab
- , Annick MontanvertAffiliated withGIPSA-lab
Recent methods for tuning a subdivision scheme create a concentric wave pattern around the extraordinary vertex (EV). We explain it as resulting from the antagonism between the rules which would create a nice limit surface at the EV and the ordinary rules used in the surrounding regular surface.
We show that even a scheme which fulfils the most recently proposed conditions for good convergence at the EV may still produce this wave pattern.
Then, in order to smooth this antagonism, we define any new vertex as a convex combination of the ideal new vertex from the EV point of view and the one defined with ordinary rules. The weight of the extraordinary rules decreases as the new vertex is topologically farther from the EV.
The concentric wave pattern shades off whereas the expected conditions are not too much spoiled. This tuning method remains simple and useful, involving no optimisation process.
- Smoothing the Antagonism between Extraordinary Vertex and Ordinary Neighbourhood on Subdivision Surfaces
- Book Title
- Mathematical Methods for Curves and Surfaces
- Book Subtitle
- 7th International Conference, MMCS 2008, Tønsberg, Norway, June 26-July 1, 2008, Revised Selected Papers
- pp 242-260
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
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- Editor Affiliations
- 16. Department of Informatics, University of Oslo
- 17. Department of Informatics and Centre of Mathematics for Applications, University of Oslo
- 18. INSA de Rennes
- 19. Department of Informatics and Centre of Mathematics for Applications, University of Oslo
- 20. Department of Mathematics, Vanderbilt University
- Author Affiliations
- 21. GIPSA-lab, Grenoble, France
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