Subdivision as a Sequence of Sampled Cp Surfaces [chapter]

Cédric Gérot, Loïc Barthe, Neil A. Dodgson, Malcolm Sabin
Mathematics and Visualization  
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 a good mathematical property of the limit surface. The good behaviour of the limit vertices is characterized with the definition of C 2 -convergence of a scheme. We propose necessary explicit conditions for C 2 -convergence of a scheme in the vicinity of any mark point being a vertex of valency greater or equal to three.
doi:10.1007/3-540-26808-1_14 fatcat:s7zvyg2fgbdqhdis3fprea3vly