Subdivision as a Sequence of Sampled Cp Surfaces

Abstract

This article deals with practical conditions for tuning a subdivisionscheme in order to control its artifacts in the vicinity of a markpoint. To do so, we look for good behaviour of the limit verticesrather than good mathematical properties of the limit surface. Thegood behaviour of the limit vertices is characterised with the definitionofC2-convergence of a scheme. We propose necessary explicit conditionsforC2-convergence of a scheme in the vicinity of any mark point beinga vertex of valency greater or equal to three.