Analysis of Csupra(k)-subdivision surfaces at extraordinary points

This paper gives an analysis of surfaces generated by subdividing control nets of arbitrary topology. We assume that the underlying subdivision algorithm is stationary on the regular parts of the control nets and described by a matrix iteration around an extraordinary point. For these subdivision schemes we derive conditions on the spectrum of the matrix and its generalized eigenvectors such that surfaces are produced which are regular and k-times differentiable at their extraordinary points