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.