  Convergence properties of binary stationary subdivision schemes for curves
have been analyzed using the techniques of z-transforms and eigenanalysis.
Eigenanalysis provides a way to determine derivative continuity at specific
points based on the eigenvalues of a finite matrix. None of the well-known
subdivision schemes for curves have complex eigenvalues. We prove when a
convergent scheme with palindromic mask can have complex eigenvalues and that a
lower limit for the size of the mask exists in this case. We find a scheme with
complex eigenvalues achieving this lower bound. Furthermore we investigate this
scheme numerically and explain from a geometric viewpoint why such a scheme has
not yet been used in computer-aided geometric design.
