"Interpolating Subdivision Meshes with Arbitrary Topology"

by D. Zorin, P. Schroeder, W. Sweldens (1996).

What kinds of functions can be represented exactly

with the regular Zorin subdivision scheme ?

How does one determine the position of a new edge-vertex

that lies between two non-regular vertices ?

How did Zorin et.al. choose the rules for determining the weights

for placing a new vertex next to an irregular one ?