We present a new non-stationary, interpolatory subdivision scheme capable of producing circles and surfaces of revolution and in the limit is C1. First, we factor the classical four point interpolatory scheme of Dyn et al. into linear subdivision plus differencing. We then extend this method onto surfaces by performing bilinear subdivision and a generalized differencing pass. This extension also provides the ability to interpolate curve networks. On open nets this simple, yet efficient, scheme reproduces the curve rule, which allows C0 creases by joining two patches together that share the same boundary. Our subdivision scheme also contains a tension parameter that changes with the level of subdivision and gives the scheme its non-stationary property. This tension is updated using a simple recurrence and, chosen correctly, can produce exact surfaces of revolution.