A factored approach to subdivision surfaces

The subdivision schemes presented here are but a small subset of the available methods. In particular, subdivision schemes are either interpolating or approximating. The averaging methods we've described are approximating in that the surfaces don't interpolate the original surface's vertices. Interpolating methods (as the name implies) interpolate the vertices of the original surface, giving the user a more intuitive feel of the final surface shape. However, these surfaces tend to be only CV and don't exhibit many of the desirable properties that averaging methods possess.