Providing local interpolation, tension and normal control in the manipulation of loop subdivision surfaces

Recursive subdivision surfaces allow a lot of freedom in designing surfaces of arbitrary topology. However, tools to manipulate them are still not as powerful as existing tools for established modeling paradigms such as B-spline surfaces. Furthermore, the most well behaved and most widely used schemes are approximating schemes, not interpolating their initial control points. We describe a new modeling paradigm providing local interpolation together with interactive normal and tension control to the approximating loop scheme, without interfering with its uniform subdivision rules. These tools are investigated for vertices both in the interior and at the border