The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.

An extended subdivision surface (ESub) is a generalization of Catmull Clark and NURBS surfaces. Depending on the knot intervals and valences of the vertices and faces, Catmull Clark as well as NURBS patches can be generated using the extended subdivision rules. Moreover, an arbitrary choice of the knot intervals and the topology is possible. Special features like sharp edges and corners are consistently supported by setting selected knot intervals to zero or by applying special rules. Compared to the prior nonuniform rational subdivision surfaces (NURSS), the ESubs offer limit-point rules which are indispensable in many applications, for example, for computer-aided design or in adaptive visualization. The refinement and limit-point rules for our nonuniform, nonstationary scheme are obtained via a new method using local Bézier control points. With our new surface, it is possible to start with existing Catmull Clark as well as NURBS models and to continue the modeling process using the extended subdivision options.