Curvature continuous flexible surfaces

prescribed local behavior is referred to as flexibility..
Parametric flexibility is the ability to represent
surfaces with prescribed derivatives up to certain order, and
geometric flexibility is the ability to represent surfaces with prescribed
normals, curvatures and higher-order geometrically invariant
quantities.

I will discuss the relationship of geometric and parametric flexibility,
obstacles for flexibility for surfaces defined on arbitrary meshes,
and flexibility of subdivision surfaces. It is known that most commonly used
subdivision surfaces lack flexibility at extraordinary vertices.
I will present a construction of c2-continuous flexible surfaces based
on subdivision for a class of control meshes.
The proposed algorithm can be easily added to existing
subdivision code, and shares many useful features with subdivision algorithms.