Subdivison Surfaces and Patching NURBS

Our research activity in the last years has been direct towards surface modelling with NURBS and trimmed NURBS surfaces; the latter presents at least two drawbacks: Recently, subdivision surfaces have been considered as a way of overcoming NURBS topological limitations without mesh degeneracy; they don't require trimming, and model smoothness is automatically guaranteed, even in deformed or animated models. The idea is to refine an irregular/regular mesh, by creating a new mesh that approximate the old one. By repeating this process, a smooth surface is formed as the limit of the process itself. Subdivision algorithms are quite simple, and are generally able to produce quite complex objects, although the basic theoretical modeling background has to be explored.

Although trends in geometric modeling community research are moving towards an exaustive exploration of the subdivision paradigm, at the momemt, NURBS modeling still remains the most complete and powerfull means for free object modeling.

This consideration motivated a line of research consisting in look for a patching NURBS of subdivision surfaces. The strengt of these methods is that they convert a subdivision surface mesh level to closed form, smoothly-connected, standard NURBS patches.