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.
- trimming is expensive and probe to numerical errors;
- it becomes difficult to maintain smoothness at the seams of the patchwork,
when a model is deformed or animated.
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
L.Pallara, Un sistema per l'analisi e sperimentazione di superfici parametriche a
topologia arbitraria per la modellazione, Degree Thesis in Computer