CGAL users discussion list

[Peter Schröder ॐ <>]

Hanjoerg Seybold wrote:
> As far as i know subdivision surfaces are some kind of tensor product 
> splines
> to preserve c1 continuity.
Dear Hanjoerg,

they are often *based* on tensor product splines but generalize them. 
Others are based on k-direction splines and many are not based on 
splines at all. In all cases they goal is to be more general than what 
standard tensor product allows for.
> Does anybody know if there are generaliyations to 3D no surfaces, but 
> c1 continuous volumes!!!
There is a construction by MacCracken et al. from many years ago which 
generalizes tri-cubic splines. And there is a construction by Schaefer 
et al. of a few years ago which is based on tet meshes. Since the 
co-dimension is 0 in these the big difficulty in practice is to avoid 
"self-overlap" (i.e., non-injectivity).

peter