Currently to make single surface with common parametrization I sample points uniformly from all source surfaces, and fit single NURBS surface from these points. And in most cases it works, but in some rare cases (When surfaces are more curved) this single surface fails to maintain acceptable accuracy at source regions. I tried to increase number of samples, and number of control points for NURBS, but it doesn't help. And btw, solution for images above will be simple planes, because source surfaces are trimmed planes too, but in general case source surfaces will be curvy.
Source surfaces are trimmed NURBS surfaces, but I can convert them to any other discrete format and work with it.
I don't care about free space between surfaces, values of a resulting surface in this space can be linear interpolation between nearby source surfaces, or even some constant value.
Source surfaces cannot overlap or coincide.
Resulting surface must contain all source regions inside (With some arbitrary tolerance), with common parametrization, also it must not have self-intersections.
Is there any other possible solution to this problem? Maybe some algorithm to order such surfaces in parameter space, or at least name of this problem to google it easily?
Thanks for any help.