Ya the thing about curves and surface splines is there are really two important issues minus big words.
Mind you im terrible at math never even took algebra. But here goes.
The continuity of the curve geometry.
Basically you want (C2 curvature) but you want some sort of ability to turn that down to at certain points for sharp edges.
In relation to uv texturing.
You want the acceleration of the curve to be non uniform so that you can control er prevent or allow stretching of a texture across the surface. This is related to the acceleration of the generated points on a curve or surface. Sometimes called G3 or G4 continuous.
This second part is the really important part the continuity is far less important (provided you have at least some control) then the ability to change uv acceleration.