> I hope it's alright.

It's alright. :)


> Is there a problem with making 3-sided NURBS patches?

Well, technically there is no problem making 3-sided NURBS patches. There is such a thing where the points are arranged in a kind of triangular grid instead a rectangular grid.

But they are not commonly used because none of the standard file formats allow for them - the standard file formats for transferring NURBS only allow for rectangular style NURBS surfaces.

So that's one reason why the normal way to do a 3-sided patch is to actually do a 4-sided patch with one side compressed down to a point.


> And I'm not use I understand why it has to be a grid layout..

Well, it is fundamentally the way a NURBS surface is defined. Having a grid layout makes the surface behave kind of like a grid network of curves. Like imagine taking one starting curve at one edge, then if you sort of step that curve along the other direction it will sweep out a surface - that's pretty much how a NURBS surface works.

Each NURBS surface has a 2d "parameter space" coordinate system defined along with its 3d points - the rectangular layout is what provides the 2d parameter space portion of the NURBS definition.


> Does that mean it's possible to make a 100% quad-based mesh that wouldn't easily
> be turned to NURBS through this Sub-D method?

I'm not sure if I understand this question, but it is possible to have all quad faces in a mesh but still have points that are shared by more than 4 common faces, like a center point with quads spiraled around it - this again creates an "extraordinary point" that doesn't have a simple automatic NURBS conversion for these faces.

- Michael