> What I kind of didn't get was whether or not you could have
> points places like thpose in the attachment.

No, not in a standard NURBS surface. This is the kind of thing that the T-Spline guys are working on as an extended type of NURBS surface, but the classic standard style does not allow for single additional points anywhere in the middle like that, if you want to add a point to a standard NURBS surface you have to add an entire row or column of points.


> Because if you make a 2-rail sweep, you can have any number of
> points on each side.. but is that because the 2-rail sweep actually makes an
> entire grid of patches?

I guess the confusing part here is that there is a point matching and refining process that happens during the 2-rail sweep.

So even though your initial rails of the 2 rail sweep can have any number of points, the resulting surface does not use those control points directly, there is a process where the swept surface is shaped to conform to those curves by an ongoing refinement. On each step of the refinement, there is an entire row of points added to the surface being calculated.

So if you turn on the points of a swept surface, you will see that they are in a grid and that they don't match the original rails for example. For multiple profiles there is a process where all the points of the profiles are merged together so that there is a common number in that direction as well.

So the initial curves with different numbers of points don't just go directly into making up the surface.


> What I don't get then is why you can't do the same with bezier patches... have 1
> side made of 2 points, one parallel maybe of 4 points, and 2 conneting those with
> sides with 3 and 5 points, and still get the computer to automatically generate a
> perfect smooth surface...

Well, the computer has to manipulate something to make a perfectly smooth surface.

If you have a bezier surface made up of just 2 points for example, that is limited in the type of shapes it can make, you can make a plane with it or a kind of limited curve if the points are not on the same plane, but there are not enough points available in a 2-point structure to adjust it to make it connect up smoothly to something that is wiggling around a lot.

It's like saying you should be able to take a 2-point line segment in the middle of something and make it smooth by changing the points. But you can only connect 2 points in a straight line, you can't make 2 points form a smooth curve.

It is possible to make Beziers have more points to give the computer something to edit to manipulate the shape. But this tends to be clumsy because it means you have to lock down the location of a whole bunch of points to make them smooth with the adjacent patch. Pretty soon you can only make clumsy edits because most of the points are locked down to provide smoothness.


> Oh and BTW... Aren't solids modelers often just NURBS modelers with good trimming?
> :P Like solidworks, or PowerNURBS/PowerSolid...

Yes, 99% of "solids" modelers are NURBS based, with trimmed NURBS surfaces and "B-Reps" (Boundary-representation) which is the name for trimmed surfaces + the ability to have shared edges beween surfaces.

But a lot of solids modelers tend to incorporate other layers of mechanisms in them such as constraint-based solvers where you can tag certain dimensions to be rigid and have it calculate other dimensions for you, and many of them sort of present a particular style of user interface for how you interact with objects. By this I mean they don't tend to give you access to stuff like the individual control points on the NURBS surfaces even though they are using those behind the scenes.

So there tends to be a package of additional mechanisms and certain types of workflow associated with the "solids" modelers.

- Michael