> Ah damn, I don't get it :S I don't get why you can't 2-rail sweep-generate a
> bezier controlled patch surface...

It's just more difficult to create longer surfaces out of Beziers because each individual Bezier is limited in the number of points it can have in it, so you would have to use a bunch of them stuck together, with the points carefully arranged to try and make them smooth.

NURBS was basically invented to solve this problem, it is a way to have a longer string of points than a bezier can have in it.


> B-splines are only defined by a point in space, while beziers are 4 vectors in space, right?

No, Beziers are also defined by points in space. Sometimes they may be displayed with stuff that looks like vectors but those are just lines connecting between the points.

A Bezier surface looks the same as a NURBS surface, it is a rectangular grid of points just like a NURBS surface.

But a bezier can only have as many points as its "Degree" + 1. The "Degree" is one part of the definition of a NURBS or Bezier, it defines the highest exponent of the math function used for the blending calculations.

So a degree 3 bezier curve is made up of 4 points. You can only make so many shapes with 4 points, to make more intricate shapes you need to use more points, which for beziers means trying to stick together a bunch of separate beziers.

NURBS allows for more points, if you have a NURBS curve of degree 3, it can have a minimum of 4 points (which makes it equivalent to a bezier), but it can have any number more than that. The NURBS blending method makes it easier to get a smooth result curve from a longer chain of points, it is built in to the smoothing formula, instead of being something that you have to do manually by arranging points which you have to do if you stick small bezier curves next to one another.

- Michael