Hi Bard,

> In fact, my perception of the NURBS was wrong, I saw NURBS
> like a sort of Illustrator in 3D; and the verb "to trim" bad
> translated by me, in context of NURBS, confused me.

Actually NURBS curves are pretty similar to Illustrator curves - but with x,y,z coordinates instead of only x,y coordinates like in Illustrator.

But in order to make a surface instead of just an infinitely thin wire curve requires a different technique - instead of just a linear-like sequence of control points it instead uses a grid of points. Any single row or column of points in that grid behaves like a single curve, and the surface is basically formed by a continuous sweep of curves across the grid.


> So, all the curves are like tensed up, drawn or bend, or
> stretched in a cubic or parallelepipedic space. <...>

Actually the name for this kind of surface that is made up of a crossing network of curves like this, is a "Tensor product" surface:
http://www.ibiblio.org/e-notes/Splines/Inter.htm

So NURBS surfaces are always a rectangle by their definition, although more like a flexible rubber rectangle and sometimes one side of the rectangle can be squished down to a point.

Then in order to be able to have irregular boundaries that can't be done with a rectangle, trim curves are used - trim curves mark areas as being holes in the surface. When you do a boolean operation the surface actually stay the same and it's really just new trim curves that are calculated on them.

This structure is particularly relevant for Flow more than many other commands since Flow is based on working on the underlying surface since it works by mapping UV space from one surface to another.


> To learn that a square is a tensed surface gives me a
> bizarre (odd, strange) apprehension of the concrete objets
> that we built in 3D; it's very virtual suddenly; almost incredible.

That's not too unusual - another thing that's pretty common is that people don't like the way that solids work. A solid is when you have defined a fully connected unbroken skin of surfaces where every edge is joined to another edge. That then divides space into a volume. Pretty often people feel like that's not "really" a solid, but actually it is since if something mathematically defines a volume it's a solid regardless of people's emotional feelings... ;)

- Michael