Hi Pilou, easy question first:
> Ps Have you a trick for input your numerous images inside the text except a
> Copy / Past address one by one from the download attachment section?
Nope, no trick other than copy/paste right now.
> About the number of control point in the case of a similar family curve than in your bath
> Seems that is not the same number for each curve
> What is the rule? Same number is better or that is no importance?
Well, I'm afraid that this explanation is rather complex, having a lot to do with specific details about NURBS. But here it is anyway....
You can get a cleaner surface if all the curves have the same structure. But there is more to a NURBS curve structure than just the number of control points, there is also a set of values called a "knot vector" which assigns an area and amount of influence that each control point has over the shape of the curve.
"Same structure" for 2 NURBS curves really means the same knot vector, not just same number of points.
If you create a curve by control points, it will get what is called a "uniform knot vector", which means each knot has the same spacing between them, for instance a sequence like 0.0, 0.5, 1.0 . So any 2 curves made by control points will have the same knot vector and therefore the same structure, and that means they combine together well into a surface without having any extra points needing to be inserted.
On the other hand if you create a curve by "Through points", it does not create a uniform knot vector, it creates a knot vector that is spaced different according to the distance between each points. So 2 "through points" curves with the same number of points do not generally share the same knot vector and therefore have different structures.
When you have curves with different structures that you want to combine into a surface there is an automatic method for combining the structures together called "knot insertion" - this inserts a knot value into each curve (also adding a control point for each knot inserted) until each curve has had all the differing knots from other curves added to it so they finally have equal knot vectors at the end.
The problem with this is that it means that the resulting surface sort of inherits the structure of all the curves added together, which in practical terms means it may have an awful lot of control points in it which can be bad. This increase in number of points is avoided if you use same-structure curves so that can be a good way to simplify things.
I do have some plans to work on some simplification and rebuilding of some of the curves when doing lofting that should help do some of this for you automatically.
Sorry that the explanation is so technical, I find this area hard to explain.
- Michael
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