Maybe this is something very simple, so I prepared a file along with several questions about NURBS curves.
Everything started from a simple assumption: I thought there would be a straightforward command to combine any set of curves (with the same degree) into a single non-uniform curve, or alternatively.. converting a polycurve composed of segments (all of the same degree) into one non-uniform NURBS curve. Is there any command that can do this? (unfortunately merge changes the geometry.. also rebuild non uniform changes the geometry)
I havenât found a solution yet. Moreover, I think it should be possible, since certain operations like extrusions (and maybe others) sometimes result in edges that are non-uniform.
In the file, youâll see that I explored this curiosity systematically, and included several related questions as well. The one that bothers me the most is why the extrusion in step 4 makes 2 surfaces? (why not 1?. why not 3?)
I have too experimented in the same file trying to understand the theory of NURBS curve.. for example that trimming any curve (e. g. degree) will result in 2 segments also degree 3 (this time non rational).. but joining these would result in a non rational degree. and while I know there is a ârationalâ solution.. is ther a way to reverse to the original curve (exercise 2)
Thank you for the time looking at this.. I really hope that command exists..
Thatâs just how NURBS curves work, also in Alias and Catia. When you join (Alias âattachâ) curves, you get kinks. Good surface modellers never accept kinks.
Observe the curvature change at the 1st kink. If, then, you use UseExtrusions with the standard Extrusion setting, you get what you got; where at the G1 kink/join the two curvatures are both convex/concave, a single surface is built. If you use the (for surface modellers) proper Polysurface setting, you get what I got.
thank you very much for the explanation on this. I got now the 3 surfaces.. but still many questions from my 1st post. Iâll keep experimenting on this
Nonetheless.. as being in Rhinoceros allows NURBS (non uniform.. ).. then in which cases would a âgood surface modellerâ.. use non-uniform geometry? or wich the 4 cases would be acceptable?
Thank you very much @spb I didnât know ToNurbs was also useful for that.
I did another exercise following the ToNURBS step and then cleaning the result, and I have two questions:
(In this Exercise 5)
Step 3 results in a non-uniform curve, but there are no visible kinks. What problems could arise from using such a curve later on?
In Step 4, I decided to rebuild the curve and âtry to simulate the original geometryâ by manually moving each control point. My question is whether thereâs a faster way to do this. I mean, Rebuild always tries to distribute the control points uniformly, but to actually simulate the original geometry, the control points cannot be completely uniform⌠right?
It depends on how the curve will be used afterward, but since you reduced the multi-knots to simple ones, the continuity within the curve will remain at least G2 through the knots even after control-point editing (with no stacking of control points).
If you need a uniform curve, you can use _MakeUniform and check whether the _CrvDeviation of the resultant curve from the input curve is acceptable.
That is correct in the case of this curve. Non-uniform geometry can be the same shape as any uniform geometry, but uniform geometry can be the same shape as only special case non-uniform geometry, such as when knots are added to curves, but the curves are not control-point edited.
