"Curve to NURBS" node

[portnov]

This node allows to:

• Convert arbitrary (non-NURBS) curve to NURBS curve
• Reparametrize any curve: given one curve, make a NURBS curve with "natural" (uniform) parametrization, or with arbitrary parametrization

General nodes setup:

If we specify Parametrization = "Keep Original", then for NURBS curves node will basically return the same curve (slightly modified due to algorithms involved):

So if you already have a NURBS curve, it does not make sense to use original parametrization. It may, however, make sense for generic curves, see below.

In the following case we already have Bezier curve, but we want to have a NURBS curve with uniform parametrization:

Note that while the curve is smooth, it's curvature comb is not smooth. If we want it to be smooth, we can use NURBS curves of higher degree:

It is possible to create NURBS curves with arbitrary parametrization. Nodes setup:

"Formula interpolate" node defines the following reparametrization curve in this case:

This gives the following result:

Let's check with arbitrary curve; in this case it's a straight line segment deformed by vector noise field:

With Parametrization = "Keep Original" this gives:

With Parametrization = "Natural" this gives:

Preflight checklist

Put an x letter in each brackets when you're done this item:

• Code changes complete.
• Code documentation complete.
• Documentation for users complete (or not required, if user never sees these changes).
• Manual testing done.
• Unit-tests implemented.
• Ready for merge.