Hi wim,
> it seems that there is different formula behind the 2 types of curve
Yup, there is... NURBS curves have an additional value that is stored with each control point, the additional value is called a "weight".
The control point curve doesn't use weights, well it technically uses them but has them all set to the same value which means they don't have any effect.
The arc curve has the weights set to particular values to make the shape of the curve come out to an exact conic section (arc, ellipse, parabola, hyperbola type shapes). Like Anto writes above when a curve uses weights the curve is called a "rational" curve, it's what the R in NURBS stands for.
You can this in action by using the Draw curve > More > conic command. That will allow you to create a variety of different conic curves where you can have the same 3 control points for each of them but have different result shapes because of different weights being applied.
So yeah the trick is that there is an additional piece of information (weights) that is being used for the arc case and that's what is different from the freeform control point case, the freeform curve has all weights set to 1.
- Michael
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