Hi Michael,
I’ve just come across something that’s puzzling me. When you offset a smooth curve with no corner points, the result is a curve with lots of corner points. However, if, for example, you extrude the curve, you don’t see any edges on the extruded surface.
Below is a small file to illustrate what I mean.

Hi Zooen, if the control points on either side of a corner point are tangent continuous the curve will be smooth at that spot and it is allowed for a single curve segment to contain such "potential corner points". Your offset case is an example of this.

If you manipulate the control points so that a tangent discontinuity (a sharp point) is formed, that is not allowed within a single segment and the segment will be divided at that discontinuity point.

re:
> However, if, for example, you extrude the curve, you don’t see any edges on the extruded surface.

It's the segmentation of the curve that controls this. Edges on the extruded surface will occur between curve segments.

- Michael

Thank you, Michael, for taking the time to satisfy my curiosity and answer the questions I’ve been asking myself.
Kind regards

Hi Zoen,

The number of generated points by offset is bigger than you expect.
There is a difference between "corner point" and the "sharp point".

You think there is many sharp points but Offset on a smooth curve don't create sharp points.
Only points to create a smooth curve. But you could resolve the problem of the "Too many points"

On your creations, if you have too many points after an offset, you can use the function Rebuild or use ReconstructCurve plugin.

Salutations, Phiro (nous sommes sur le même continent !).

La réponse de Michael est éclairante. Mais je te remercie pour ton post, qui est une autre manière de répondre à ma curiosité.
C'est la fonction Rebuild qui a ma préférence, car elle a trois modes et plusieurs options intéressantes selon le résultat que l'on souhaite obtenir.

Hi Phiro (we’re on the same continent!).

Michael’s reply is very helpful. But thank you for your post, which offers another way of satisfying my curiosity.
I prefer the Rebuild function, as it has three modes and several interesting options depending on the result you want to achieve.

Kind regards.