[legosexmagic]

thats pretty much it yes. the reason they dont just say 2nd derivative is that the derivative isnt a geometry property. you can have two curves with the same shape but different derivatives.

curvature only depends on the shape of the object.

[phkahler]

It's called C2 continuity.

[kelsolaar]

The Continuity of Splines: https://youtu.be/jvPPXbo87ds

[harywilke]

I came here to post exactly this excellent video on splines by Freya Holmér. This discontinuity of reflections effect is directly mentioned at 29 minutes in chapter 4 on geometric continuity.

[milosmns]

Thank you.

[jsjohnst]

Actually, you only need G2 continuity for the reflection to be continuous (yes, C2 is also G2 for regular curves).

[yshklarov]

Do you know whether it's usual nowadays in industrial design to make curves that are actually smooth (I mean, derivatives of all orders are continuous) and not just C2? Or is it technically challenging for some reason, or not useful?