Apple's Unique Device Curvature

Re:Apple's Unique Device Curvature by legosexmagic on Saturday December 24, 2022 @12:39PM (#34119043)

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.

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Re:Apple's Unique Device Curvature by phkahler on Saturday December 24, 2022 @01:16PM (#34119470)

It's called C2 continuity.

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Re:Apple's Unique Device Curvature by kelsolaar on Saturday December 24, 2022 @01:33PM (#34119646)

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

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Re:Apple's Unique Device Curvature by harywilke on Saturday December 24, 2022 @03:30PM (#34120795)

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.

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Re:Apple's Unique Device Curvature by milosmns on Saturday December 24, 2022 @06:26PM (#34122285)

Thank you.

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Re:Apple's Unique Device Curvature by yshklarov on Saturday December 24, 2022 @01:20PM (#34119518)

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?

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Re:Apple's Unique Device Curvature by jsjohnst on Saturday December 24, 2022 @01:51PM (#34119839)

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

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