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Curvature consistency in Apple hardware and software products (2017)

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41–50 of 94 posts

Re: Curvature consistency in Apple hardware and software products (2017)

#41
post #38

> Apple doesn’t have the patent on this. But they do: D558,757 and D670,286. Don't people remember Apple v. Samsung case? https://patents.google.com/patent/USD558757S1/en https://patents.google.com/patent/USD670286S1/en

Afaik those patents don’t describe continuous curvature, but just general curved bodies.

Apple’s use of continuous curvature in iPhones came around iOS 7 iirc. I might be mistaken but I think they’re subtly but consequentially different subjects.

Re: Curvature consistency in Apple hardware and software products (2017)

#42
post #38

> Apple doesn’t have the patent on this. But they do: D558,757 and D670,286. Don't people remember Apple v. Samsung case? https://patents.google.com/patent/USD558757S1/en https://patents.google.com/patent/USD670286S1/en

Your links explicitly refer to the complete designs of entire devices, not a kind of curve.

Re: Curvature consistency in Apple hardware and software products (2017)

#43
post #7

Last year I wanted to have a table custom built using those shapes. It's easy with CNC: https://shapescience.xyz/blog/creating-a-super-ellipsis-tabl...

> It’s unlikely you can do it at home…

I think you could if you had a small bench top cnc or laser cutter.

You’d have to split up the DXF into pieces that fit on your bed, but you’d be able to make a template by joining the parts together.

Then rough cut your workpiece to the template, followed by a flush bit router.

Re: Curvature consistency in Apple hardware and software products (2017)

#44

I guess I have really bad eyes but I can’t tell the difference at all. They both look like rounded corners to me. I don’t think the aesthetic effect is that pronounced. I’d like to see the author do a blind taste test and be able to identify this magical “curvature comb” without seeing the brands.

Out of curiosity, are you really not able to tell which is which in this unlabeled image? https://imgur.com/a/xhCZgds

Re: Curvature consistency in Apple hardware and software products (2017)

#45
post #23

The curvature combs are confusing to me. Is this equivalent to saying that Apple’s rounded corners have a continuous second derivative while naïve rounded corners only have a continuous first derivative but a discontinuous second derivative? Or am I misunderstanding this?

That is roughly correct. For a curve with smooth parametrization f(t) = (x(t), y(t)), with f'(t) ≠ 0 for all t, the curvature at the point f(t) is defined to be κ := |(f'(t)/|f'(t)|)'| -- the magnitude of the first derivative of the unit tangent vector. This is a nonnegative quantity, and is well defined, that is, independent of the specific parametrization of the curve (as legosexmagic said, you need to do something like this to get a quantity independent of the parametrization, but it is essentially a "normalized" second derivative).

The curvature comb consists (it seems to me) of a normal line segment at each point, whose length is directly proportional to the curvature there.

Re: Curvature consistency in Apple hardware and software products (2017)

#46
post #23

The curvature combs are confusing to me. Is this equivalent to saying that Apple’s rounded corners have a continuous second derivative while naïve rounded corners only have a continuous first derivative but a discontinuous second derivative? Or am I misunderstanding this?

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.

It's called C2 continuity.

Re: Curvature consistency in Apple hardware and software products (2017)

#47

I guess I have really bad eyes but I can’t tell the difference at all. They both look like rounded corners to me. I don’t think the aesthetic effect is that pronounced. I’d like to see the author do a blind taste test and be able to identify this magical “curvature comb” without seeing the brands.

I think it’s definitely something that’s visible in 3d on a somewhat reflective surface, but it’s definitely harder to tell projected top down in 2d for me.

edit: it’s definitely subtly noticeable in the image posted by sibling

Re: Curvature consistency in Apple hardware and software products (2017)

#48

I guess I have really bad eyes but I can’t tell the difference at all. They both look like rounded corners to me. I don’t think the aesthetic effect is that pronounced. I’d like to see the author do a blind taste test and be able to identify this magical “curvature comb” without seeing the brands.

Out of curiosity, are you really not able to tell which is which in this unlabeled image? https://imgur.com/a/xhCZgds

(Not parent) Seeing this, it’s definitely noticeable but it’s very subtle.

Re: Curvature consistency in Apple hardware and software products (2017)

#49

Earlier quoted context omitted.

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.

It's called C2 continuity.

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?

Re: Curvature consistency in Apple hardware and software products (2017)

#50

Earlier quoted context omitted.

My apple cables are consistently the first to wear out. I must be using them wrong.

It's always weird to read things like that because I definitely mistreat my cables, and I've had lots die, but my Apple ones hold up very well. I have just one Lighthing cable that recently broke and that one was from 2013 IIRC so I guess that's ok. Everything else seems to hold up about as well as expensive Anker cables, if not better, including Macbook chargers going back to 2005 or so. I'm in the EU though, maybe…

Different folks mistreat in different ways. I’m struck by the number of people who will yank their laptop to move the power brick, for example, which is of course the worst case scenario for cable strain relief and leads to premature socket failure in the laptop.
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