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Curvature consistency in Apple hardware and software products (2017)

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

#51

Post by gruez »

Waterluvian wrote: post #22
crazygringo wrote: post #19

Earlier quoted context omitted.

What are you talking about, every Apple USB and Lightning cable I've ever had has had strain relief on both ends. There's the main plug in a plastic housing, and then there's an extra-thick rubber part about a centimeter long which is the strain relief wrapped around the cable, and then the rest of the cable itself. Clearly visible in any product photograph close-up.

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

On the other hand all my cables are just fine, apple cables included. It's probably not due to lack of use; I use them nearly every day for years now.

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

#52

Post by kelsolaar »

phkahler wrote: post #46
legosexmagic wrote: post #35

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.

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

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

#53

Post by tinus_hn »

muro wrote: post #3
muro wrote: post #2

I wish they would put in at least some basic effort into smoothing that sharp edge where wrists often rest when using the MacBook, rather than just the curvature of the corner. Any cheap laptop is nicer to my wrists than a MacBook.

Also: if they could create a gap between the screen and the keys, so the screen is not always smudged after closing the MacBook. Aka, if you use your MacBook as a laptop, the screen will be dirty even if you are careful to never mistakenly touch it.

Do the keys also scratch the screen like on a Dell or HP?

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

#55

Post by jsjohnst »

phkahler wrote: post #46
legosexmagic wrote: post #35

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.

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

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

#58

Post by nickpinkston »

The fun hardware aspects of this are how they choose to form curves for the aluminum MacBooks using cold forging to get create the broad curves of the device and then post-machining the keyboard, chamfered (angled) edges, and form tapping the screw boss threads - ie pressing not cutting the threads into the material.

Variable radii curves take forever to machine and must be polished, so that's only done on the cold forging die (and takes forever to do), so the die can then impart the geometry on the aluminum blank in only seconds in the forging press.

This is also how high-end aluminum car wheels are made with all their complex curvature.

Funny enough, they don't cover the forging in this video that describes most of the rest of the process, so I think Apple must've not wanted to talk about it, as least back then.

https://www.youtube.com/watch?v=sxbiIpXZfG8

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

#60

Post by virtualritz »

This is standard knowledge in product design.

Most people doing font design also have a keen understanding of this.

Even if often more intuitively that through maths.

That said, in 2D you can get away with tangent continuity (C1) and stuff looks good.

I.e. while people may be able to tell the difference between a square with corners that have been rounded using quadratic arcs and one that uses cubic arcs or is a superellipse of some sort, these are all still looking fine.

In 3D, outlines will also look ok but a soon as you have shading anything that is not curvature continuous (C2) will stick out sorely.

The term most often used for the visual artifact that ensures is 'broken highlights' (see the photos in the article).

For example, if you write displacement or bump shaders and you transition between ('smooth') functions and want to maintain a smooth surface appearance, smoothstep()[0] is not enough. It is only C1 continuous.

You need a higher order variant, e.g. Ken Perlin's own improved version that is C2 continuous[1].

CAD software usually has zebra strip analysis shading which makes these things stick out so they can be fixed by rebuilding/retopologizing surfaces.

[0] https://en.m.wikipedia.org/wiki/Smoothstep

[1] https://en.m.wikipedia.org/wiki/Smoothstep#Variants

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