Curvature consistency in Apple hardware and software products (2017)
hackernoon.com
hackernoon.com
So you can go and make those transitions flawless by making sure the curvature combs transition into each other as well (basically a set of spaced out lines which you draw perpendicular to the line in question where the magnitude equals the curvature). If the curvature combs meet at the transition, the transition looks okay. If the curvature combs are tangential to each other it looks better. You can also add a second order curvature comb to the first one and make sure these connect as well etc.
Would this be like the illustrations in the article labled "curvature comb showing tangency" and "cuvature comb showing curvature continuity"?
(Submitted title was "Apple's Unique Device Curvature". I assume that rewrite was intended to replace the linkbaitiness of the article title, which is in keeping with the site guidelines: https://news.ycombinator.com/newsguidelines.html)
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.
Do you put your laptop in a bag where it gets squished between books and other stuff to cause the display to be pushed in?
Bad design, imo.
It's basically just Bauhaus design but with a few nice soft features, it's gonna be a bit uncomfortable, it's gonna be expensive, it might compromise functionality, all to create a sense of precision, authenticity, and high-endness.
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.
Apple has been notorious for sacrificing good strain relief on their cables in pursuit of aesthetics for years. Possibly things have improved now that Ive has left, but there was a period a few years ago when everyone I knew with a Macbook had wrapped the power cable in electrical tape because the cable housing had failed just above the (useless) strain relief sleeve you describe.
But they have changed the design a lot since then so I no longer think this is an issue. The brick is now usb c so you can swap the cable without needing an expensive brick, and the MagSafe cables they now include are braided instead of rubber.
Whether the cables with the braided sleeve are better is something that remains to be seen.
Just wanted to say, you aren’t alone. I don’t do anything special with mine, I’m sure I mistreat them as much as the next person, but like never have the kind of damage I’ve seen others have or complain about.
There's guides on how to workaround it using things like Sugru or tape, but still frustrating.
Over time their strain relief has gotten shorter or longer https://cdn0.tnwcdn.com/wp-content/blogs.dir/1/files/2012/03...
So a lot of people's memories about Apple's strain relief may come from one of their darker periods when they were super short, stiff and useless.
In my personal experience their previous laptop MagSafe had absolutely useless strain relief and mine would always start going bad within 6-12 months. https://cdn.vox-cdn.com/uploads/chorus_asset/file/13878908/2...
The current braided MagSafe cables actually have zero visible strain relief but seem like they're simply stronger, mine has held up well so far.
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?
You don't want a train to suddenly experience a sideways force as it enters a curve. So the 2nd derivative of the position, acceleration, should not instantly go from 0 to a constant, instead, it should grow smoothly, like pictured in TFA. So you want a non-zero 3rd derivative, and possibly even a non-zero 4th derivative.
Cubic splines of course give you a nice 3rd derivative. In fact, you can't make a perfect circle using cubic splines, because of that. Draw your device's shape in Illustrator or Inkscape, and you likely make it Apple-like :)
curvature only depends on the shape of the object.
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.
App: https://squircley.app/ Code: https://dev.to/georgedoescode/codepen-soften-up-your-designs...
Please follow-up on this thread with any discoveries or learnings, would be interesting and cool to learn how to replicate the nice soft curve for web assets. Depending on how many different semi-reasonable approaches exist, this subject and analysis would also make for a compelling and blog article.
Edit: Thank you Charles - wow you're so quick to have unearthed and replied with squircle resources in the time it took for me to compose the three sentences above.
p.s. CharlesW: thanks for your helpful and informative comments in general, I consistently look forward to reading your comments whenever I see one. Cheers and happy holidays!
https://iamvdo.me/en/blog/smooth-corners-with-css-houdini
I would love it to be built into browsers as standard.
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.
import numpy as np
import pandas as pd
import seaborn as sns
import sympy as spI 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.
As seen on HN this month.
She covers the insightful "reflection test" around the 28:05 mark: https://youtu.be/jvPPXbo87ds?t=1685 and actual "curvature combs" at 32:26.
Finally, she covers the continuity of curvature combs that B-Splines exhibit around the 54:00 mark: https://youtu.be/jvPPXbo87ds?t=3240
But they do: D558,757 and D670,286. Don't people remember Apple v. Samsung case?
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.
edit: it’s definitely subtly noticeable in the image posted by sibling
Apple’s Icons Have That Shape for a Very Good Reason - https://news.ycombinator.com/item?id=16294455 - Feb 2018 (5 comments)
Apple’s Icons Have That Shape for a Very Good Reason - https://news.ycombinator.com/item?id=13484728 - Jan 2017 (5 comments)
Usually, small radii are emulated by beziers: https://spencermortensen.com/articles/bezier-circle/