Apple Corner 1. Approximated Clothoidal Transition
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- Опубліковано 12 вер 2024
- I've had a few comments since posting the MacBook Air M1 video, regarding the 'Apple Corner'. I decided to investigate the clothoid/Euler spiral again and found a post from 2023 on the Rhino forums, with a Grasshopper definition that creates a clothoid transition between a line and an arc. In the past I have given up as I do not have the programming know how to figure this out. Using the Grasshopper definition, I have matched an approximated clothoid transition to the MacBook Air corner, then created ratios from the result, to make it easy to recreate the corner in Solidworks, as well as creating the corner for different target radii. The ratios worked to match geometry to a 2020 iPad Pro, which has a larger corner radius than the M1 Macbook Air.
Thanks to Ivan Gálik and Matej Fitoš for the Grasshopper definition.
Here's a link to the Rhino thread. discourse.mcne...
Here's a link to the Macbook Air M1 video
• MacBook Air M1 Exterio...
Here's a link to the Apple Corners Part 2 video
• Apple Corner 2. Variat...
Here's a link to the Apple Corner Part 3 video
• Apple Corner 3. Clotho...
Please visit my site for more information. ajdesignstudio...
For more Solidworks videos, please visit my channel.
/ @andrewjacksondesignst...
#solidworks #industrialdesign #surface #macbookair #applecorner
I have no idea what I have just watched, but the amount of thinking, math and time that goes into creating the corner is mind blowing...
Definitely a black hole for time!
@@AndrewJacksonDesignStudio Someone has to do it 😀
@@Puleczech I mean as a fellow idiot, I would say just round the corner somehow
@@Minecraftzocker135 I feel like watching the first guy who came up with a wheel, explaining how it is going to change the world and I am just standing there laughing at him with my booming square brick bike rental business.
Love to see this Andrew. I once tried a similar experiment tracing apple corners and built my own equation to define a style spline...but it was always approximated - I see now I hadn't realised there was a perfect arc in the centre of it! Really appreciate you sharing these tips and experiments.
I've tried several ways to achieve the corner, like you have. One piece, three piece (similar to this vid, except assuming the arc was tangent to the sides) etc. It's all good learning though, that we can apply to other work
@@CraigMcG oh the time I have spent on this. Pre 2020 not a lot of this was discussed in product design forums
Thanks for all your videos, so insightful. Slowly going through them to up my game in surfacing and study of form
All good
Thank you so much, truly the treasure on UA-cam
Cheers!
Very interesting. That's the kind of content you won't find anywhere else. I am already looking forward to more videos demystifying the way Apple is modelling their surfaces
Thanks for watching. This is all guess work :) but educated guesses!
This is huge! Thank you so much for the investigation and for putting in the time to share it back. Legend.
All good!
Looking forward to the updated video!!!!!! Great content mate!
and once again, this man anticipated all of our wishes and exceeded all expectations
this is true passion for the game
Thanks for the shoutout Andrew!😊😊
That script is a god send!
I’m travelling right now, I will write some detailed comments this weekend!!
Sounds good Tony. Looking forward to seeing what you think. I'm going to check the effect of the three piece corner on the pillowed surface/pinched corner. Might have to decouple the corner and pinch surfaces.
@@AndrewJacksonDesignStudio so here are some thoughts:
1) How about other angles? We have covered 90 but need to cover other common angles like 60, 45. 120 and also apply this for the perfect “pill profile”.
2) we can’t be too sure if this is indeed what Apple is doing. Visually it is a very close match. I had some success replicating this rounded corner approximately with a single spline. This would be similar to achieving a g3 continuity between the clothoid segment and the circle. All I remember is I did not use style spline in solidworks to achieve this. Instead used regular spline and manipulated the control polygons.
3) 3 pieces seem very complex. Looking forwarding to see the challenges in making surfaces out of them.
Imagine having to construct this for multiple guide curves and what not. Tedious.
4) a protocol for offsetting: I think you should try out various ways to offset this 3 piece corner (both inward and outward). What way of offsetting looks visually pleasing and what way of offsetting strikes a balance between looks and speed.
The radius setback makes total sense now that I’ve seen it. If the radius was tangent to the sides, the only solution for a “blend” that stays outside the radius and inside the sides would just be the points of tangency.
Any blend with nonzero length and some sections with curvature less than that of the radius would either:
-start tangent to the side and require either a section of greater curvature or a loop to meet the radius, or
-start tangent to the radius and require either a section of greater curvature or a “hump” that ran proud of the sides.
This is sort of the “hump” option with the sides moved up to meet the apex of the hump.
You can get a g3 blend in between a line and arc, with the arc being tangent to the sides. That is one way how I make a lozenge form. I have two angles coincindent to the arc centre, one pushes the line start point back and the other controls the arc size. This can be done with none of the blend CVs extending outside of the line, so no hump. But when used on a 90deg corner, it definitely looks forced compared to having the arc off set or set back.
@@AndrewJacksonDesignStudio Oh for sure it’s doable. I’ve made some pretty ugly G3 splines trying to get smooth curves to fit the wrong constraints. I think the reason it seems forced in this case that we expect the curvature to peak (or in this case plateau) once in the middle of the corner and run downhill both ways from there with no local maxima. It’s possible to blend a radius into a tangent line with a g3 curve, but I don’t think it’s possible to do so with the maximum curvature being at the endpoint.
I've been unreasonably intrigued by this concept for years. I've noticed that Apple makes less use of this type of corner on hardware and more often in software. My hypothesis about their reasoning is that a neat, constant radius corner is hard to achieve in reality so when it's done, it looks premium. However, on screens, it's easy to achieve and therefore abundant, so a smoother corner feels more premium in that case.
It features on the vast majority of hardware that they make. Phones, iPads, MacBooks, iMacs, apple tv and watches. Watches have the added complexity of non flat sides. Even the Vision Pro has the same corner, on the battery etc. maybe it is because it is repeated on every UI item it seems to be used more often? Definitely part of their brand DNA.
@@AndrewJacksonDesignStudio Really? I guess I'm just mistaken about what I'm seeing when I look their products.
This corner (or a variation of it) is on pretty much every rectangular/square piece of hardware they make. Maybe we are discussing different things?
@@AndrewJacksonDesignStudio I think we’re talking about the same thing. I just frankly assumed they didn’t use it on hardware because it didn’t look like it to me. It definitely sees like you’re more informed than me.
Cool stuff! This video brought me back to some old Rhino files, trying to draw perfect Apple-like corners and pill shapes. Do the "real" Apple corners contain an actual arc, or is it a spline with about eight or so control points?
I do need to check if this works with pill/lozenge forms, thanks for the reminder. I do not know if they use a single spline or a multi-curve solution. There is no way to know really. Their product drawings for marketing do not show multiple tangent breaks around the corners, but the drawings are no doubt cleaned up.
@@AndrewJacksonDesignStudio Cant post the link, but google: "Apple Accessory-Design-Guidelines.pdf" and go to page 283 🤯, I just found that, didnt know apple released actual technical drawings.
okay, i think you get the key what ppl wanna watch, hope it will be 10k & 100k soon.(3k now)
Yeah.. corners. Who'd have thought?!
@@AndrewJacksonDesignStudio Corners, how do they work? *Sorry to any insane clown posse fans :)
@@mikedoell well, if I'm on my MTB, outside pedal down, mass on the outside.
TY for the tutorial
Yep, all good!
Nice, maybe you could get someone to cnc a few sample corners to compare it!
I’ve defined the corner several ways and printed some off. It’s spot on match for the MacBook corner
Really interesting!
Apple pays huge amounts of attention to corners.
In your demo; I was only missing a simple extrusion and zebra on it to see how the surface flows.
What CAD software does Apple use for industrial design? Before Rhino’s macOS release I think Alias and Siemens NX was the only nurbs surface modellers available for Mac. Both Alias and Siemens have now discontinued their macOS versions. Maybe they didn’t find it financially viable to port their software to a new CPU architecture once again.
Hi there. There's a zebra at the end, 13:20. Also I have a follow up looking at different transitions between the line and arc sections. ua-cam.com/video/mOOebAttW-c/v-deo.html
Apple uses Alias for the A side ID surfaces (maybe for B as well?) and the ID surfaces are imported into NX for ME development. They use Rhino/Grasshopper as well. I bet they use other CAD software too...
@@AndrewJacksonDesignStudio Ah! My bad, I didn't watch the SolidWorks stuff that carefully, although impressive. Was waiting for zebra in Rhino :D
I have been wondering what degree Apple uses for their corners, but I didn't know the term "clothoid transition". Excellent stuff.
Yeah no idea how they construct corners! This is all speculation. It looks like they have the same corner across multiple products, except with differing scales
Cool, never heard about clothoidal, thanks! Some people say the Apple corner is based on the “squircle”. No idea if that’s true, but continuous curvature seems to be the consensus online.
All good. I’m pretty sure a squircle has non linear sides. If you get a straight edge and check an iPhone, Apple TV etc, the sides are linear.
@@AndrewJacksonDesignStudio you’re right, it’s not a mathematically perfect fit. But I think the idea is you’d use each quadrant for each corner, offset them, and connect with lines. That technically creates a microscopic curvature discontinuity where you join them, but it’s so tiny that it doesn’t feel like cheating to ignore it. If you can stomach that, the squircle (“super ellipse”) has otherwise smooth curvature change: it’s not piecewise and has no linear sections. It’s also simple to calculate.
Out of interest, do you think the mathematical “truth” is important? Or are you just looking for a practical “continuous curvature” radius shape?
Any curve defined in a cad system is a mathematical truth. Therefore it’s more about what the designers intent was. All radii are continuous in curvature as they are arcs. Im interested in investigating this as are others as there are different ideas around the ‘mystery’ of how apple may define their corners. The placement of the arc and blends in the grasshopper definition gives a result that is quite close to my reference. I suspect a squircle segment will be a bit too pointy, like a conic with a higher rho value
@@aaaidan nah nah throw the squircle away. It is too pinched. It is more organic and doesn’t gel well with straight lines
why do you use solidworks for surface modeling after doing all this in rhino? is there any reason for you to use solidworks over rhino?
The grasshopper clothoid cannot be defined in Solidworks as far as I know. The geometry/ratios are interchangable as both Rhino and SW are using single span bezier splines.
I mainly use Solidworks for client projects. Completely different approaches as well for product development. Rhino you have to layer off progress, in case you need to go back and change something. SW, tree based, so easier to tweak things. Downside is SW surfaces can be average and analysis tools in SW are not fantastic.
How to blend control points equally in rhinos?
I did it manually with endbulge command
Hello! What is the relation between 10.25 and 14.16? At 10:50 . Thanks a lot!
Hi there. They are ratios that I took from the original Grasshopper clothoid output at the start of the video. Those ratios are based around a target corner radius of 10mm
@@AndrewJacksonDesignStudio Thanks!