Hacker News Reader

Comment by cloud9193 | Hacker News Reader

A small but crucial detail that sets Apple apart from almost everyone else in both digital and physical design is the use of curvature continuity.

"Posers" use G1 continuity, Apple uses G2 at a minimum if not G3. More complex math but smoother corners and surfaces. There's actually no 'radii' on Apple products.

https://medium.com/@kennethlinzj/curvature-continuity-5a1c4c...

A good 99 Percent Invisible podcast on this:

https://99percentinvisible.org/article/circling-square-desig...

View on HN

Squircles were actually part of the visual language of Nokia years before iOS 7 added G2+ continuity.

https://interuserface.net/2011/06/own-a-shape/

If you’re looking for “smoothness”, check out my treatise on the Euler spiral: https://xixixao.github.io/euler-spiral-explanation/

I have used superellipses as oscillators.

They look much better than rounded rectangles, and probably work with less and more equally spaced polygons in 3d. You can probably calculate the points as slices in azimuth, or as a continuous helical spiral.

They give larger curvature smoothness than rounded rectangles, and superformula gives a wide variety of shapes and smooth transition between a circle and a square with changing parameters.

Superformula is a generalisation of superellipse, and works in 2D and 3D. Superellipsoid is the 3D counterpart:

* [Superformula - Wikipedia] (https://en.wikipedia.org/wiki/Superformula)

* [Superellipse - Wikipedia](https://en.wikipedia.org/wiki/Superellipse)

* [Superellipsoid - Wikipedia](https://en.wikipedia.org/wiki/Superellipsoid)

Squircle is a special case of superellipse with parameters a and b equal and n set to 4:

* [Squircle - Wikipedia](https://en.wikipedia.org/wiki/Squircle)

Danish Piet Hein invented the Superegg:

* [Superegg - Wikipedia](https://en.wikipedia.org/wiki/Superegg)

An intuitive understanding or the mathematical formulas is that they describe an oscillating radius, which results in the various shapes as you move along the angle in polar coordinates.

I find it vaguely amusing that the author (and apparently yourself) claim that using simply rounded corners would be a "lack of care and detail". I mean if you prefer Apple's fancier corners then great, but shaming a manufacturer for using a perfectly serviceable rounded corner is a bit much IMO.

To quote Charles and Ray Eames: “The details are not the details; they make the product”.

For sure, but what details matter is often subjective. I've looked around my desk and surely the vast majority of the objects here use the simpler rounded corner but I really fail to see how it's bad craftsmanship.

If anything I'd argue that for professional appliances the circular corners convey a less organic, more industrial look that feels, to me, more suitable.

But then again, I enjoy brutalist architecture, so you can probably safely discard my opinion.

Can you explain the advantage of using these Gn curves instead of just using a larger radius?

In the Medium article, the comparison between the Apple and non-Apple would be less striking if the non-Apple version had a larger radius.

The difference is subtle, but there’s still a perceptible type of “corner” where the square meets the circle. So if you round a sharp 90 degree angle with a circle, you end up with two very subtle corners on either side of the circle, where the circle touches the flat edges. A larger radius doesn’t fix this, it’s inherent to the connection between a square and a circle.

One way to think about it is in terms of the derivative of the path (which is what “Gn” means). A straight edge has a constant straight derivative, parallel to the path. A circle has a constant derivative perpendicular to the path. When you connect the two, there is a discontinuity in the derivative, the rate of change of the path jerks suddenly from circle to straight edge. And you can see it visually, even though it’s pretty subtle. With a smoother curve, the derivative is also smooth, and then there’s no abruptness in the curvature where the two edges meet.

Reply on news.ycombinator.com