While it is a shame that Apple doesn’t release the official shape for designers to use, I can understand why.

Apple has been using variations of this curve on its products for many years before iOS 7. Over the years, I have admired the curve on my old MacBook, iMacs and more recently, iPad. The curve is like a piece of intellectual property; one of those subtle design features that sets Apples products apart from the competition. It permeates their hardware and user interfaces. Releasing the construction method for this curve, or even a vector file, could result in it being adopted more easily by competitors. Its construction method may not even be patentable, so keeping it a secret would be to Apple’s advantage.

For the iOS icon mask, I think the corner curve is a bezier approximation of a traditionally constructed elliptical curve. Ellipses, as are other curves derived from conic sections, are easy to construct with basic drawing tools, e.g., A pair of compasses and a ruler. For this reason, but not this reason alone, I don’t think a squircle algorithm is used.

Here is my more traditional exploration of the curve using conic sections.

http://www.designbygeometry.com/ios-icon-mask-corner-curve-study/