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Desperately Seeking Squircles

In a famous 1972 interview, Charles Eames answered a short sequence of fundamental questions about the nature of design.

First, there is the surprising fact that the iOS version of the formula (at least at the time of investigation) was found to have some quirks — the corners aren’t exactly symmetrical, and one side has a minuscule straight segment which clearly doesn’t belong. As smoothing slowly increases, we want the height of the tabletop to stay fixed while its cliff edges start turning into steep slopes, yielding an isosceles trapezoidal curvature profile (still with a total area of π/2, of course). We can actually plot this pair of equations (given some reasonable choices for ξ, θ and R) to get a path as a function of s. If we had access to arbitrarily many terms and could compute the sums, we’d see that as s increases, the curve begins to spiral in on itself, though this happens far from the domain we’re interested in, which is the flatter ramp-up section.

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