Superellipse Family

A superellipse is a closed curve defined by |x/a|^p + |y/b|^p = 1. The shape was systematically studied by Gabriel Lamé in 1818 and later popularized by Danish designer Piet Hein, who used p \approx 2.5 to design the iconic Sergels Torg roundabout in central Stockholm. The exponent p smoothly interpolates between an astroid, a diamond, a circle, and increasingly square-cornered shapes, making superellipses a flexible family for industrial and product design.

Here a single implicit zero set is driven by an animated exponent n, with a = b = 1. As n sweeps from 0.5 to 4 the curve morphs continuously: hollowed astroid cusps below 1, the diamond at n = 1, the ordinary circle at n = 2, and squared-off squircles as n grows past 2. Equal aspect ratio keeps the morph honest, so the cornering and hollowing read directly as the exponent changes.