Geometric Continuity & Lamé Curves
Solving the tangent discontinuity of standard border-radius.
When utilizing the standard CSS border-radius property, browsers render corners by appending a literal quarter-circle arc to the ends of straight lines. In mathematics, this is known as G1 geometric continuity. Because the curvature drops instantly from zero (on the straight line) to a fixed radius (at the start of the arc), the human eye detects a harsh, abrupt tangent transition—often perceived as a subtle visual "bump".
Hardware manufacturers, most notably Apple in their Human Interface Guidelines (HIG), abandoned simple circular arcs in favor of the "squircle" (technically a Lamé curve or superellipse). This shape possesses G2/G3 continuity, meaning the curvature rate increases gradually before reaching the apex of the corner, creating a seamlessly smooth transition that looks vastly more organic and premium.
Historically, recreating true squircles on the web required complex SVG masks or JavaScript-driven CSS Houdini worklets. However, modern engines process clip-path: inset(0 round X) using superior path-smoothing algorithms. By applying this mask over an element, we force the browser compositor to truncate the harsh intersections of standard border radii, yielding near-perfect continuous curvature natively.