Hyperbezier curves: a new family that could replace cubic Béziers

The mathematical beauty of hyperbezier curves

Raph Levien, creator of Spiro curves, proposes a new curve family for 2D vector graphics that he believes can surpass cubic Béziers. The hyperbezier, defined by a Cesàro equation, offers smoother curvature variation, contains exact Euler spirals and circular arcs, and handles sharp corners and hyperbolas with ease. It approximates cubic Béziers well at low angles and shows promise for interactive design, though it can't represent curves with two inflection points. Levien shares the math, interactive demos, and future plans for spline integration and curve fitting.