video

Freya Holmér: The Continuity of Splines

by Freya Holmér

Seventy-four minutes on why splines are built the way they are. It runs from lerp to Bézier curves to the whole ladder of parametric (C⁰ to C∞) and geometric (G¹, G²) continuity, with curvature combs and osculating circles animated live in a game engine. It's the clearest visual treatment of smoothness and curvature on YouTube, and it explains why the pen tool in every design program behaves the way it does.