The Continuity of Splines

Caption notes

Freya Holmér starts by joining Bézier curves and breaks smoothness into testable conditions: connected positions, continuous velocity and acceleration, and matching geometric tangents and curvature. She compares how Bézier, Hermite, Catmull–Rom and B-splines handle control points, local edits and continuity. Different forms can even generate the same individual curve; their promises concern how a whole path is constructed. The main discussion concerns uniform cubic splines. She explicitly notes that implications from parametric to geometric continuity require regular curves, with nonzero velocity.