HackerThe Beauty of Bézier Curves
Freya HolmérYouTube ↗
Further reading 2
What becomes visible when you change representation? →An average, a spectrum and a geometric diagram each foreground a different structure. Before asking which view is intuitive, ask which comparison you need it to support.This video helps answer · Halfway through the parameter: halfway along the path?The path looks smooth. Why does the camera still jerk? →Follow two complementary explanations by Freya Holmér: first inspect how progress along one curve is measured, then how two curves join. Constant speed, continuous tangents and continuous curvature are different requirements.This video helps answer · A parameter percentage is not a distance percentage
Caption notes
Freya Holmér constructs Bézier curves through repeated linear interpolation, then rewrites the same curve as a weighted sum of control points. Derivatives expose tangents, bounds and curvature. The later examples reveal an animation trap: advancing the parameter t uniformly does not necessarily move an object uniformly along the path. A sampled table relates accumulated distance to t, enabling approximate distance-based movement while making the tradeoff between sampling cost and accuracy explicit.
Archived captions (transcription method unspecified) ↗Original passages · 2
equally spaced t values are not equally spaced by distancegenerate what's called a lookup table