The Continuity of Splines
Why Hacker News recommends it
It is the go-to recommendation for anyone who wants to genuinely understand Bezier curves and splines, and commenters repeatedly call it one of the best programming-related educational videos.
What it is
Freya Holmer's 74-minute video essay on splines, covering Bezier curves, B-splines, derivatives and the different levels of continuity (C0, C1, C2), built with custom animation tools. She notes she did not cover non-uniform splines.
Recommended by 10 HN commenters across 11 different months, 2022 to 2026.
What Hacker News said
Strong rec AceJohnny2 · 2022-12 · on “Apple's Unique Device Curvature”
Another upvote for Freya Holmér's amazing video "The Continuity of Splines". She covers the insightful "reflection test" around the 28:05 mark: [this video] and actual "curvature combs" at 32:26. Finally, she covers the continuity of curvature combs that B-Splines exhibit around the 54:00 mark: [this video]
Strong rec zxexz · 2023-10 · on “Why can't you multiply vectors? [video]”
Oh lovely, can't wait to give this a watch. Freya dives deep, and gives wonderful talks. Her video "The Continuity of Splines"[0] is my favorite watch of the past year. [0] [this video]
Strong rec viggity · 2023-12 · on “Interpolation Methods”
If this paper is interesting to you, you may also be interested in this amazingly well done video on the continuation of splines. It isn't exactly the same thing, and delves into some deeper concepts, but I've watched it like 3 times over the last year. [this video]
Strong rec aaronblohowiak · 2024-02 · on “Look, ma, no matrices”
the splines yt video ( [this video] ) is (IMHO) one of the best educational videos on a programming topic, full stop.
Strong rec ixwt · 2024-05 · on “Hobby's algorithm for aesthetic Bézier splines (2020)”
I didn't really understand Bézier splines until I watched this excellent video [0] from Freya Holmér. It talks about various kinds of splines, and the various equations behind them. Explains the importance of the derivatives of splines (as other comments here have pointed out). [0]: [this video]
Strong rec viggity · 2025-02 · on “Jacksonpollock.org (2003)”
If splines/beziers are of any interest to you, I could not recommend these videos from Freya Holmer enough. [this video] [LINK]
Strong rec WillAdams · 2025-06 · on “Ask HN: What cool skill or project interests you, but feels out of reach?”
For me, it's Bézier curves --- Freya Holmér has a wonderful video on them: [this video] and I've been trying to read through _METAFONT: The Program_ and [LINK] and I keep wondering if I shouldn't just try scripting Inkscape.... I want to do a couple of different things, and not sure if they all fit in one project or no: - implement a single line font in my current project: [LINK] - implement a way to convert arbitrary curves into smooth arcs (for DXFs or G2/G3 arcs for G-code) - work up an interactive version of METAFONT/METAPOST which allows both programming and drawing
Strong rec viggity · 2025-08 · on “Bezier-rs – algorithms for Bézier segments and shapes”
Anytime béziers are mentioned on HN, I feel compelled to share these absolutely incredible videos from Freya Holmér [this video] (73 minutes) [LINK] (24 minutes)