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    The Continuity of Splines

    Freya Holmér

    10 HN recommenders · recommended in 13 months, 2022–2026

    YouTube

    1:13:50 · 1.9M views · Dec 7, 2022

    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.

    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.

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    20 comments from Hacker News

    1. @WillAdamsJun 2025· in “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

      Strongly recommendsView on HN
    2. @AceJohnny2Dec 2022· in “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

      Strongly recommendsView on HN
    3. @ixwtMay 2024· in “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

      Strongly recommendsView on HN
    4. @viggityDec 2023· in “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

      Strongly recommendsView on HN
    5. @zxexzOct 2023· in “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

      Strongly recommendsView on HN