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The Continuity of Splines

Freya Holmér · explainer · Watch on YouTube

Computer graphics & renderingRecreational & visual math

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.

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.

  • 10 people recommended it
  • 11 different months
  • 8 strong recommendations
  • first 2022, last 2026

What HN commenters said

  1. “Another upvote for Freya Holmér's amazing video "The Continuity of Splines".”

    Timestamps on reflection test, curvature combs, B-spline continuity.

    AceJohnny2, 2022-12 · Strong recommendation · in “Apple's Unique Device Curvature”

  2. “Her video "The Continuity of Splines"[0] is my favorite watch of the past year.”

    Deep dive on splines, commenter's favorite watch of the year.

    zxexz, 2023-10 · Strong recommendation · in “Why can't you multiply vectors? [video]”

  3. “I've watched it like 3 times over the last year.”

    Amazingly well done, deeper dive on splines; watched repeatedly.

    viggity, 2023-12 · Strong recommendation · in “Interpolation Methods”

  4. “is (IMHO) one of the best educational videos on a programming topic, full stop.”

    One of the best educational videos on a programming topic.

    aaronblohowiak, 2024-02 · Strong recommendation · in “Look, ma, no matrices”

  5. “I didn't really understand Bézier splines until I watched this excellent video [0] from Freya Holmér.”

    Explains kinds of splines, equations, and importance of derivatives.

    ixwt, 2024-05 · Strong recommendation · in “Hobby's algorithm for aesthetic Bézier splines (2020)”

  6. “Freya Holmér has a wonderful video on them”

    Wonderful video on Bezier curves.

    WillAdams, 2025-06 · Strong recommendation · in “Ask HN: What cool skill or project interests you, but feels out of reach?”

  7. “Also from her - The Continuity of Splines [0].”

    Additional spline material from the same creator.

    fuzzythinker, 2023-09 · Recommendation · in “Bézier Curves and the logic behind them”

  8. “It's a detailed discussion of how you derive Bèzier and higher-order curves to serve your purposes.”

    Detailed derivation of Bezier and higher-order curves.

    nick-of-time, 2023-09 · Recommendation · in “Circles Do Not Exist”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: bezier, b-splines, continuity, interpolation, computer graphics, math visualization

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