The Beauty of Bézier Curves

Freya Holmér
20 HN recommenders · recommended in 20 months, 2021–2026
YouTube
2.2M views · 5 years ago · explainer · intermediate · evergreen

Freya Holmér builds up Bézier curves from scratch with animated, interactive visuals, starting from simple linear interpolation and working up to higher-order curves, derivatives and how they are used in graphics. It treats the topic as geometry you can see rather than a formula to memorize.

HN treats it as one of the best educational videos on YouTube, the one that makes Bézier curves finally click through animation.

“is in the running for one of the best educational videos on YouTube”
Explorable explanations & visual explanationComputational & parametric design
#béziercurves#splines#vectorgraphics#animatedmath#interpolation

25 comments from Hacker News

j
@jedimastert2026 · in “A Primer on Bézier Curves – So What Makes a Bézier Curve?”
Related, I think Freya Holmér's "The Beauty of Bézier Curves" is in the running for one of the best educational videos on YouTube. ▶ this video
Strongly recommendsView on HN
e
@eveningtree2022 · in “A Primer on Bézier Curves”
Another beautifully explained piece on bézier curves is: The beauty of bézier curves by Fréya Holmer ▶ this video Found this via a contest by Grant Sanderson, and it absolutely blew me away(and most people I forwarded it to)
Strongly recommendsView on HN
g
@gadgetoid2026 · in “Curvature Beziers: Improving on a timeless recipe”
Well that’s wild because I had a disagreement with beziers recently and did a similar thing! [1] albeit with more madness and less polish. Driven by the a/s/d/f keys with find edges snap to reference images and curve fitting to construction geometry. Feel I should also call out Freyr’s videos for anyone who has missed them - continuity of splines [2] and the beauty of Bézier curves [3] [1] link [2] link [3] ▶ this video
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v
@viggity2025 · in “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 link (73 minutes) ▶ this video (24 minutes)
RecommendsView on HN
v
@viggity2025 · in “Jacksonpollock.org (2003)”
If splines/beziers are of any interest to you, I could not recommend these videos from Freya Holmer enough. link ▶ this video
RecommendsView on HN
W
@WillAdams2025 · in “Desmos Animated Graphing Calculator”
A wonderful example of this is: The Continuity of Splines link and The Beauty of Bézier Curves ▶ this video by Freya Holmér link While not animated, I find: _Euclid's Elements_ (Joyce's Java Version) very helpful link Since my current project has pretty much devolved to putting a UI on various trigonometric functions and allowing the user to program them, I'd be very glad of other resources in this space (currently working through Hilbert's _Geometry and the Imagination_ and the book which matches link and just finished the _Make:Geometry/Trigonometry/Calculus_ series, and have had recommended Curves and Surfaces for CAGD: A Practical Guide by Gerald Farin)
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W
@WillAdams2025 · in ““A Course of Pure Mathematics” – G. H. Hardy (1921) [pdf]”
You're welcome! Hopefully someone can make recommendations for books (or other references) which address the next two aspects of math I'll need, conic sections and Bézier curves/surfaces. I have found: - _Practical Conic Sections_ by J.W. Downs - link - ▶ this video and I'm reading through _METAFONT: The Program_ but if someone could provide a list of math texts which build from the Make: <foo> series (the coverage of conic sections in them was sparser than I was hoping for) I'd be glad of it. Links to helpful Github repositories would be welcome as well (for reviewing once I've digested the books).
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p
@passion__desire2023 · in “Cubic spline interpolation”
Best resource on this topic: link ▶ this video
RecommendsView on HN
A
@AlphaCerium2023 · in “New Bézier curves for vector graphics”
Might I also add: ▶ this video Which works through them from first principles with beautiful animations.
RecommendsView on HN
z
@zoogeny2023 · in “An interactive guide to SVG paths”
If you are looking for solid content on Bezier curves then Freya Holmér's video on The Beauty of Bézier Curves [1] is well worth the time it takes to watch. 1. ▶ this video
RecommendsView on HN
a
@alonp992023 · in “The Beauty of Bézier Curves (2021) [video]”
Submitted the video to Hacker News.
RecommendsView on HN
j
@joshu2022 · in “When splines were physical objects (2016)”
i think - but am not sure - they use clothoid definitions to characterize jerk, as it is more restrictive regarding the maximum rate of turn change. you can make quite a sharp turn with a mathematical spline. but i can see how they would use the physical spline to solve this… Googling “railroad spline clothoid” got some intriguing hits — and this HN comment. link semi-relatedly, this is a fun watch. ▶ this video even less relatedly, here is a drawing i did by torturing a clothoid optimizer link
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