Freya Holmér
16 HN recommenders · recommended in 14 months, 2021–2026
24:26 · 2.2M views · Aug 19, 2021
Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.
HN repeatedly calls it one of the best math and graphics explainers on YouTube, praised for bridging game dev and math.
20 comments from Hacker News
Bezier curves. Cubic bezier curves (generally the most common type) are represented by cubic polynomials x(t) and y(t) (or just one polynomial P(t) where the coefficients are vectors). The first derivative gives you the tangent and normal. The second derivative gives you the direction the normal will gradually become as t increases. The third derivative gives you the change in this change (the fourth derivative is zero). Curvature is also computed from the first and second derivatives: K = det(P', P'')/||P'||^3 Other kinds of bezier curves are similar. In quadratic ones the first and second derivatives are normal and normal change but the third derivative is zero. In higher-polynomial bezier curves the third derivative changes over time as the fourth is non-zero, and so on. Source is a really interesting video on bezier curves which I highly recommend: this video .
Probably "The Beauty of Bézier Curves" [1], one of the choices by 3B1B, comes closest. It is already a relatively large channel although usually focused on game dev tutorials rather than math explanations. This video bridges those two areas and is absolutely beautiful. [1] this video
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)
I'm really glad the article links to Freya's "Beauty of Bezier Curves" videos, it's genuinely one of the best math/graphics/explainer videos ever made this video
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)