Mathematical beauty of hyperbezier curves
Archived — this story has rotated out of today’s deck. It is kept here in full.
The gist
Raph Levien proposes hyperbezier curves, a new family defined by a Cesàro equation. They aim to surpass cubic Béziers in 2D vector graphics by combining smooth curvature with high-tension regions.
Background
Cubic Béziers are widely used in vector graphics but have limitations: they can have up to two inflection points and don't naturally fit curves with asymptotic behavior like hyperbolas. Euler spirals are smoother but fail at high-tension regions. Levien's hyperbezier family aims to combine the strengths of both, offering a versatile alternative for interactive design.
How it unfolded
- Aug 8, 2026Raph Levien publishes a blog post introducing hyperbezier curves, defined by a Cesàro equation, and demonstrates their properties.
- Aug 10, 2026The post gains attention on X (Twitter) with shares from users like Masayuki Hatta.
- Aug 11, 2026daily.dev features the story, summarizing the curve family's capabilities; Vivek Galatage tweets about it, wishing such foundations were taught in CG classes.
- Aug 15, 2026The post appears on Hacker News, sparking discussion among developers.
Who’s saying what
- Developer
- Vivek Galatage appreciates the illustrated foundations, wishing they were part of CG education.
- Analyst
- daily.dev notes that neither cubic Béziers nor Euler spirals are strictly superior, highlighting the hyperbezier's potential.
Still unverified
The parameter mapping for approximating cubic Béziers is described as a 'first usable draft' and may change; the exact accuracy of hyperbezier fits for superellipses is noted as slightly worse than the best cubic Bézier for moderate exponents.