Quaternions - Freya Holmer | NGJ2025

Freya Holmer explains the mathematics of 3D rotations, why Euler angles fail, and how quaternions work intuitively for game developers.

Rotations often get weirdly complicated - even when it feels like they should be simple. To add insult to injury, the commonly accepted "best solution" to 3D rotations are quaternions, an arcane mathematical construct very few dare unpack. So why are they so ubiquitous in game development? Why can't we just use euler angles? What are quaternions even? Is Freya dedicating an entire talk just to explain quaternions? Turns out yes, she is. Freya is an independent technical artist who used to make games for 10 years, until she was imprisoned by mathematics. As a tool developer, she created Shader Forge, Shapes, and the upcoming Half-Edge, a 3D modeling tool. As a game developer, she's done freelance work, as well as co-founded Neat Corp, the developers of Budget Cuts. As an educator, she's made YouTube videos about mathematics, and has held occasional guest lectures around the world. Check out Freya Holmer! acegikmo.com/ This video was recorded at Nordic Game Jam 2025 📅 03-06 April 2025 📍 Aalborg University, Copenhagen Follow us at: ➡️ nordicgamejam.com ➡️ facebook.com/nordicgamejam/ ➡️ instagram.com/nordicgamejam/ ➡️ bsky.app/profile/nordicgamejam.bsky.social ➡️ linkedin.com/company/nordic-game-jam/ And thanks to all the amazing sponsors of this year!