Math in Game Development Summit: A Visual Guide to Quaternions and Dual Quaternions

Hamish Todd provides an intuitive, visual explanation of how quaternions and dual quaternions are created, composed, and interpolated.

Sometimes people say "Quaternions are 4 dimensional". They are trying to scare you. It's no more true than "3x3 matrices are 9 dimensional", and no more helpful either. There is a concrete, 3D way to visualize quaternions. In this GDC 2023 session, Hamish Todd dives into how quaternions are created, interpolated, and composed together. GDC returns to San Francisco in March 2025! For more information, be sure to visit our website and follow the #GDC2025 hashtag on social media. Subscribe to the GDC newsletter and get regular updates via Facebook, Twitter, LinkedIn, or RSS. Join the GDC mailing list: gdconf.com/subscribe Follow GDC on Twitter: twitter.com/Official_GDC GDC talks cover a range of developmental topics including game design, programming, audio, visual arts, business management, production, online games, and much more. We post a fresh GDC video every day. Subscribe to the channel to stay on top of regular updates, and check out GDC Vault for thousands of more in-depth talks from our archives.