GDC is part of the Informa Tech Division of Informa PLC

This site is operated by a business or businesses owned by Informa PLC and all copyright resides with them. Informa PLC's registered office is 5 Howick Place, London SW1P 1WG. Registered in England and Wales. Number 8860726.

View, browse and sort the ever-growing list of sessions by pass type, topic, and format. All registered attendees will be able to build their personal schedule in the mobile event app, once live early 2022.

GDC Masterclass courses require a paid pass to attend. Class sizes are kept intentionally small and seats are limited to ensure every student receives one-on-one assistance from the instructor. Pass pricing per course varies, please review the passes and pricing page for more details and secure your spot today!

Math In Game Development Summit: Deep Dive: Quaternion Springs

John Austin  (Founder, Pontoco)

Pass Type: All Access Pass, Summits Pass - Get your pass now!

Topic: Programming

Format: Session

Vault Recording: TBD

Audience Level: Yes

It seems like a rather simple challenge: apply a spring to a quaternion so that it smoothly rotates between different orientations. However, most simple approaches will fail, creating oddly curved trajectories or failing under large forces. This is a common behavior that many games might need for targeting, animation, and physics. Why is this so challenging?

In this talk, we will do a deep dive into the creation of a mathematically accurate quaternion spring. We'll learn how to take the derivative of a quaternion, explore concepts such as the swing-twist decomposition, and emerge on the other side with a fully working quaternion spring implementation, fit to be dropped into any game project.

The math isn't all that complex, and plus, visualizing the 4th dimension is a ton of fun!


Attendees will take away a better intuition for using quaternions in their day-to-day work, as well as a concrete implementation of a quaternion spring that can be easily used in their own projects.

Intended Audience

This talk is intended for an intermediate audience interested in the math behind quaternions, although in most cases we will focus on intuition over formula. Some understanding of physical systems such as springs will be helpful but not required.