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Math In Game Development Summit: Deep Dive: Quaternion Springs

John Austin  (Founder, Pontoco)

Location: Room 202, South Hall

Date: Tuesday, March 22

Time: 2:10 pm - 2:40 pm

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

Topic: Programming

Format: Session

Viewing Experience: In-Person/Virtual

Vault Recording: Video

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.