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Use the GDC 2021 Session Viewer to browse and sort the ever-growing list of sessions by pass type, topic, and format. You will be able to build your personal schedule directly within the event platform, once live early July 2021.

Math in Game Development Summit: Projective Geometric Algebra and Dual Quaternions

Eric Lengyel  (Computer Scientist, Terathon Software)

Pass Type: All Access Pass, Summits Pass

Topic: Programming

Format: Session

Vault Recording: TBD

This session begins by reviewing the fundamentals of the four-dimensional homogeneous model of
Grassmann algebra described in past GDC sessions. It then discusses the geometric origin of quaternions
in three dimensions before introducing an analogous but converse origin of dual quaternions in four
dimensions. Practical applications are finally presented with a focus on computer graphics and animation.


Attendees will leave with a deeper understanding of the rigid transformations of points, lines, and planes
in homogeneous coordinates because they will have been exposed to a bigger picture of the underlying
mathematics. By learning how dual quaternions really work and how best to use them, they will be more
comfortable adding them to their own projects.

Intended Audience

This session is intended for all game programmers, but especially those who work with 3D geometric
algorithms. The only prerequisite is a familiarity with vector spaces and operations such as the dot
product and cross product.