Visualizing quaternions: course notes for Siggraph 2007

Andrew J. Hanson

Abstract: This intermediate-level tutorial provides a comprehensive approach to the visualization of quaternions and their relationships to computer graphics and scientific visualization. The introduction focuses on a selection of everyday phenomena involving rotating objects whose explanation is essentially impossible without a quaternion visualization. The presentation will then pursue selected examples of quaternion-based visualization methods to help explain the behavior of quaternion manifolds: quaternion representations of orientation frames attached to curves, surfaces, and volumes.