Visualizing quaternions

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 for an audience that is technically trained but not pure mathematicians is essentially impossible without a quaternion visualization. The course 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.

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