“Visualizing Quaternions” by Hanson

  • ©Andrew J. Hanson


Entry Number: 09


    Visualizing Quaternions

Course Organizer(s):



    Comfort with and an appreciation for conventional mathematical methods of 3D computer graphics and geometry used in geometric transformations and polygon rendering. Designed for those who wish to deepen their intuitive understanding of moving coordinate frames and quaternion-based animation techniques.

    Basic methods of orientation frames and orientation interpolation, novel quaternion visualizations that provide alternative intuitions, and advanced applications of these quaternion techniques to coordinate frames and animation splines.

    This tutorial provided an intuitive connection between quaternion lore and many standard problems in representation, interpolation, and exploitation of orientation frames in graphics and visualization. It began with an entirely pictorial intuition of what quaternions are and why we should use them to study orientation frames. It then presented a range of visualization methods, including images that represent individual quaternion rotations, the action of rotations in quaternion space, and the visual properties of quaternion splines and related animation optimization procedures.