“Visualizing Quaternions” by Hanson

  • ©Andrew J. Hanson


Entry Number: 05


    Visualizing Quaternions

Course Organizer(s):



    Comfort with and appreciation for conventional mathematical methods of 3D computer graphics and geometry used in geometric transformations and polygon rendering.

    Basic methods of orientation frames and orientation interpolation, novel quaternion visualizations that provide alternative intuitions, advanced applications of these quaternion techniques to coordinate frames and animation splines, and interactive visualization tools for quaternion curves relevant to proper construction and understanding of coordinate frame interpolation.

    An intuitive connection between quaternion lore and many standard problems in representation, interpolation, and exploitation of orientation frames in graphics and visualization. The tutorial presents a range of visualization methods, including images of individual quaternion rotations, the action of rotations in quaternion space, and visual properties of quaternion splines and related animation optimization procedures. It also examines natural applications of quaternions beyond animation splines, such as the study of quaternion frames attached to curves and surfaces.