Skip to Main Content
Visualizing Quaternions
book

Visualizing Quaternions

by Andrew J. Hanson
February 2006
Intermediate to advanced content levelIntermediate to advanced
600 pages
8h 57m
English
Elsevier Science
Content preview from Visualizing Quaternions

Chapter 23. Quaternion Volumes

We have now treated in detail two fundamental families of frames: the 1D family of frames corresponding to points on a curve carrying a continuous frame, with one axis following the curve’s tangent vector and the 2D family of frames attached to a surface, with one axis following the normal vector perpendicular to the surface at each point. By transforming each of these families of frames to quaternion form, we achieved a map from each point in the manifold to a manifold of the same dimension in quaternion space. Because the metric properties of quaternion space permit quantitative evaluation of proximity among frames, the geometry of these maps reveals both local and global properties of the frame assignments to ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Advanced Mathematics

Advanced Mathematics

Stanley J. Farlow
Geometry for Programmers

Geometry for Programmers

Oleksandr Kaleniuk
Geometric Algebra for Computer Science

Geometric Algebra for Computer Science

Leo Dorst, Daniel Fontijne, Stephen Mann

Publisher Resources

ISBN: 9780120884001