Research Catalog

Title

Visualizing quaternions / Andrew J. Hanson.

Author

Hanson, Andrew (Andrew J.)

Publication

San Francisco, CA : Morgan Kaufmann ; Amsterdam ; Boston : Elsevier Science [distributor], [2006], ©2006.

Items in the Library & Off-site

Details

Description

xxxi, 498 pages : illustrations (some co.); 25 cm.

Summary

"Andrew Hanson's new book is a fresh perspective on quaternions. Features include: illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing; covers both non-mathematical and mathematical approaches to quaternions; and a companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities."--BOOK JACKET.

Series Statement

Morgan Kaufmann series in interactive 3D technology

Uniform Title

Morgan Kaufmann series in interactive 3D technology.

Subject

• Quaternions

Bibliography (note)

• Includes bibliographical references (p. 471-486) and index.

Contents

Pt. I. Elements of quaternions -- 1. The discovery of quaternions -- 2. Folklore of rotations -- 3. Basic notation -- 4. What are quaternions? -- 5. Road map to quaternion visualization -- 6. Fundamentals of rotations -- 7. Visualizing algebraic structure -- 8. Visualizing spheres -- 9. Visualizing logarithms and exponentials -- 10. Visualizing interpolation methods -- 11. Looking at elementary quaternion frames -- 12. Quaternions and the belt trick : connecting to the identity -- 13. Quaternions and the rolling ball : exploiting order dependence -- 14. Quaternions and gimbal lock : limiting the available space -- Pt. II. Advanced quaternion topics -- 15. Alternative ways of writing quaternions -- 16. Efficiency and complexity issues -- 17. Advanced sphere visualization -- 18. More on logarithms and exponentials -- 19. Two-dimensional curves -- 20. Three-dimensional curves -- 21. 3D surfaces -- 22. Optimal quaternion frames -- 23. Quaternion volumes -- 24. Quaternion maps of streamlines -- 25. Quaternion interpolation -- 26. Quaternion rotator dynamics -- 27. Concepts of the rotation group -- 28. Spherical Riemannian geometry -- Pt. III. Beyond quaternions -- 29. The relationship of 4D rotations to quaternions -- 30. Quaternions and the four division algebras -- 31. Clifford algebras -- 32. Conclusions -- App. A. Notation -- App. B. 2D complex frames -- App. C. 3D quaternion frames -- App. D. Frame and surface evolution -- App. E. Quaternion survival kit -- App. F. Quaternion methods -- App. G. Quaternion path optimization using surface evolver -- App. H. Quaternion frame integration -- App. I. Hyperspherical geometry.

ISBN

0120884003 (hbk.)

LCCN

9780120884001

OCLC

• 67987935
• ocm67987935
• SCSB-5240208

Owning Institutions

Columbia University Libraries