Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)

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.--jacket. Pt. I. Elements Of Quaternions -- 1. 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. 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. Andrew J. Hanson. Includes Bibliographical References (p. 471-486) And Index.