Visualizing More Quaternions

ISBN-13: 9780323992022 / Angielski / Miękka / 2024

Andrew J. Hanson

Spis treści

1. Introduction and Review of Quaternion Methodology 2. Synopsis of Useful Applications of Quaternions 3. Quaternion maps of global protein orientation-frame structure 4. Quaternion methods for the Root Mean Square Deviation (RMSD) problem 5. Quaternion methods for the Quaternion Frame Alignment (QFA) problem for 3D molecular and protein structures 6. Quaternion methods for the RMSD coordinate matching problem in 4D 7. Quaternion methods for Quaternion Frame Alignment QFA of molecular and protein structures in 4D 8. Quaternion methods for the robotics hand-eye matching problem 9. Quaternion methods for the machine vision multicamera alignment problem 10. Elements and applications of Dual Quaternions for 6 degree-of-freedom motion analysis 11. Bar-Itzhack method for finding quaternions from numerical rotation matrices 12. Methods for calculating the quaternion barycenter 13. Quaternion frame approach to Cryo-Electron-Microscopy 14. Extraction of quaternion camera viewpoint information from 3D data using deep AI and machine learning methods 15. Quaternion projective geometry and invariant cross-ratios 16. Special Relativity using complexified quaternions18. Relativistic spinning top dynamics with quaternions 17. Skyrmions in Quaternion Form 18. Quaternion maps of the Kleinian Groups 19. Extension of quaternion shape matching methods in 3D and 4D to arbitrary dimension N using Clifford Algebras 20. Conclusion and Philosophical Remarks on QuaternionsAppendicesations