Visualizing More Quaternions, Volume Two updates on proteomics-related material that will be useful for biochemists and biophysicists, including material related to electron microscopy (and specifically cryo-EVisualizing. Dr. Andrew J. Hanson's groundbreaking book updates and extends concepts that have evolved since the first book published in 2005, adding entirely new insights that Dr. Hanson's research has recently developed. This includes the applications of quaternion methods to proteomics and molecular crystallography problems, which are domains with significant current research and application activity. In addition to readers interested in quaternions for their own sake, scientists involved in computer graphics, animation, shape modeling, and scientific visualization, and readers from several other disciplines will benefit from this new volume. Foremost among these, and the target of the first several chapters, are scientists involved in molecular chemistry where techniques based on quaternion eigensystems have become a standard tool for evaluating the quality of shape matching. Provides a richly illustrated resource for researchers and practitioners in the fields of mathematics, computer science, engineering, computer graphics, scientific visualization, molecular chemistry, biochemistry, biophysics, robotics and mathematical physics Provides key applications that appeal to a broad population of scientific specialties while also treating a wide spectrum of difficulties, from fairly straightforward to very sophisticated applications Includes a companion website with an assortment of quaternion utilities, sample code, and datasets for the book's illustrations, including interactive device-independent web-based visualization applications INDICE: 1. Introduction and Review of Quaternion Methodology 2. Synopsis of Useful Applications of Quaternions3. Quaternion maps of global protein orientation-frame structure4. Quaternion methods for the Root Mean Square Deviation (RMSD) problem5. Quaternion methods for the Quaternion Frame Alignment (QFA) problem for 3D molecular and protein structures6. Quaternion methods for the RMSD coordinate matching problem in 4D7. Quaternion methods for Quaternion Frame Alignment QFA of molecular and protein structures in 4D8. Quaternion methods for the robotics hand-eye matching problem9. Quaternion methods for the machine vision multicamera alignment problem10. Elements and applications of Dual Quaternions for 6 degree-of-freedom motion analysis11. Bar-Itzhack method for finding quaternions from numerical rotation matrices12. Methods for calculating the quaternion barycenter13. Quaternion frame approach to Cryo-Electron-Microscopy14. Extraction of quaternion camera viewpoint information from 3D data using deep AI and machine learning methods16. Quaternion projective geometry and invariant cross-ratios17. Special Relativity using complexified quaternions18. Relativistic spinning top dynamics with quaternions19. Skyrmions in Quaternion Form20. Quaternion maps of the Kleinian Groups21. Extension of quaternion shape matching methods in 3D and 4D to arbitrary dimension N using Clifford Algebras22. Conclusion and Philosophical Remarks on QuaternionsAppendicesA. Summary and Selected Useful Quaternion IdentitiesB. Details of 2D, 3D, and 4D quaternion-based orientation frame representation and manipulationC. Details of the exact algebraic solutions of the quartic equation applicable to quaternion matrix eigensystem problemsD. Details of the relation between Singular Value Decomposition and the family of quaternion eigensystemsE. Details of the Clifford Algebra approach to higher-dimensional rotations
- ISBN: 978-0-323-99202-2
- Editorial: Morgan Kaufmann
- Encuadernacion: Rústica
- Páginas: 500
- Fecha Publicación: 01/03/2023
- Nº Volúmenes: 1
- Idioma: Inglés