続・四元数の可視化 Visualizing More Quaternions

著者名：Hanson, Andrew J.

Morgan Kaufmann（2024/07/01発売）

• 言語：ENG
• ISBN：9780323992022
• eISBN：9780323993906

Description

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.- Establishes basic principles for visual display of quaternions and their applications.- Explores quaternion based approaches to the matching of point cloud pairs, including approaches to data from orthographic and perspective projections.- Develops extensive applications of quaternion frames to protein orientation analysis.- Analyzes the application of quaternion methods to physics problems ranging from quantum computing to special relativity and gravitational instantons.

Table of Contents

1. Introduction and Review of Quaternion Methodology2. 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 methods15. Quaternion projective geometry and invariant cross-ratios16. Special Relativity using complexified quaternions18. Relativistic spinning top dynamics with quaternions17. Skyrmions in Quaternion Form18. Quaternion maps of the Kleinian Groups19. Extension of quaternion shape matching methods in 3D and 4D to arbitrary dimension N using Clifford Algebras20. Conclusion and Philosophical Remarks on Quaternions