Andrew J. Hanson

Visualizing More Quaternions (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Elsevier Science & Techn.
• Seitenzahl: 500
• Erscheinungstermin: 1. Juli 2024
• Englisch
• ISBN-13: 9780323993906
• Artikelnr.: 72251650

Autorenporträt

Andrew J. Hanson Ph.D. is an Emeritus Professor of Computer Science at Indiana University. He earned a bachelor's degree in Chemistry and Physics from Harvard University in 1966 and a PhD in Theoretical Physics from MIT under Kerson Huang in 1971. His interests range from general relativity to computer graphics, artificial intelligence, and bioinformatics; he is particularly concerned with applications of quaternions and with exploitation of higher-dimensional graphics for the visualization of complex scientific contexts such as Calabi-Yau spaces. He is the co-discoverer of the Eguchi-Hanson "gravitational instanton Einstein metric (1978), author of Visualizing Quaternions (Elsevier, 2006), and designer of the iPhone Apps "4Dice and "4DRoom (2012) for interacting with four-dimensional virtual reality.

Inhaltsangabe

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 Quaternions