Visualizing More Quateions

by: Andrew J. Hanson (Author)

Publisher: Morgan Kaufmann

Edition: 1st

Publication Date: 2024/8/1

Language: English

Print Length: 600 pages

ISBN-10: 0323992021

ISBN-13: 9780323992022

Book Description

Visualizing More Quateions is a sequel to Dr. Andrew J. Hanson’s first book, Visualizing Quateions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author’s attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson’s own published and unpublished investigations relating to quateion applications. Among the topics covered are the introduction of new approaches to depicting quateions and their properties, applications of quateion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quateion adjugate variables are introduced to embody the nontrivial quateion topology on the three-sphere and incorporate it into machine leaing tasks. Other subjects include quateion applications to a wide variety of problems in physics, including quantum computing, complexified quateions in special relativity, and a detailed study of the Kleinian “ADE”discrete groups of the ordinary two-sphere. Quateion geometry is also incorporated into the isometric embedding of the Eguchi–Hanson gravitational instanton corresponding to the k = 1 Kleinian cyclic group. Visualizing More Quateions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.Establishes basic principles for visual display of quateions and their applications.Explores quateion based approaches to the matching of point cloud pairs, including approaches to data from orthographic and perspective projections.Develops extensive applications of quateion frames to protein orientation analysis.Analyzes the application of quateion methods to physics problems ranging from quantum computing to special relativity and gravitational instantons.

About the Author

Visualizing More Quateions is a sequel to Dr. Andrew J. Hanson’s first book, Visualizing Quateions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author’s attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson’s own published and unpublished investigations relating to quateion applications. Among the topics covered are the introduction of new approaches to depicting quateions and their properties, applications of quateion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quateion adjugate variables are introduced to embody the nontrivial quateion topology on the three-sphere and incorporate it into machine leaing tasks. Other subjects include quateion applications to a wide variety of problems in physics, including quantum computing, complexified quateions in special relativity, and a detailed study of the Kleinian “ADE”discrete groups of the ordinary two-sphere. Quateion geometry is also incorporated into the isometric embedding of the Eguchi–Hanson gravitational instanton corresponding to the k = 1 Kleinian cyclic group. Visualizing More Quateions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.Establishes basic principles for visual display of quateions and their applications.Explores quateion based approaches to the matching of point cloud pairs, including approaches to data from orthographic and perspective projections.Develops extensive applications of quateion frames to protein orientation analysis.Analyzes the application of quateion methods to physics problems ranging from quantum computing to special relativity and gravitational instantons.