Dual Quaternions And Their Associated Clifford Algebras
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Author |
: Ronald Goldman |
Publisher |
: CRC Press |
Total Pages |
: 215 |
Release |
: 2023-09-29 |
ISBN-10 |
: 9781000903522 |
ISBN-13 |
: 1000903524 |
Rating |
: 4/5 (22 Downloads) |
Synopsis Dual Quaternions and Their Associated Clifford Algebras by : Ronald Goldman
Clifford algebra for dual quaternions has emerged recently as an alternative to standard matrix algebra as a computational framework for computer graphics. This book presents dual quaternions and their associated Clifford algebras in a new light, accessible to and geared toward the computer graphics community. Collecting all the associated formulas and theorems in one place, this book provides an extensive and rigorous treatment of dual quaternions, as well as showing how two models of Clifford algebra emerge naturally from the theory of dual quaternions. Each section comes complete with a set of exercises to help readers sharpen and practice their understanding. This book is accessible to anyone with a basic knowledge of quaternion algebra and is of particular use to forward-thinking members of the computer graphics community.
Author |
: Ron Goldman |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2023 |
ISBN-10 |
: 1003398146 |
ISBN-13 |
: 9781003398141 |
Rating |
: 4/5 (46 Downloads) |
Synopsis Dual Quaternions and Their Associated Clifford Algebras by : Ron Goldman
"Amid recent interest in Clifford algebra for dual quaternions as a more suitable method for Computer Graphics than standard matrix algebra, this book presents dual quaternions and their associated Clifford algebras in a new light, accessible to and geared towards the Computer Graphics community. Collating all the associated formulas and theorems in one place, this book provides an extensive and rigorous treatment of dual quaternions, as well as showing how two models of Clifford algebras emerge naturally from the theory of dual quaternions. Each chapter comes complete with a set of exercises to help readers sharpen and practice their knowledge. This book is accessible to anyone with a basic knowledge of quaternion algebra and is of particular use to forward-thinking members of the Computer Graphics community"--
Author |
: Eckhard Hitzer |
Publisher |
: CRC Press |
Total Pages |
: 475 |
Release |
: 2021-09-21 |
ISBN-10 |
: 9781000429343 |
ISBN-13 |
: 1000429342 |
Rating |
: 4/5 (43 Downloads) |
Synopsis Quaternion and Clifford Fourier Transforms by : Eckhard Hitzer
Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth. The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists, and engineers (signal and color image processing, electrical engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.). Features Intuitive real geometric approach to higher-dimensional Fourier transformations A comprehensive reference, suitable for graduate students and researchers Includes detailed definitions, properties, and many full step-by-step proofs Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information
Author |
: Rafal Ablamowicz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 231 |
Release |
: 2011-06-28 |
ISBN-10 |
: 9780817681906 |
ISBN-13 |
: 0817681906 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Lectures on Clifford (Geometric) Algebras and Applications by : Rafal Ablamowicz
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
Author |
: Ron Goldman |
Publisher |
: Morgan & Claypool Publishers |
Total Pages |
: 177 |
Release |
: 2010 |
ISBN-10 |
: 9781608454204 |
ISBN-13 |
: 1608454207 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Rethinking Quaternions by : Ron Goldman
In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text."--P. 4 of cover.
Author |
: Pertti Lounesto |
Publisher |
: Cambridge University Press |
Total Pages |
: 352 |
Release |
: 2001-05-03 |
ISBN-10 |
: 9780521005517 |
ISBN-13 |
: 0521005515 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Clifford Algebras and Spinors by : Pertti Lounesto
This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
Author |
: Rafal Ablamowicz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 328 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461581574 |
ISBN-13 |
: 1461581575 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Clifford Algebras with Numeric and Symbolic Computations by : Rafal Ablamowicz
This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.
Author |
: Alexander McAulay |
Publisher |
: |
Total Pages |
: 280 |
Release |
: 1898 |
ISBN-10 |
: PRNC:32101020182810 |
ISBN-13 |
: |
Rating |
: 4/5 (10 Downloads) |
Synopsis Octonions by : Alexander McAulay
Author |
: Gerald Sommer |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 559 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662046210 |
ISBN-13 |
: 3662046210 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Geometric Computing with Clifford Algebras by : Gerald Sommer
This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.
Author |
: Andrew J. Hanson |
Publisher |
: Elsevier |
Total Pages |
: 602 |
Release |
: 2024-07-01 |
ISBN-10 |
: 9780323993906 |
ISBN-13 |
: 0323993907 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Visualizing More Quaternions by : Andrew J. Hanson
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.