Dual Quaternions And Their Associated Clifford Algebras
Download Dual Quaternions And Their Associated Clifford Algebras full books in PDF, epub, and Kindle. Read online free Dual Quaternions And Their Associated Clifford Algebras ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Ronald Goldman |
| Publisher | : CRC Press |
| Total Pages | : 215 |
| Release | : 2023-09-29 |
| Genre | : Computers |
| ISBN | : 1000903524 |
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 |
| Genre | : Clifford algebras |
| ISBN | : 9781003398141 |
"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 | : Pertti Lounesto |
| Publisher | : Cambridge University Press |
| Total Pages | : 352 |
| Release | : 2001-05-03 |
| Genre | : Mathematics |
| ISBN | : 0521005515 |
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 | : Gerald Sommer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 559 |
| Release | : 2013-06-29 |
| Genre | : Computers |
| ISBN | : 3662046210 |
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 | : Jayme Vaz Jr. |
| Publisher | : Oxford University Press |
| Total Pages | : 257 |
| Release | : 2016 |
| Genre | : Mathematics |
| ISBN | : 0198782926 |
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
| Author | : Andrew J. Hanson |
| Publisher | : Elsevier |
| Total Pages | : 530 |
| Release | : 2006-02-06 |
| Genre | : Mathematics |
| ISBN | : 0080474772 |
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. - Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. - Covers both non-mathematical and mathematical approaches to quaternions.
| Author | : Eduardo Bayro-Corrochano |
| Publisher | : Springer |
| Total Pages | : 753 |
| Release | : 2018-06-20 |
| Genre | : Technology & Engineering |
| ISBN | : 3319748300 |
The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.
| Author | : Peng Du |
| Publisher | : Nova Science Publishers |
| Total Pages | : 197 |
| Release | : 2020 |
| Genre | : Mathematics |
| ISBN | : 9781536185539 |
"Quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. They form an interesting algebra where each object contains 4 scalar variables, instead of Euler angles, which is useful to overcome the gimbal lock phenomenon when treating the rotation of objects. This book is about the mathematical basics and applications of quaternions. The first four chapters mainly concerns the mathematical theories, while the latter three chapters are related with three application aspects. It is expected to provide useful clues for researchers and engineers in the related area. In detail, this book is organized as follows: In Chapter 1, mathematical basics including the quaternion algebra and operations with quaternions, as well as the relationships of quaternions with other mathematical parameters and representations are demonstrated. In Chapter 2, how quaternions are formulated in Clifford Algebra, how it is used in explaining rotation group in symplectic vector space and parallel transformation in holonomic dynamics are presented. In Chapter 3, the wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates. In Chapter 4, hyperbolic Lobachevsky and spherical Riemann models, parameterized coordinates with spherical and cylindric symmetry are studied. In Chapter 5, ship hydrodynamics with allowance of trim and sinkage is investigated and validated with experiments. In Chapter 6, the ballast flying phenomenon based on Discrete Discontinuous Analysis is presented. In Chapter 7, a numerical study is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the rubble mound breakwater"--
| Author | : David Hestenes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 340 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 9789027725615 |
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
| Author | : B. Rosenfeld |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 424 |
| Release | : 1997-02-28 |
| Genre | : Mathematics |
| ISBN | : 9780792343905 |
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
