Download or read book Visualizing Quaternions written by Andrew J. Hanson and published by Elsevier. This book was released on 2006-02-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Conformal Geometry of Surfaces in S4 and Quaternions written by Francis E. Burstall and published by Springer Science & Business Media. This book was released on 2002-03-05 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Download or read book Notes and Queries written by and published by . This book was released on 1873 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Elementary Treatise on Quaternions written by Peter Guthrie Tait and published by . This book was released on 1890 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Elementary Treatise on Quaternions by Peter Guthrie Tait, first published in 1890, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.

Download or read book Notes and Queries A Medium of Inter Communication for Literary Men Artists Antiquaries Genealogists Etc written by and published by . This book was released on 1873 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quaternions for Computer Graphics written by John Vince and published by Springer Nature. This book was released on 2021-09-02 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you have ever wondered what quaternions are — then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.

Download or read book The Bodleian Manuscript of Jerome s Version of the Chronicle of Eusebius Reproduced in Collotype written by Caesariensis Eusebius and published by . This book was released on 1905 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Bodleian Manuscript of Jerome s Version of the Chronicles of Eusebius written by Eusebius (of Caesarea, Bishop of Caesarea) and published by . This book was released on 1905 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Encyclopaedia Britannica written by and published by . This book was released on 1902 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Knowledge Based Intelligent Information and Engineering Systems written by Vasile Palade and published by Springer Science & Business Media. This book was released on 2003-08-28 with total page 1510 pages. Available in PDF, EPUB and Kindle. Book excerpt: During recent decades we have witnessed not only the introduction of automation into the work environment but we have also seen a dramatic change in how automation has influenced the conditions of work. While some 30 years ago the addition of a computer was considered only for routine and boring tasks in support of humans, the balance has dramatically shifted to the computer being able to perform almost any task the human is willing to delegate. The very fast pace of change in processor and information technology has been the main driving force behind this development. Advances in automation and especially Artificial Intelligence (AI) have enabled the formation of a rather unique team with human and electronic members. The team is still supervised by the human with the machine as a subordinate associate or assistant, sharing responsibility, authority and autonomy over many tasks. The requirement for teaming human and machine in a highly dynamic and unpredictable task environment has led to impressive achievements in many supporting technologies. These include methods for system analysis, design and engineering and in particular for information processing, for cognitive and complex knowledge [1] engineering .

Download or read book Regular Functions of a Quaternionic Variable written by Graziano Gentili and published by Springer. This book was released on 2023-09-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.

Download or read book The Encyclopaedia Britannica written by Thomas Spencer Baynes and published by . This book was released on 1878 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Encyclop dia Britannica written by and published by . This book was released on 1893 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Critical Dictionary of English Literature and British and American Authors Living and Deceased written by Samuel Austin Allibone and published by . This book was released on 1896 with total page 1150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Critical Dictionary of English Literature and British and American Authors Living and Deceased from the Earliest Accounts to the Latter Half of the Nineteenth Century written by Samuel Austin Allibone and published by . This book was released on 1899 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Encyclop dia Britannica A ZYM written by Day Otis Kellogg and published by . This book was released on 1903 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Encyclopedia Britannica written by Thomas Spencer Baynes and published by . This book was released on 1878 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: