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Visualizing quaternions /
"Andrew Hanson's new book is a fresh perspective on quaternions. Features include: illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing; covers both non-mathematical and mathematical approaches to quater...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Francisco, CA : Amsterdam ; Boston :
Morgan Kaufmann ; Elsevier Science [distributor],
©2006.
|
| Colección: | Morgan Kaufmann series in interactive 3D technology.
|
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
MARC
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| 100 | 1 | |a Hanson, Andrew |q (Andrew J.) | |
| 245 | 1 | 0 | |a Visualizing quaternions / |c Andrew J. Hanson. |
| 260 | |a San Francisco, CA : |b Morgan Kaufmann ; |a Amsterdam ; |a Boston : |b Elsevier Science [distributor], |c ©2006. | ||
| 300 | |a 1 online resource (xxxi, 498 pages) : |b illustrations (some co.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file | ||
| 490 | 1 | |a Morgan Kaufmann series in interactive 3D technology. | |
| 504 | |a Includes bibliographical references (pages 471-486) and index. | ||
| 505 | 0 | |a Cover -- Contents -- Foreword -- Preface -- Acknowledgments -- Elements of Quaternions -- The Discovery of Quaternions -- Hamilton's Walk -- Then Came Octonions -- The Quaternion Revival -- Folklore of Rotations -- The Belt Trick -- The Rolling Ball -- The Apollo 10 Gimbal-lock Incident -- 3D Game Developer's Nightmare -- The Urban Legend of the Upside-down F16 -- Quaternions to the Rescue -- Basic Notation -- Vectors -- Length of a Vector -- 3D Dot Product -- 3D Cross Product -- Unit Vectors -- Spheres -- Matrices -- Complex Numbers -- What Are Quaternions? -- Road Map to Quaternion Visualization -- The Complex Number Connection -- The Cornerstones of Quaternion Visualization -- Fundamentals of Rotations -- 2D Rotations -- Quaternions and 3D Rotations -- Recovering theta and n -- Euler Angles and Quaternions -- Optional Remarks -- Conclusion -- Visualizing Algebraic Structure -- Algebra of Complex Numbers -- Quaternion Algebra -- Visualizing Spheres -- 2D: Visualizing an Edge-On Circle -- The Square Root Method -- 3D: Visualizing a Balloon -- 4D: Visualizing Quaternion Geometry on S3 -- Visualizing Logarithms and Exponentials -- Complex Numbers -- Quaternions -- Visualizing Interpolation Methods -- Basics of Interpolation -- Quaternion Interpolation -- Equivalent 3 x 3 Matrix Method -- Looking at Elementary Quaternion Frames -- A Single Quaternion Frame -- Several Isolated Frames -- A Rotating Frame Sequence -- Synopsis -- Quaternions and the Belt Trick: Connecting to the Identity -- Very Interesting, but Why? -- The Details -- Frame-sequence Visualization Methods -- Quaternions and the Rolling Ball: Exploiting Order Dependence -- Order Dependence -- The Rolling Ball Controller -- Rolling Ball Quaternions -- Commutators -- Three degrees of freedom from two -- Quaternions and Gimbal Lock: Limiting the Available Space -- Guidance System Suspension -- Mathematical Interpolation Singularities -- Quaternion Viewpoint -- Advanced Quaternion Topics -- Alternative Ways of Writing Quaternions -- Hamilton's Generalization of Complex Numbers -- Pauli Matrices -- Other Matrix Forms -- Efficiency and Complexity Issues -- Extracting a Quaternion -- Efficiency of Vector Operations -- Advanced Sphere Visualization -- Projective Method -- Distance-preserving Flattening Methods -- More on Logarithms and Exponentials -- 2D Rotations -- 3D Rotations -- Using Logarithms for Quaternion Calculus -- Quaternion Interpolations Versus Log -- Two-Dimensional Curves -- Orientation Frames for 2D Space Curves -- What Is a Map? -- Tangent and Normal Maps -- Square Root Form -- Three-Dimensional Curves -- Introduction to 3D Space Curves -- General Curve Framings in 3D -- Tubing -- Classical Frames -- Mapping the Curvature and Torsion -- Theory of Quaternion Frames -- Assigning Smooth Quaternion Frames -- Examples: Torus Knot and Helix Quaternion Frames -- Comparison of Quaternion Frame Curve Lengths -- 3D Surfaces -- Introduction to 3D Surfaces -- Quaternion Weingarten Equations -- Quaternion Gauss Map --T. | |
| 520 | 1 | |a "Andrew Hanson's new book is a fresh perspective on quaternions. Features include: 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; and a companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities."--Jacket. | |
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 590 | |a O'Reilly |b O'Reilly Online Learning: Academic/Public Library Edition | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Quaternions. | |
| 650 | 6 | |a Quaternions. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Quaternions. |2 blmlsh | |
| 650 | 7 | |a Quaternions |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Hanson, Andrew (Andrew J.). |t Visualizing quaternions. |d San Francisco, CA : Morgan Kaufmann ; Amsterdam ; Boston : Elsevier Science [distributor], ©2006 |z 9780120884001 |z 0120884003 |w (DLC) 2006273596 |w (OCoLC)67987935 |
| 830 | 0 | |a Morgan Kaufmann series in interactive 3D technology. | |
| 856 | 4 | 0 | |u https://learning.oreilly.com/library/view/~/9780120884001/?ar |z Texto completo (Requiere registro previo con correo institucional) |
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| 994 | |a 92 |b IZTAP | ||