Visualizing quaternions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Francisco, CA
Morgan Kaufmann
©2006
|
| Schriftenreihe: | Morgan Kaufmann series in interactive 3D technology
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 471-486) and index 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. "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 |
| Beschreibung: | 1 Online-Ressource (xxxi, 498 pages) |
| ISBN: | 0080474772 0120884003 1280968176 9780080474779 9780120884001 9781280968174 |
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| 500 | |a Includes bibliographical references (pages 471-486) and index | ||
| 500 | |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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - Introduction to 3D Surfaces -- Quaternion Weingarten Equations -- Quaternion Gauss Map --T. | ||
| 500 | |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 | ||
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| 650 | 7 | |a Quaternions |2 blmlsh | |
| 650 | 7 | |a Quaternions |2 fast | |
| 650 | 4 | |a Quaternions | |
| 650 | 0 | 7 | |a Quaternion |0 (DE-588)4176653-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804175641272123392 |
|---|---|
| any_adam_object | |
| author | Hanson, Andrew, (Andrew J.) |
| author_facet | Hanson, Andrew, (Andrew J.) |
| author_role | aut |
| author_sort | Hanson, Andrew, (Andrew J.) |
| author_variant | a a j h aaj aajh |
| building | Verbundindex |
| bvnumber | BV043166077 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)441776427 (DE-599)BVBBV043166077 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043166077 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:31Z |
| institution | BVB |
| isbn | 0080474772 0120884003 1280968176 9780080474779 9780120884001 9781280968174 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028590267 |
| oclc_num | 441776427 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xxxi, 498 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Morgan Kaufmann |
| record_format | marc |
| series2 | Morgan Kaufmann series in interactive 3D technology |
| spelling | Hanson, Andrew, (Andrew J.) Verfasser aut Visualizing quaternions Andrew J. Hanson San Francisco, CA Morgan Kaufmann ©2006 1 Online-Ressource (xxxi, 498 pages) txt rdacontent c rdamedia cr rdacarrier Morgan Kaufmann series in interactive 3D technology Includes bibliographical references (pages 471-486) and index 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. "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 Quaternions MATHEMATICS / Algebra / Linear bisacsh Quaternions blmlsh Quaternions fast Quaternion (DE-588)4176653-2 gnd rswk-swf Visualisierung (DE-588)4188417-6 gnd rswk-swf Quaternion (DE-588)4176653-2 s Visualisierung (DE-588)4188417-6 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=189455 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hanson, Andrew, (Andrew J.) Visualizing quaternions Quaternions MATHEMATICS / Algebra / Linear bisacsh Quaternions blmlsh Quaternions fast Quaternion (DE-588)4176653-2 gnd Visualisierung (DE-588)4188417-6 gnd |
| subject_GND | (DE-588)4176653-2 (DE-588)4188417-6 |
| title | Visualizing quaternions |
| title_auth | Visualizing quaternions |
| title_exact_search | Visualizing quaternions |
| title_full | Visualizing quaternions Andrew J. Hanson |
| title_fullStr | Visualizing quaternions Andrew J. Hanson |
| title_full_unstemmed | Visualizing quaternions Andrew J. Hanson |
| title_short | Visualizing quaternions |
| title_sort | visualizing quaternions |
| topic | Quaternions MATHEMATICS / Algebra / Linear bisacsh Quaternions blmlsh Quaternions fast Quaternion (DE-588)4176653-2 gnd Visualisierung (DE-588)4188417-6 gnd |
| topic_facet | Quaternions MATHEMATICS / Algebra / Linear Quaternion Visualisierung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=189455 |
| work_keys_str_mv | AT hansonandrewandrewj visualizingquaternions |