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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.
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| Colección: | Morgan Kaufmann series in interactive 3D technology.
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| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- 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.