UID:
edoccha_9958132165302883
Umfang:
1 online resource (531 p.)
ISBN:
1-280-96817-6
,
9786610968176
,
0-08-047477-2
Serie:
Morgan Kaufmann series in interactive 3D technology
Inhalt:
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 boo
Anmerkung:
Description based upon print version of record.
,
Front Cover; Visualizing Quaternions; Copyright Page; Contents; About the Author; Foreword; Preface; Acknowledgments; Part I: Elements of Quaternions; Chapter 1. The Discovery of Quaternions; 1.1 Hamilton's Walk; 1.2 Then Came Octonions; 1.3 The Quaternion Revival; Chapter 2. Folklore of Rotations; 2.1 The Belt Trick; 2.2 The Rolling Ball; 2.3 The Apollo 10 Gimbal-lock Incident; 2.4 3D Game Developer's Nightmare; 2.5 The Urban Legend of the Upside-down F16; 2.6 Quaternions to the Rescue; Chapter 3. Basic Notation; 3.1 Vectors; 3.2 Length of a Vector; 3.3 3D Dot Product; 3.4 3D Cross Product
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8.2 The Square Root Method8.3 3D: Visualizing a Balloon; 8.4 4D: Visualizing Quaternion Geometry on S3; Chapter 9. Visualizing Logarithms and Exponentials; 9.1 Complex Numbers; 9.2 Quaternions; Chapter 10. Visualizing Interpolation Methods; 10.1 Basics of Interpolation; 10.2 Quaternion Interpolation; 10.3 Equivalent 3 x 3 Matrix Method; Chapter 11. Looking at Elementary Quaternion Frames; 11.1 A Single Quaternion Frame; 11.2 Several Isolated Frames; 11.3 A Rotating Frame Sequence; 11.4 Synopsis; Chapter 12. Quaternions and the Belt Trick: Connecting to the Identity
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12.1 Very Interesting, but Why?12.2 The Details; 12.3 Frame-sequence Visualization Methods; Chapter 13. Quaternions and the Rolling Ball: Exploiting Order Dependence; 13.1 Order Dependence; 13.2 The Rolling Ball Controller; 13.3 Rolling Ball Quaternions; 13.4 Commutators; 13.5 Three degrees of freedom from two; Chapter 14. Quaternions and Gimbal Lock: Limiting the Available Space; 14.1 Guidance System Suspension; 14.2 Mathematical Interpolation Singularities; 14.3 Quaternion Viewpoint; Part II: Advanced Quaternion Topics; Chapter 15. Alternative Ways of Writing Quaternions
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15.1 Hamilton's Generalization of Complex Numbers15.2 Pauli Matrices; 15.3 Other Matrix Forms; Chapter 16. Efficiency and Complexity Issues; 16.1 Extracting a Quaternion; 16.2 Efficiency of Vector Operations; Chapter 17. Advanced Sphere Visualization; 17.1 Projective Method; 17.2 Distance-preserving Flattening Methods; Chapter 18. More on Logarithms and Exponentials; 18.1 2D Rotations; 18.2 3D Rotations; 18.3 Using Logarithms for Quaternion Calculus; 18.4 Quaternion Interpolations Versus Log; Chapter 19. Two-Dimensional Curves; 19.1 Orientation Frames for 2D Space Curves; 19.2 What Is a Map?
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19.3 Tangent and Normal Maps
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English
Weitere Ausg.:
ISBN 1-4832-9988-0
Weitere Ausg.:
Visualizing quaternions ISBN 0-12-088400-3
Sprache:
Englisch
