Visualizing Quaternions
Andrew J. Hanson (Emeritus Professor of Computer Science, Indiana University, IN, USA)
Visualizing Quaternions
Andrew J. Hanson (Emeritus Professor of Computer Science, Indiana University, IN, USA)
7 ½ X 9 ¼ in
ABOUT THE AUTHOR FOREWORD by Steve Cunningham PR EFACE ACKNOWLEDGMENTS PART I ELEMENTS OF QUATERN IONS
01 THE DISCOVERY OF QUATERNIONS
1.1 Hamilton ‘s Walk 1.2 Then Came Octonions 1.3 The Quaternion Reviv al
02 FOLKLORE OF ROTATIONS
2.1 The Belt Trick< /li>2.2 The Rolling Ball 2.3 The Apollo 10 Gimbal-lock Incid ent 2.4 3D Game Developer’s Nightmare 2.5 The Urban Lege nd of the Upside-down F16 2.6 Quaternions to the Rescue
03 BASIC NOTATION
3.1 Vectors 3.2 Length of a V ector 3.3 3D Dot Product 3.4 3D Cross Product 3. 5 Unit Vectors 3.6 Spheres 3.7 Matrices 3.8 Comp lex Numbers
04 WHAT ARE QUATERNIONS? 05 ROAD M AP TO QUATERNION VISUALIZATION
5.1 The Complex Number Connection< /li>5.2 The Cornerstones of Quaternion Visualization
< li>06 FUNDAMENTALS OF ROTATIONS
6.1 2D Rotations
6.1.1 Rel ation to Complex Numbers 6.1.2 The Half-angle Form 6.1.3 understanding of quaternions through visual representations. Visualizing Quaternions introduces new developers to this powerful technique and will provide the definitive explanation to those who have been struggling to use them.
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