Visualizing Quaternions

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.