Quaternions provide a singularity-free way to represent 3D rotations. Every unit quaternion q = w + xi + yj + zk encodes a rotation by angle 2·arccos(w) around the axis (x, y, z).
Animate
Current Quaternion
q = 0.924 + 0.000i + 0.383j + 0.000k
|q|² = w² + x² + y² + z² = 1
Key Properties
• Unit quaternions ≅ SU(2) ≅ S³
• Double cover of SO(3): q and −q encode the same rotation