Big picture of quaternions

• - Complex value object with 4 components \(q=(x,y,z,w)\)
• - Unit quaternions represent rotations \(q/\|q\|\).
• - Quaternion product represent rotation composition \(q_1\,q_2\)

• - 3D vectors are points in pure quaternion subspace \(q_v=(x,y,z,0)\)
• - Applying quaternion to points \(q_{v'}=q\,q_v\,q^{\star}\)

• - Interpolation works well in quaternion space (interpolation of points on sphere).