Interpolation of Quaternion - LERP

• - Consider two rotations with corresponding quaternion \(q_1\), \(q_2\).
• - The linearly interpolated quaternion at parameter \(t\in[0,1]\) is

• • \(\displaystyle q(t) = \frac{(1-t)\, q_1 + t\, q_2}{\|(1-t)\, q_1 + t\, q_2\|}\)

• (+) Follows a shortest path (great circle on 4D sphere)
• (+) Can be generalized to more general parametric curves (Splines, etc)

• (-) Angular speed of orientation is not-constant
• • ex. extreme case of two opposite quaternions