Square root of a small number

Square root of a small number

The recent post Converting between quaternions and rotation matrices describes an algorithm as “a mathematically correct but numerically suboptimal method/” Let’s just look at a small piece of that post. The post explains how to find a rotation matrix to describe the same rotation as pre- and post- multiplying by a unit quaternion q, and how to recover q from a rotation. The latter involves q0 = ½ √(1 + r11 + r22 + r33). If you look at the defin…