ABSTRACT
One of the main insights regarding quaternions is that rotations, reflections, and perspective projections in 3-dimensions can all be modeled by rotations in 4-dimensions. Rotations in n-dimensions are linear isometries, linear maps that preserve angles and lengths. So to determine if rigid motions in 3-dimensions are really represented by rotations in 8-dimensions, the authors need to consider how linear isometries can be represented by dual quaternions. If the authors compose several rigid motions represented by unit dual quaternions using dual quaternion multiplication with floating point arithmetic, then due to floating point errors eventually the products will no longer be unit dual quaternions. Objects will be distorted if they use these unnormalized dual quaternions to transform a scene. Therefore, they need a method to renormalize dual quaternions.
