ABSTRACT
Matrices provide an alternative way to compute translations, rotations, screw transformations, and reflections as well as perspective and pseudo-perspective. Therefore, it is natural to compare representations and computations using homogeneous coordinates and matrices to representations and computations using dual quaternions. The authors conclude then that although dual quaternion representations for rigid motions are twice as compact as matrix representations, matrix representations are far more efficient for computing rigid motions and equally as efficient for composing these transformations. With dual quaternions they can use ScLERP to interpolate between two rigid motions; there is no such simple, effective method to interpolate between two rigid motions represented by matrices. Also, they can renormalize dual quaternions that get distorted due to floating point arithmetic. There is no simple, effective way to renormalize rigid motions represented by matrices.
