Implementing skeletal animation using dual quaternion skinning

Matrix palette skinning suffers from candy wrapping artefacts, especially in regions like shoulder and elbow, where there are several rotations across various axes. If dual quaternion skinning is employed, these artefacts are minimized. In this recipe we will implement skeletal animation using dual quaternion skinning.

Before understanding dual quaternions, let us first see what quaternions are. Quaternions are a mathematical entity containing three imaginary dimensions (which specify the axis of rotation) and a real dimension (which specifies the angle of rotation). Quaternions are used in 3D graphics to represent rotation, since they do not suffer from gimbal lock, as Euler angles do. In order to store translation with rotation simultaneously, dual quaternions are used to store dual number coefficients instead of real ones. Instead of four components, as in a quaternion, dual quaternions have eight components.

Even in dual quaternion...