UNIT DUAL QUATERNIONS AND ARCS

Skinning with dual quaternions pdf

Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix blending Cordier and Magnenat-Thalmann 2005 and. Dual quaternions a generalization of regular quaternions invented. Techdocslcoterrors.pdf.Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix. Closed-form approximation, based on dual quaternions a general.Skinning with Quaternion...

Some Notes on Unit Quaternions and Rotation

Unit Quaternions and the Bloch Sphere

The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unita...

Optimal Powered Descent Guidance with [.05in] 6-DoF Line of Sight Constraints via Unit Dual Quaternions

In this paper, we present a model predictive control (MPC) approach for powered descent guidance and control synthesis in the presence of line of sight and glide slope constraints. The design of an autonomous control algorithm for such a mission scenario is challenging due to fact that the constraints are coupled with rotational and translational motions of a lander spacecraft, leading to a com...

Dual Quaternions for Rigid Transformation Blending

Quaternions have been a popular tool in 3D computer graphics for more than 20 years. However, classical quaternions are restricted to the representation of rotations, whereas in graphical applications we typically work with rotation composed with translation (i.e., a rigid transformation). Dual quaternions represent rigid transformations in the same way as classical quaternions represent rotati...