in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

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...

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre’ s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.

Though Combination of Quaternions and matrix has been a popular tool in skeletal animation for more than 20 years, classical quaternions are restricted to the representation of rotations. In skeletal animation and many other applications of 3D computer graphics, we actually deal with rigid transformation including both rotation and translation. Dual quaternions represent rigid transformations n...

In this paper we generalize established techniques and blending algorithm for quaternions to dual quaternions to represent rigid transformations compactly. With the visualization of OpenGL, we employ dual quaternions to achieve character animation in real time. Classical quaternions are only able to characterize rotations although combination of matrix calculation and quaternions operator has b...

In this paper, we give a beginners guide to the practicality of using dual-quaternions to represent the rotations and translations in character-based hierarchies. Quaternions have proven themselves in many fields of science and computing as providing an unambiguous, un-cumbersome, computationally efficient method of representing rotational information. We hope after reading this paper the reade...