ON QUATERNIONS By
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چکیده
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A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices
The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
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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...
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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...
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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...
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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...
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An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
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