نتایج جستجو برای: real quaternions

تعداد نتایج: 530991  

2013
Xiang Feng Wanggen Wan

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...

2005
Stephen J. Sangwine

The roots of -1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are studied and it is shown that there is an infinite number of non-trivial complexified quaternion roots (and two degenerate solutions which are the complex imaginary operator and the set of unit pure real quaternions). The non-trivial roots are shown t...

2016
Murat Bekar Yusuf Yayli

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.

Journal: :J. Visual Communication and Image Representation 2010
Jesús Angulo

Please cite this article in press as: J. Angulo, Geom I: Colour quaternions, J. Vis. Commun. (2009), d The definition of morphological operators for colour images requires a total ordering for colour points. A colour can be represented by different algebraic structures, in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied differ...

Journal: :Advances in Applied Clifford Algebras 2013

Journal: :Journal of Pure and Applied Algebra 2021

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .

2005
Drahoslava Janovská Gerhard Opfer DRAHOSLAVA JANOVSKÁ

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...

2006
Gerhard Opfer

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...

Journal: :Australasian J. Combinatorics 2009
Ying Zhao Jennifer Seberry Tianbing Xia Beata J. Wysocki Tadeusz A. Wysocki

This paper introduces some construction methods for amicable orthogonal designs over the real and quaternion domain which have not been explored for code design before. The proposed construction methods generate a large number of amicable orthogonal designs of quaternions. It is also shown that amicable orthogonal designs of quaternions can be used to construct restricted quaternion orthogonal ...

2013
Matthew Smith

Quaternions have long been integral to the field of computer graphics, due to their minimal and robust representation of rotations in three dimensional space. Dual quaternions represent a compact method of representing rigid body transformations (that is rotations and translations) with similar interpolation and combination properties. By comparing them to two other kinds of rigid transformatio...

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