On geometric applications of quaternions
Authors : Burcu Bektaş Demirci, Nazım Aghayev
Pages : 1289-1303
Doi:10.3906/mat-1907-120
View : 10 | Download : 0
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane} N $ and $\mbox{Line} N $, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry using quaternion.Keywords : Quaternions, reflection, orthogonal projection, sandwiching maps, involution and antiinvolution