certain applications of the dual quaternion algebra to 2D geometry. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions...

{H} .} Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient...

Conversion between quaternions and Euler angles Covering space Dual quaternion Applications of dual quaternions to 2D geometry Elliptic geometry Rotation formalisms...

points. Dual Quaternions then allow the screw, twist and wrench model of classical mechanics to be constructed. The plane-based approach to geometry may be...

additional structure of a distinguished subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex...

asymptotic to the standard metric of Euclidean 4-space (and are therefore complete but non-compact). In differential geometry, self-dual Einstein 4-manifolds...

Lipschitz in 1886 generalized Clifford's interpretation of the quaternions and applied them to the geometry of rotations in n {\displaystyle n} dimensions. Later...

and Applications. 31 (6): 84–89. doi:10.1109/MCG.2011.92. PMID 24808261. Coutsias, E.; Romero, L. (2004). "The Quaternions with an application to Rigid...

unit quaternions. Multiplication of rotation matrices is homomorphic to multiplication of quaternions, and multiplication by a unit quaternion rotates...

In geometry, the dual snub 24-cell is a 144 vertex convex 4-polytope composed of 96 irregular cells. Each cell has faces of two kinds: 3 kites and 6 isosceles...