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

{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...

described in terms of quaternions. In general, if a vector [a1, a2, a3] is represented as the quaternion a1i + a2j + a3k, the cross product of two vectors can...

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

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

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

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...

facets, with 3 around each edge. Its dual polytope is the 600-cell. The 120-cell incorporates the geometries of every convex regular polytope in the first...

supergravity. Hyperkähler and quaternion Kähler manifolds (which are special kinds of Einstein manifolds) also have applications in physics as target spaces...

{C} ,} the quaternions H , {\displaystyle \mathbb {H} ,} and lastly the octonions O , {\displaystyle \mathbb {O} ,} where the dimensions of these spaces...

In geometry and group theory, a lattice in the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of points in this space with...

Berthold K. P. (1987-04-01). "Closed-form solution of absolute orientation using unit quaternions". JOSA A. 4 (4): 629–642. Bibcode:1987JOSAA...4..629H...

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...

complex plane. Pseudo-Euclidean geometry is supported by alternative complex planes where points are split-complex numbers or dual numbers. Just as the Möbius...

[11 Jan 1994]. Applications of Quaternions to Dynamical Simulation, Computer Graphics and Biomechanics (Thesis). Delft University of Technology. doi:10...

In geometry and physics, spinors (pronounced "spinner" IPA /spɪnər/) are elements of a complex vector space that can be associated with Euclidean space...

for an example. The quaternions provide a representation for ( p , q ) = ( 0 , 3 ) . {\displaystyle (p,q)=(0,3).} The presentation of the gamma group G...

points on a sphere Generalized quaternion interpolation — generalizes slerp for interpolation between more than two quaternions Irrational base discrete weighted...

S2CID 55989582. Rabin, J. M. (1995). "Super elliptic curves". Journal of Geometry and Physics. 15 (3): 252–280. arXiv:hep-th/9302105. Bibcode:1995JGP....

concerning the fundamental group: all forms of E8 are simply connected in the sense of algebraic geometry, meaning that they admit no non-trivial algebraic...

to definitions, CNN types, dynamics, implementations, and applications. "Cellular Neural Networks and Visual Computing Foundations and Applications"...