The two-sided quaternionic Fourier transformation (QFT) was introduced in [2] for the analysis of 2D linear time-invariant partialdifferential systems. In further theoretical investigations [4, 5] a special split of quaternions was introduced, then called ±split. In the current chapter we analyze this split further, interpret it geometrically as an orthogonal 2D planes split (OPS), and generali...

The widespread use of unmanned aerial vehicles during warfare has intensified the problem their management, especially when they are used in large groups. One main tasks is to ensure coordinated movement group's aircraft space. Optimizing each device group three-dimensional space expedient mathematical models. any vehicle can be presented as a combination translational and rotational movements,...

To relate measurements made by a sensor mounted on a mechanical link to the robot’s coordinate frame, we must first estimate the transformation between these two frames. Many algorithms have been proposed for this so-called hand-eye calibration, but they do not treat the relative position and orientation in a unified way. In this paper, we introduce the use of dual quaternions, which are the al...

Dual numbers, split-quaternions, split-octonions, and other number systems with nilpotent spaces have received sporadic yet persistent interest, beginning from their roots in the 19th century, to more recent attention in connection with supersymmetry in physics. In this paper, a number system in the 2D plane is investigated, where the squares of its basis elements p and q each map into the coor...

In this paper, a representational model is proposed for the description and transformation of three-dimensional geometric entities in computer graphics. The structure of the proposed representation is based on dual unit vectors, while the corresponding transformations are carried out through dual unit quaternions or dual orthogonal matrices. The main advantage of this representation is its comp...

In this paper, we explain how dual quaternion theory can extend to quaternions with generalized complex number (GCN) components. More specifically, algebraically examine new type and give several matrix representations both as a GCN.