|Title||An analysis of the dual-complex unit circle with applications to line geometry|
|Publication Type||Journal Article|
|Year of Publication||Submitted|
|Journal||Computer Aided Geometric Design|
|Keywords||adjoint trigonometric representation of displacements, Computational kinematics, generalized complex numbers, Lie theory, Paden–Kahan problems, principle of transference|
This article contributes to the conception of oriented dual angles by introducing two geometric representations of the dual-complex unit circle in context of Cayley-Klein geometries. By means of these representations and the principle of transference, line-geometric trigonometric constraint equations are stated and solved analytically. The trigonometric constraints and their solutions build the foundation to obtain closed-form solutions to generalized, line-geometric variants of Paden-Kahan problems.