An analysis of the dual-complex unit circle with applications to line geometry

TitleAn analysis of the dual-complex unit circle with applications to line geometry
Publication TypeJournal Article
Year of PublicationSubmitted
AuthorsBongardt B
JournalComputer Aided Geometric Design
Keywordsadjoint trigonometric representation of displacements, Computational kinematics, generalized complex numbers, Lie theory, Paden–Kahan problems, principle of transference
Abstract

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.