naa a22 4500 510737064 CHVBK 20180411083014.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s13366-013-0154-6 doi (NATIONALLICENCE)springer-10.1007/s13366-013-0154-6 Kinematic mappings for Cayley-Klein geometries via Clifford algebras [Elektronische Daten] [Daniel Klawitter, Markus Hagemann] This paper unifies the concept of kinematic mappings by using geometric algebras. We present a method for constructing kinematic mappings for certain Cayley-Klein geometries. These geometries are described in an algebraic setting by the homogeneous Clifford algebra model. Displacements correspond to Spin group elements. After that Spin group elements are mapped to a kinematic image space. Especially for the group of planar Euclidean displacements $$\mathrm{{SE} }(2)$$ SE ( 2 ) the result is the kinematic mapping of Blaschke and Grünwald. For the group of spatial Euclidean displacements $$\mathrm{{SE} }(3)$$ SE ( 3 ) the result is Study's mapping. Furthermore, we classify kinematic mappings for Cayley-Klein spaces of dimension $$2$$ 2 and $$3$$ 3 . The Managing Editors, 2013 Kinematic mapping nationallicence Kinematic image space nationallicence Cayley-Klein geometry nationallicence Study's quadric nationallicence Clifford algebra nationallicence Klawitter Daniel Technical University of Dresden, Institute of Geometry, Zellescher Weg 12-14, 01062, Dresden, Germany aut Hagemann Markus Technical University of Dresden, Institute of Geometry, Zellescher Weg 12-14, 01062, Dresden, Germany aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 737-761 0138-4821 54:2<737 2013 54 13366 https://doi.org/10.1007/s13366-013-0154-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-013-0154-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Klawitter Daniel Technical University of Dresden, Institute of Geometry, Zellescher Weg 12-14, 01062, Dresden, Germany aut NATIONALLICENCE 700 1- Hagemann Markus Technical University of Dresden, Institute of Geometry, Zellescher Weg 12-14, 01062, Dresden, Germany aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 737-761 0138-4821 54:2<737 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer