Paper Info
Title
Quaternionic approach to equiform kinematics and line-elements of Euclidean 4-space and 3-space.
Abstract
We extend the quaternionic kinematic mapping of Euclidean displacements of Euclidean 4-space E 4 to the group of equiform transformations S ( 4 ) . As a consequence the equiform motions of basic elements (points, oriented lines, oriented planes, oriented hyperplanes) of E 4 can be written compactly in terms of 2 × 2 quaternionic matrices. This representation is extended to oriented line-elements of E 4 and to instantaneous screws of S ( 4 ) , for which a classification (incl. corresponding normal forms) is given. Based on this preparatory work we study the relation between instantaneous equiform motions and the geometry of line-elements (path normal-elements, path tangent-elements) in E 4 . Finally, we show that the line-elements of projective 3-space can be mapped bijectively on the Segre variety Σ 3 , 2 . A kinematic mapping for the equiform motion group S ( 4 ) of Euclidean 4-space is given.Elements of S ( 4 ) can be written compactly in terms of 2 × 2 quaternionic matrices.A classification of instantaneous screws (incl. normal forms) of S ( 4 ) is provided.The relation between these screws and the geometry of line-elements is studied.Line-elements of projective 3-space are mapped bijectively on the Segre variety Σ 3 , 2 .
Year
DOI
Venue
2016
10.1016/j.cagd.2016.06.003
Computer Aided Geometric Design
Keywords
Field
DocType
Kinematic mapping,Equiform motion,Quaternion,Instantaneous screw,Line-element
Topology,Kinematics,Matrix (mathematics),Quaternion,Euclidean geometry,Line element,Hyperplane,Mathematics
Journal
Volume
Issue
ISSN
47
C
0167-8396
Citations 
PageRank 
References 
1
0.38
2
Authors
1
Name
Order
Citations
PageRank
Georg Nawratil1225.94