Models and Representations

  • Daniel Klawitter


In this chapter we give a survey on methods that are used nowadays to describe spatial displacements and other transformations. Therefore, point models for lines and spatial displacements in three-dimensional Euclidean space are presented. Moreover, different methods to describe displacements are examined. We review old concepts such as dual numbers, quaternions, and dual quaternions. Furthermore, we give a short review about homogeneous coordinates and how to ” linearize ” displacements. After that we consider Clifford algebras and special Clifford algebra models. These models are a current field of research.


Null Vector Geometric Algebra Algebra Element Geometric Product Exterior Product 
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Copyright information

© Springer Fachmedien Wiesbaden 2015

Authors and Affiliations

  1. 1.Institut für GeometrieTU DresdenDresdenGermany

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