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Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition

  • Leo Dorst
  • Robert Valkenburg

Abstract

Conformal transformations are described by rotors in the conformal model of geometric algebra (CGA). In applications there is a need for interpolation of such transformations, especially for the subclass of 3D rigid body motions. This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA. It also classifies the types of conformal transformations and their orbits. To derive the results, we employ a novel polar decomposition for the even subalgebra of 3D CGA and an associated norm-like expression.

Keywords

Conformal Transformation Rigid Body Motion Geometric Algebra Invertible Element Polar Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Intelligent Systems LaboratoryUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Industrial Research LimitedAucklandNew Zealand

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