Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra

  • Robert Valkenburg
  • Leo Dorst


The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric data such as points, spheres, circles, lines, planes, directions, and tangents; and the different types of geometric data are combined naturally in a single framework. Also, it excludes the possibility of a reflection unlike some matrix formulations. It returns the motor with the smallest translation and rotation angle when the optimal motor is not unique.


Object Representation Geometric Object Geometric Data Polar Decomposition Rigid Body Transformation 
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This work was supported by the New Zealand Foundation for Research, Science and Technology.


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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