Mathematical Geology

, Volume 34, Issue 6, pp 671–677 | Cite as

Kriging of Regionalized Directions, Axes, and Orientations II: Orientations

  • K. Gerald van den Boogaart
  • Helmut Schaeben


The problem to predict a rotation (orientation) from corresponding geocoded data is discussed and a general solution by virtue of embedding the group of rotations in a real vector space is presented. It is referred to as kriging in embedding spaces as developed in part I of this contribution, and basically the same arguments apply and lead to equivalent results. However, the assumptions of isotropy have to be restated and reinterpreted. A one-to-one correspondence of reasonable isotropy assumptions for rotations represented as axes and for rotations represented by matrices does not seem to exist.

geostatistic manifolds regionalized rotations isotropy assumptions 


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  1. Boogaart, K. G. v.d., Schaeben, H., 2002, Kriging of regionalized directions, axes, and orientations, I. Directions and axis: Math. Geol. v. 34, no 5, p. 479–503.Google Scholar
  2. Altmann, S. L., 1986, Rotations, quaternions, and double groups: Clarendon Press, Oxford, 315 p.Google Scholar
  3. Kuipers, J. B., 1999, Quaternions and rotation sequences: A primer with applications to orbits, aerospace, and virtual reality: Princeton University Press, Princeton, 371 p.Google Scholar

Copyright information

© International Association for Mathematical Geology 2002

Authors and Affiliations

  • K. Gerald van den Boogaart
    • 1
  • Helmut Schaeben
  1. 1.Mathematical Geology and Computer Sciences in GeologyFreiberg University of Mining and TechnologyFreibergGermany

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