Statistics of ambiguous rotations

R. Arnold, P. E. Jupp, H. Schaeben

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
3 Downloads (Pure)


The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.
Original languageEnglish
Pages (from-to)73-85
JournalJournal of Multivariate Analysis
Early online date21 Nov 2017
Publication statusPublished - May 2018


  • Frame
  • Orientation
  • Regression
  • Symmetric array
  • Symmetry
  • Test of location
  • Test of uniformity


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