Abstract
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 language | English |
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Pages (from-to) | 73-85 |
Journal | Journal of Multivariate Analysis |
Volume | 165 |
Early online date | 21 Nov 2017 |
DOIs | |
Publication status | Published - May 2018 |
Keywords
- Frame
- Orientation
- Regression
- Symmetric array
- Symmetry
- Test of location
- Test of uniformity