Spherical coordinate systems handedness #95
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Lestropie
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Jun 5, 2024
- FSL bedpostx command fibre orientations stored as spherical coordinates are confirmed to use the "bvec" reference frame. - Enforcing azimuth angle to obey the right hand rule about the zenith axis would necessitate direct modification of image intensities from bedpostx outputs to store. Therefore it would be preferable to instead define the sign of the azimuth angle based on the direction of the second reference axis. Closes #95. Closes #94.
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Came across an interesting conundrum while writing an MRtrix3 command to convert between fibre orientations defined using different formats. I'm writing this command partly for verifying handling of metadata in MRtrix3, partly for confirming for this project the convention that is used in FSL (and confirming by being able to convert between FSL and MRtrix3 formats and having data from each display properly in the other).
Currently, the BEP draft states that azimuth angles should be computed relative to the first axis, using the right hand rule around the third axis. However the image axes may themselves define a left-handed rather than right-handed coordinate system; in which case I'm not sure if imposing a right-hand rule makes sense. I wonder if instead the angle should be defined in terms of cosine relative to the first axis, and sine relative to the second axis.
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