The Z, Y', X'' rotation scheme, intrinsic or extrinsic, sounds like an application of Euler (sounds like "Oiler") angles [1,2].
Tom Kunicki Center for Integrated Data Analytics U.S. Geological Survey 8505 Research Way Middleton, WI 53562 [1] http://en.wikipedia.org/wiki/Euler_angles [2] http://mathworld.wolfram.com/EulerAngles.html On Mar 6, 2013, at 2:17 PM, Seth McGinnis <mcgin...@ucar.edu> wrote: > So there are an infinite number of ways to decompose a 3-D orientation into > three orthogonal rotations. Specifying the projection in terms of the final > location of the north pole and an optional rotation around that point means > that CF is actually agnostic about exactly how you get there. > > That said, given that it's being specified in that way, the decomposition that > maps most straightforwardly to those parameters is a Z-Y-X rotation sequence > using an extrinsic (space-fixed) coordinate system: > > First rotate by angle phi around the north pole in space-fixed coordinates. > Then rotate by angle theta around 0N 90E in space-fixed coordinates. > Finally, rotate by angle psi around 0N 0E in space-fixed coordinates. > > The location of the grid's north pole in the original lat-lon coordinate > system > is now at longitude = phi, colatitude = minus theta. > > (I'm not sure how psi relates to north_pole_grid_longitude mathematically; it > defaults to zero and I've never seen it in use, so I think it's included > mostly > for completeness. I agree that we may well want to change it to something more > obvious like an azimuth angle.) > > Switching to the GRIB2 convention where you use the south pole instead of the > north should be just a matter of adding 180 degrees to phi and negating theta. > > Cheers, > > --Seth > > > On Wed, 6 Mar 2013 18:29:47 +0000 > David Hassell <d.c.hass...@reading.ac.uk> wrote: >> Hello, >> >> It is a bit of mess! As I understand it, the full rotation described >> is a sequence of rotations about three different axes: >> >> Z = 90S - 90N >> Y' = 90W' - 90E' >> X" = 0E" - 180E" >> >> where it is understood that the definitions of the N-S and W-E axes >> change after each rotation (hence the primes and double >> primes). Therefore the order in which they are done matters. >> >> I suspect that the usual and assumed order is Z, Y', X"? >> >>> From the GRIB-2 stuff John posted the north_pole_grid_longitude gives >> the rotation about the X" axis. >> >> Something like John's "Angle of rotation" seems right to me. >> >> The apparent lack of consistency between the parameter names irks >> me. Perhaps one solution could be to: >> >> i) Add some text to the conventions state the order (Z, Y', X", say) >> and direction of rotations. >> >> ii) add three new, consistent, self-describing parameters (e.g.) >> >> angle_of_rotation_z >> angle_of_rotation_y >> angle_of_rotation_x >> >> iii) allow aliases for backwards compatibility >> >> grid_north_pole_longitude <=> angle_of_rotation_z >> grid_north_pole_latitude <=> angle_of_rotation_y >> north_pole_grid_longitude <=> angle_of_rotation_x >> >> Or would that just obfuscate things even more? >> >> All the best, >> >> David >> >> P.S. If you have a copy available, there are some nice descriptions in >> "Coordinate Systems and Map Projections" by D. H. Maling >> >> -- >> David Hassell >> National Centre for Atmospheric Science (NCAS) >> Department of Meteorology, University of Reading, >> Earley Gate, PO Box 243, >> Reading RG6 6BB, U.K. >> >> Tel : 0118 3785613 >> Fax : 0118 3788316 >> E-mail: d.c.hass...@reading.ac.uk >> _______________________________________________ >> CF-metadata mailing list >> CF-metadata@cgd.ucar.edu >> http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata > > _______________________________________________ > CF-metadata mailing list > CF-metadata@cgd.ucar.edu > http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata _______________________________________________ CF-metadata mailing list CF-metadata@cgd.ucar.edu http://mailman.cgd.ucar.edu/mailman/listinfo/cf-metadata
