Implement FAC coordinate system options available in IDL SPEDAS, but not yet in PySPEDAS.

[jameswilburlewis]

Right now the only supported option in PySPEDAS is 'xgse'. We should implement the others:

;         'Xgse', (DEFAULT) translates from gse or gsm into FAC
;                    Definition(works on GSE, or GSM):
;                    X Axis = on plane defined by Xgse - Z
;                    Second coordinate definition: Y = Z x X_gse
;                    Third coordinate, X completes orthogonal RHS
;                    (right hand system) triad: XYZ
;                    Note: X_gse is a unit vector pointing in direction from
;                          earth to the sun
;         'Rgeo',translate from geo into FAC using radial position vector
;                    Rgeo is radial position vector, positive radialy outwards.
;                    Second coordinate definition: Y = Z x Rgeo (eastward)
;                    Third coordinate, X completes orthogonal RHS XYZ.
;         'mRgeo',translate into FAC using radial position vector
;                    mRgeo is radial position vector, positive radially inwards.
;                    Second coordinate definition: Y = Z x mRgeo (westward)
;                    Third coordinate, X completes orthogonal RHS XYZ.
;         'Phigeo', translate into FAC using azimuthal position vector
;                    Phigeo is the azimuthal geo position vector, positive Eastward
;                    First coordinate definition: X = Phigeo x Z (positive outwards)
;                    Second coordinate, Y ~ Phigeo (eastward) completes orthogonal RHS XYZ
;         'mPhigeo', translate into FAC using azimuthal position vector
;                    mPhigeo is minus the azimuthal geo position vector; positive Westward
;                    First coordinate definition: X = mPhigeo x Z (positive inwards)
;                    Second coordinate, Y ~ mPhigeo (Westward) completes orthogonal RHS XYZ
;         'Phism', translate into FAC using azimuthal Solar Magnetospheric vector.
;                 Phism is "phi" vector of satellite position in SM coordinates.
;                 Y Axis = on plane defined by Phism-Z, normal to Z
;                 Second coordinate definition: X = Phism x Z
;                 Third completes orthogonal RHS XYZ
;         'mPhism', translate into FAC using azimuthal Solar Magnetospheric vector.
;                 mPhism is minus "phi" vector of satellite position in SM coordinates.
;                 Y Axis = on plane defined by Phism-Z, normal to Z
;                 Second coordinate definition: X = mPhism x Z
;                 Third completes orthogonal RHS XYZ
;         'Ygsm', translate into FAC using cartesian Ygsm position as other dimension.
;                 Y Axis on plane defined by Ygsm and Z
;                 First coordinate definition: X = Ygsm x Z
;                 Third completes orthogonal RHS XYZ

There are several places where individual missions implement their own method of computing basis vectors for the transforms listed above, for example, see erg_pgs_make_fac.py.

[jameswilburlewis]

It looks like projects/themis/examples/advanced/thm_crib_fac.pro has the widest selection of other_dim arguments to thm_fac_matrix_make.