NTv2 bicubic and bilinear interpolators are not currently 'reversible'; Add a (single) iteration to find grid shift values in the CRS of the grid

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Assessment

Difficulty
2/5
Estimated time
1-3 hours
Newbie friendliness
76/100
Issue type
Bug
Clarity
Clearly specified
Activity status
Quiet
Tech stack
python
Domain
backend

Research direction

Start at GeodePy.transform.ntv2_2d() and trace its calls to interpolate_ntv2(), using gda94_gda2020_conformal_and_distortion.gsb and the EAST and WEST examples as reference cases. Check the reverse-transformation path and verify that one iteration obtains shifts at the nominal grid CRS location, then confirm GDA94 → GDA2020 → GDA94 returns coordinates to the expected precision.

Written by the indexing model from the issue text.

Description

It is possible to identify locations in the NTv2 grid gda94_gda2020_conformal_and_distortion.gsb
where the forward and reverse transformations are not perfectly reversible in the current GeodePy NTv2 functions
i.e. GeodePy.transform.ntv2_2d() (either method = 'bilinear', or method = 'bicubic')
i.e. GDA94 => GDA2020 => GDA94 does not return the original coordinate to the expected precision

This is caused by the current functions applying the input lat and long as if they are in the CRS of the grid.
However, where grid shift values change quickly between neighbouring nodes, even a 1-2m difference in inputs has a noticeable effect.

This could become problematic if repeated transformations are performed,
or if a process expects the original coordinate to be returned at a very high precision (e.g. if attempting to identifying nodes as identical when comparing datasets from different sources, e.g. if (re)providing a client with GDA94 data before an after a migration of primary datasets to GDA2020)

e.g. below using 'bilinear'; GDA94 => GDA2020 => GDA94, at
-31.6, 141.5 (in 'EAST' subgrid) => => -31.5999999992, 141.5000000011 (approx 0.15mm different per iteration)
-20.0, 122.6 (in 'WEST' subgrid => => -20.0000000000, 122.6000000083 (approx 0.87mm different per iteration)

This issue can be solved by iterating (when transforming in the reverse direction),
so that the grid shifts which are applied are derived at their nominal location in the CRS of the grid.
e.g. determine the shift at the GDA94 location, and apply those SAME shifts, whether in the forward OR reverse direction.

def ntv2_2d(...)
   ...
    if forward_tf:
        tf_lat = lat + shifts[0] / 3600
        tf_lon = lon - shifts[1] / 3600
    else:
        tf_lat = lat - shifts[0] / 3600
        tf_lon = lon + shifts[1] / 3600

      ##### ADD THE FOLLOWING ####
      # iterate to obtain shifts at the nominal coords in the CRS of the grid
      # e.g. gda94 location for gda94_gda2020_conformal_and_distortion.gsb
        shifts = interpolate_ntv2(ntv2_grid, tf_lat, tf_lon, method=method)
        if shifts[0] is None:
            raise ValueError('Coordinate outside of grid extents')
        tf_lat = lat - shifts[0] / 3600
        tf_lon = lon + shifts[1] / 3600
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