[PROJ] Krovak S-JTSK centimeter accuracy

[Lesparre, Jochem]

>> What do you mean by local: a grid that deal with projected coordinates ? Is it really the case here ? (sorry didn't have time to read thoroughly your links). We've had instances where the data producer originally provided grids referenced to projected coordinates, like the OSGB15 geoid model, and the contributor to PROJ-data reprojected them to geographic coordinates to make them more usable by PROJ. Of course this only worked for a geoid model. If the content of the grid itself is shifts in eastings, northings, then a more complex transformation has to be done. Otherwise PROJ would need a few changes to deal with grids that would operate on projected coordinates.
> Yes, it is in projected coordinates with corrections in the X and Y directions (easing, northing). I was thinking of reprojecting to geodetic coordinates to be able to use `hgridshift`, but there is nuance/complexity like you mentioned.

>> I would strongly suggest that you, or more appropriately the Czech geodesic authority register those grids with IOGP in the EPSG dataset.

A horizontal grid on projected coordinates is not supported ISO, EPSG and GIS software packages, right? In the Netherlands we tried for some years to find other European countries to team up for a lobby to get it supported, without success. So in the end we decided to convert the horizontal grid for our national CRS.

Converting a horizontal grid from projected corrections to ellipsoidal corrections is not too difficult. A problem (1) is that you never get transformation to give exactly the same results due to the resampling of the grid. Because it is common in PROJ (and required by ISO, EPSG and GIS software packages) to include the datum transformation in the ellipsoidal grid, you’ll get two additional problems. (2) The datum transformation becomes 2D instead of 3D. This is convenient for many users, but it introduces horizontal differences between the 3D and the 2D datum transformation that depend on the height. (3) No datum transformation is applied outside the grid, limiting the area where the transformation can be used or causing a discontinuity at the grid edge.

As an official workaround with PROJ, we use a fixed height (43 m in ETRS89 / 0 m in national CRS) for a 3D Helmert datum transformation next to a horizontal grid to get the same results as a grid that includes the datum transformation. This approach also gives results outside the grid, without discontinuities on the grid edge (since the values of our grid fade-out to zero at the grid edge):

+proj=pipeline
+step +proj=unitconvert +xy_in=deg +xy_out=rad
+step +proj=axisswap +order=2,1
+step +proj=push +v_3
+step +proj=set +v_3=43 +omit_inv
+step +proj=cart +ellps=GRS80
+step +proj=helmert +x=-565.7346 +y=-50.4058 +z=-465.2895 +rx=-0.395023 +ry=0.330776 +rz=-1.876073 +s=-4.07242 +convention=coordinate_frame +exact
+step +proj=cart +inv +ellps=bessel
+step +proj=hgridshift +inv +grids=rdcorr2018.tif,null
+step +proj=sterea +lat_0=52.156160556 +lon_0=5.387638889 +k=0.9999079 +x_0=155000 +y_0=463000 +ellps=bessel
+step +proj=set +v_3=0 +omit_fwd
+step +proj=pop +v_3

Regards, Jochem






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