[PROJ] geoid model + Helmert

[Javier Jimenez Shaw]

Hi

This is a question to understand what should be more correct, not a request
to change anything in PROJ. The numerical difference is very small.

The 3D transformation from EPSG:4258 to EPSG:4150+5729 has two components:
a grid file for the geoid model of LHN95 height, interpolated in ETRS89,
and the Helmert transformation from ETRS89 (EPSG:4258) to CH1903+
(EPSG:4150).
The input of the Helmert transformation should be ellipsoidal heights, but
in this pipeline they are orthometric heights. Right?
Technically that would change also the horizontal output because of the
change in elevation in the input of the Helmert (again, the difference is
very small. 1 or 2 mm. I just want to understand it).

PROJ_NETWORK=ON projinfo EPSG:4258 EPSG:4150+5729 -o proj --3d

+proj=pipeline
  +step +proj=axisswap +order=2,1
  +step +proj=unitconvert +xy_in=deg +xy_out=rad
  +step +inv +proj=vgridshift +grids=ch_swisstopo_chgeo2004_ETRS89_LHN95.tif
        +multiplier=1
  +step +proj=push +v_3
  +step +proj=cart +ellps=GRS80
  +step +inv +proj=helmert +x=674.374 +y=15.056 +z=405.346
  +step +inv +proj=cart +ellps=bessel
  +step +proj=pop +v_3
  +step +proj=unitconvert +xy_in=rad +xy_out=deg
  +step +proj=axisswap +order=2,1


Would this be more correct? (undoing the vgridshift before calling Helmert,
but after "push +v_3")

+proj=pipeline
  +step +proj=axisswap +order=2,1
  +step +proj=unitconvert +xy_in=deg +xy_out=rad
  +step +inv +proj=vgridshift +grids=ch_swisstopo_chgeo2004_ETRS89_LHN95.tif
        +multiplier=1
  +step +proj=push +v_3
  +step +proj=vgridshift +grids=ch_swisstopo_chgeo2004_ETRS89_LHN95.tif
        +multiplier=1
  +step +proj=cart +ellps=GRS80
  +step +inv +proj=helmert +x=674.374 +y=15.056 +z=405.346
  +step +inv +proj=cart +ellps=bessel
  +step +proj=pop +v_3
  +step +proj=unitconvert +xy_in=rad +xy_out=deg
  +step +proj=axisswap +order=2,1

Thanks.

Javier.

PS to get output in meters use EPSG:2056, that uses the Swiss projection. I
removed it to simplify the pipelines.
Just replace the last two lines of the pipeline with
+step +proj=somerc +lat_0=46.9524055555556 +lon_0=7.43958333333333 +k_0=1
+x_0=2600000 +y_0=1200000 +ellps=bessel
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