[PROJ] Strange (non) 3D transformation - EPSG:4322 to EPSG:4222

[Javier Jimenez Shaw]

Hi

I am testing a conversion from WGS72 (EPSG:4322) to Cape (EPSG:4222), and I
expect to get a noticeable difference in Z, due to the significant datum
shift.
However I do not get it.

To avoid any misunderstanding, I am converting everything to 3D with this
command:
as3d () { projinfo EPSG:$1 --single-line -o WKT2:2019 --3d -q }

Using projinfo with "--spatial-test intersects" returns a reasonable
transformation (I think), that composes two Helmert transformations.
What am I doing wrong?

Pivoting manually via EPSG:4326 gives reasonable values in Z

Run with PROJ 7.2.1 compiled in Ubuntu 18.04, without any grid file.

Thanks

$ echo -33.9 18.4 0 | cs2cs "$(as3d 4322)" "$(as3d 4222)" -d 8
-33.89987620 18.40079770 0.00000000

$ echo -33.9 18.4 0 | cs2cs "$(as3d 4322)" "$(as3d 4326)" -d 8 | cs2cs
"$(as3d 4326)" "$(as3d 4222)" -d 8
-33.89987619 18.40079770 -34.18419224
$ echo -33.9 18.4 0 | cs2cs "$(as3d 4322)" "$(as3d 4326)" -d 8
-33.89996800 18.40015389 -3.05061427
$ echo -33.9 18.4 0 | cs2cs "$(as3d 4326)" "$(as3d 4222)" -d 8
-33.89990820 18.40064382 -31.13371642

$ projinfo -s "$(as3d 4322)" -t "$(as3d 4222)" --spatial-test intersects
Candidate operations found: 5
-------------------------------------
Operation No. 1:

unknown id, WGS 72 to WGS 84 (2) + Inverse of Cape to WGS 84 (1), 11 m,
South Africa - mainland onshore.

PROJ string:
+proj=pipeline
  +step +proj=axisswap +order=2,1
  +step +proj=unitconvert +xy_in=deg +z_in=m +xy_out=rad +z_out=m
  +step +proj=push +v_3
  +step +proj=cart +ellps=WGS72
  +step +proj=helmert +x=0 +y=0 +z=4.5 +rx=0 +ry=0 +rz=0.554 +s=0.219
        +convention=position_vector
  +step +proj=helmert +x=136 +y=108 +z=292
  +step +inv +proj=cart +a=6378249.145 +rf=293.4663077
  +step +proj=pop +v_3
  +step +proj=longlat +a=6378249.145 +rf=293.4663077
  +step +proj=unitconvert +xy_in=rad +z_in=m +xy_out=deg +z_out=m
  +step +proj=axisswap +order=2,1
...

.___ ._ ..._ .. . ._.  .___ .. __ . _. . __..  ... .... ._ .__
Entre dos pensamientos racionales
hay infinitos pensamientos irracionales.
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