[PROJ] Proj transformation for arbitrary (quaternion/Euler) spatial rotation

[Duncan Agnew]

It looks as though these conventions are for "where do I put the (new)
geographic pole?", which is "what aspect will this projection have?'' But
this is different from "what is the pole of rotation (about which I rotate
everything)?" which is the usual question for finite spherical rotations.
This
could be added to the General Oblique Transformation by adding parameters;
say    lat_r, long_r, alpha_r.

How does Proj actually do the G.O.T? I don't mean what are the parameters,
I mean what is the actual code that does the arithmetic?
(Github is not something I've used much--but a link would be good).


On Wed, Nov 9, 2022 at 7:39 AM Even Rouault <even.rouault at spatialys.com>
wrote:

> Daven,
>
> finding the right parameters is always a bit tricky. For example, for
> meteorological data, there are at least 2 different conventions to express
> angles.
>
> See PROJ_WKT2_NAME_METHOD_POLE_ROTATION_GRIB_CONVENTION and
> PROJ_WKT2_NAME_METHOD_POLE_ROTATION_NETCDF_CF_CONVENTION at
> https://github.com/OSGeo/PROJ/blob/ae3180303d974653b126bc65dcfdad3cecb5a313/src/iso19111/operation/conversion.cpp#L3783
> <https://urldefense.com/v3/__https://github.com/OSGeo/PROJ/blob/ae3180303d974653b126bc65dcfdad3cecb5a313/src/iso19111/operation/conversion.cpp*L3783__;Iw!!Mih3wA!CLqRz9MqXF-PSnAEuYeY5ZvHpRdIzdPBOk7sZ-arOkP9TgEEjtjlBw7cQbwsGqV4lhKPrdhoZgWyMSyVDt-lZ_c2$>
> where there's a mapping from south pole / north pole conventions to
> +proj=ob_tran. Setting lon_0 is often necessary.
>
> Even
> Le 09/11/2022 à 13:00, DAVEN P QUINN via PROJ a écrit :
>
> Hello all,
>
> I’m a geologist who is working with paleogeographic reconstructions (see
> example here
> <https://urldefense.com/v3/__https://davenquinn.com/viz/corelle-demo-pbdb/?time=295__;!!Mih3wA!CLqRz9MqXF-PSnAEuYeY5ZvHpRdIzdPBOk7sZ-arOkP9TgEEjtjlBw7cQbwsGqV4lhKPrdhoZgWyMSyVDvT4V4JT$>).
> These require composite reproductions where different parts of a feature
> dataset (continents) are rotated with different axis-angle transformations.
> I’ve had good luck doing these rotations with quaternion math in the
> browser/Python environments, but I am now trying to use Proj
> transformations in order to apply rotations directly within PostGIS queries.
>
> This linked image
> <https://urldefense.com/v3/__https://pbs.twimg.com/media/Fgpx4UGXEAQmPOt?format=jpg&name=4096x4096__;!!Mih3wA!CLqRz9MqXF-PSnAEuYeY5ZvHpRdIzdPBOk7sZ-arOkP9TgEEjtjlBw7cQbwsGqV4lhKPrdhoZgWyMSyVDiL82wyr$>
>  shows the desired result, a plate reconstruction to 250 Ma with a
> different rotation applied to each plate. This was produced by applying the
> desired quaternions through pl/pgsql math. Moving this math to Proj
> internals would result in a ~50-100x speedup.
>
> The tool that seems most fitting is the `ob_trans` family of projections,
> but I have been unable to define a rotation that can handle my preferred
> representation (a pole defined in Lon-lat coordinates and an associated
> angle of rotation around it). From my reading of the docs, I believe the
> `o_lon_c`, `o_lat_c` and `o_alpha` parameters should do this, but I cannot
> get them to work reliably. In fact, I can’t even reliably define a ’no-op’
> transformation that leaves coordinates unchanged. Perhaps I have the
> angular coordinate system wrong, or the rotation is being done in Cartesian
> space even though `proj=lonlat` is used.
>
> Is it possible to define an arbitrary spherical spatial rotation in Proj
> transformations? Maybe I need to use pipelines instead? I’d appreciate any
> guidance! More details below the fold...
>
> Regards,
>
> *Daven P. Quinn*
> Research scientist II · *U of Wisconsin Madison*
> PhD · structural geology · *Caltech* ‘18
> https://davenquinn.com
> <https://urldefense.com/v3/__https://davenquinn.com__;!!Mih3wA!CLqRz9MqXF-PSnAEuYeY5ZvHpRdIzdPBOk7sZ-arOkP9TgEEjtjlBw7cQbwsGqV4lhKPrdhoZgWyMSyVDtXQU_j5$>
> +1 704 920 8487
>
> -------------
>
> Here is an example of the pl/pgsql I am currently using to assemble a
> projection (I have gone through many iterations testing different offsets
> and the different ways to specify the transformation):
> ```
> RETURN '+proj=ob_tran +o_proj=longlat +o_alpha=' || pi()/2+angle || 'r
> +o_lon_c=' || pi()/2+lon || 'r +o_lat_c=' || lat || 'r' proj
> ```
> where (lat, lon, angle) defines a rotation pole.
>
> This results in some geometries (with a fortuitous set of poles, I guess)
> attaining ballpark-correct transformations while other features are shifted
> far outside of their origin tiles.
>
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