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

[Javier Jimenez Shaw]

Maybe it does help: https://proj.org/operations/transformations/affine.html
I used it in a derived projected crs (PROJ 9.1.0 fixed some bugs on that).
I do not know if it will work as you expect with a geographic system

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



On Wed, 9 Nov 2022 at 13:00, DAVEN P QUINN via PROJ <proj at lists.osgeo.org>
wrote:

> Hello all,
>
> I’m a geologist who is working with paleogeographic reconstructions (see
> example here <https://davenquinn.com/viz/corelle-demo-pbdb/?time=295>).
> 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://pbs.twimg.com/media/Fgpx4UGXEAQmPOt?format=jpg&name=4096x4096> 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
> +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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