Matching projected tiles from carto with a another tile service

Question

Web Mercator projection is not a good match for polar region, and I need to use "Sphere Azimuthal Equidistant" for a project: https://epsg.io/53032

I'm able to add the projection to PostGIS/Carto by running this query:

INSERT into spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext) values ( 53032, 'ESRI', 53032, '+proj=aeqd +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs ', 'PROJCS["Sphere_Azimuthal_Equidistant",GEOGCS["GCS_Sphere",DATUM["Not_specified_based_on_Authalic_Sphere",SPHEROID["Sphere",6371000,0]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Azimuthal_Equidistant"],PARAMETER["False_Easting",0],PARAMETER["False_Northing",0],PARAMETER["Central_Meridian",0],PARAMETER["Latitude_Of_Origin",0],UNIT["Meter",1],AUTHORITY["EPSG","53032"]]');

This gives me this top level tile (0/0/0) from Carto:

I need to match this tile with another service (WMTS), where I need to specify the extent and resolution. Is there somehow I can get this information from Carto? How is the top level tile defined?

About projections in Carto: https://carto.com/blog/free-your-maps-web-mercator/

Answer 1

Even though you've set your backend project to something fun and polar, every other part of the Carto infrastructure is still assuming you're working in web mercator. That includes the tiler. So, what are the extents of tile zero in web mercator? If it's a whole-world tile at zoom zero (check) then it's

(-20037508 -20037508), (20037508 20037508)

And you can use those same extents in your polar projection to work out the extents of tiles in your custom pyramid.