What to use as extent when defining a morecantile custom TMS grid?

Question

I am looking at the Define custom grid section of the morecantile documentation. They define an EPSG:3031 based custom grid this way:

import morecantile
from pyproj import CRS

crs = CRS.from_epsg(3031)
extent = [-948.75, -543592.47, 5817.41, -3333128.95]  # From https:///epsg.io/3031
customEPGS3031 = morecantile.TileMatrixSet.custom(extent, crs, id="MyCustomTmsEPSG3031")

The comment says the values are from https:///epsg.io/3031. Unfortunately, I haven't found the values -948.75, -543592.47, 5817.41, -3333128.95 on that website.

How can I find out what extent should be used for a custom TMS grid?

Answer 1

This variable extent = [-948.75, -543592.47, 5817.41, -3333128.95] looks like the bbox of the Antarctica bounds transformed from the WGS84 to the EPSG:3031.

from pyproj import CRS, Transformer

crs1 = CRS.from_epsg(4326)
crs2 = CRS.from_epsg(3031)

bbox_dict = dict(crs2.to_json_dict()).get("bbox")
bbox = list(bbox_dict.values())

print(bbox) # [-90, -180, -60, 180]

transformer = Transformer.from_crs(crs2, crs1)

extent = [-948.75, -543592.47, 5817.41, -3333128.95]
bbox_ = list(transformer.transform(extent[0], extent[1]))
bbox_.extend(transformer.transform(extent[2], extent[3]))

print(bbox_) # [-85.00000000152139, -179.89999987377152, -60.00000000847028, 179.90000005782724]

Also, after verifying extent-coordinates by means http://projfinder.com/ it is possible to see

Pair #1:

Pair #2: