Moving from basemap to cartopy

Question

I am trying to move from Basemap in python2 to cartopy in python3. However, I am finding it difficult to transform some Basemap code block to cartopy:

Basemap (python2.7)

from mpl_toolkits.basemap import Basemap
bmap = Basemap(projection='merc', resolution='c', llcrnrlon=-125, llcrnrlat=26, urcrnrlon=-56, urcrnrlat=46)

print bmap.makegrid(4, 4)[0]
[[-125. -102.  -79.  -56.]
 [-125. -102.  -79.  -56.]
 [-125. -102.  -79.  -56.]
 [-125. -102.  -79.  -56.]]

print bmap.makegrid(4, 4)[1]
[[26.         26.         26.         26.        ]
 [33.23223798 33.23223798 33.23223798 33.23223798]
 [39.91267019 39.91267019 39.91267019 39.91267019]
 [46.00000132 46.00000132 46.00000132 46.00000132]]

cartopy (python 3.7)

import cartopy.crs as ccrs
mrc = ccrs.Mercator()
lons = np.array([-125, -56])
lats = np.array([26, 46])
width = 4
height = 4
projected_corners = mrc.transform_points(ccrs.PlateCarree(), lons, lats)
xs = np.linspace(
    projected_corners[0, 0], projected_corners[1, 0], width)
ys = np.linspace(
    projected_corners[0, 1], projected_corners[1, 1], height)
print(xs)
[-14248894.82153902  -6567849.95680314]
print(ys)
[2736034.98592771 6413524.59416364]

Note: I am trying to follow steps mentioned here using Mercator projection to get behavior similar to makegrid but the result does not match with Basemap as seen above.

Answer 1

The results are in good agreement if compared on the same basis (coordinate system). Here is the runnable code and the results:

import numpy as np
import cartopy.crs as ccrs
import matplotlib.pyplot as plt

mrc = ccrs.Mercator()
lons = np.array([-125, -56])
lats = np.array([26, 46])
width = 4
height = 4
projected_corners = mrc.transform_points(ccrs.PlateCarree(), lons, lats)
xs = np.linspace(projected_corners[0, 0], projected_corners[1, 0], width)
ys = np.linspace(projected_corners[0, 1], projected_corners[1, 1], height)
x2d, y2d = np.meshgrid(xs, ys)

ax = plt.axes(projection = mrc)
ax.coastlines()
ax.scatter(x2d, y2d)
ax.gridlines(draw_labels=True)

plt.show()

Output plot:

And the computation for coordinates (long, lat) of the grid points:

platecarr = ccrs.PlateCarree()
lon_lat_list = platecarr.transform_points(ccrs.Mercator(), xs, ys)
print(lon_lat_list)

[[-125.           26.            0.        ]
 [-102.           33.23738591    0.        ]
 [ -79.           39.91736844    0.        ]
 [ -56.           46.            0.        ]]