matplotlib text in display coordinate

Question

I try to understand how different coordinate systems work in matplotlib. My understanding is that if I add some texts using data coordinates, then I can achieve the same effect if I first transform the data coordinates to the display coordinates and then add the text using these display coordinates. In the following snippet, I expect the 'x' in green are right on top of the 'x' in red. But they are not. What do I miss here? Thank you!

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.set_xlim(0, 10)
ax.set_ylim(-1, 1)
ax.grid()
ax.text(4,0,'x', horizontalalignment='center', verticalalignment='center', color='r')

_x2, _y2 = ax.transData.transform((4.0, 0))
ax.text(_x2,_y2,'x', horizontalalignment='center', verticalalignment='center', transform=None, color='g')

Result:

Answer 1

Once again, we have examined the FIGURE, DATA, and AXIS criteria. We have modified them for clarity from the data range in question. The same is obtained with the figure criterion, divided by the graph size in inches and dpi value. The position of the origin of the axis is also obtained with the figure reference, and when drawn, it overlaps with the origin of the graph. The origin of the graph is shown in black.

import matplotlib.pyplot as plt

fig_x, fig_y =  plt.rcParams['figure.figsize']
dpi = plt.rcParams['figure.dpi']
print(fig_x, fig_y, dpi)

fig, ax = plt.subplots()
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.grid()
g = ax.text(0,0,'o', horizontalalignment='center', verticalalignment='center', color='r')
print('get_position', g.get_position())

_x2, _y2 = ax.transData.transform((0.0, 0))
print('ax.transData', _x2, _y2)

_x3, _y3 = ax.transAxes.transform((0.0, 0))
print('ax.transAxes', _x3, _y3)

# From  Figure position  to ax.transData 
ax.text(_x2/fig_x/dpi,_y2/fig_y/dpi,'x', horizontalalignment='center', verticalalignment='center', color='g', transform=fig.transFigure)
# From  Figure position  to ax.transAxes
ax.text(_x3/fig_x/dpi,_y3/fig_y/dpi,'x', horizontalalignment='center', verticalalignment='center', color='b', transform=fig.transFigure)
# Figure x0, y0
ax.text(0,0,'x', horizontalalignment='center', verticalalignment='center', color='k', transform=fig.transFigure)
plt.show()