In mpltern, tick markers, tick labels, and grid lines are plotted based on ax.get_{t,l,r}axis_transform() like ax.get_{x,y}axis_transform() in Matplotlib.

For ax.get_taxis_transform(), for example, the first coordinate is for the t-axis values. For the second coordinate, 0 and 1 corresponds to the "tick1" and the "tick2" positions, respectively. Therefore, for the t-axis value of t, the tick-marker positions of "tick1" and "tick2" are given by (t, 0) and (t, 1), respectively, and the grid line spans between (t, 0) and (t, 1).

Using these transforms, we can e.g. plot the region where the ratio of l and r is in a certain range in a bit sementic way as follows.

import matplotlib.pyplot as plt
import mpltern  # noqa: F401

ax = plt.subplot(projection="ternary", ternary_sum=100.0)

x0 = 0.0
x1 = 100.0

ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_taxis_transform())
ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_laxis_transform())
ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_raxis_transform())

y = [0.4, 0.6]

ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_taxis_transform())
ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_laxis_transform())
ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_raxis_transform())


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