How to fix overlapping annotations / text

I'm trying to stop annotation text overlapping in my graphs. The method suggested in the accepted answer to Matplotlib overlapping annotations looks extremely promising, however is for bar graphs. I'm having trouble converting the "axis" methods over to what I want to do, and I don't understand how the text lines up.

import sys
import matplotlib.pyplot as plt


# start new plot
plt.clf()
plt.xlabel("Proportional Euclidean Distance")
plt.ylabel("Percentage Timewindows Attended")
plt.title("Test plot")

together = [(0, 1.0, 0.4), (25, 1.0127692669427917, 0.41), (50, 1.016404709797609, 0.41), (75, 1.1043426359673716, 0.42), (100, 1.1610446924342996, 0.44), (125, 1.1685687930691457, 0.43), (150, 1.3486407784550272, 0.45), (250, 1.4013999168008104, 0.45)]
together.sort()

for x,y,z in together:
    plt.annotate(str(x), xy=(y, z), size=8)

eucs = [y for (x,y,z) in together]
covers = [z for (x,y,z) in together]

p1 = plt.plot(eucs,covers,color="black", alpha=0.5)

plt.savefig("test.png")

Images (if this works) can be found here (this code):

and here (more complicated):

I just wanted to post here another solution, a small library I wrote to implement this kind of things: https://github.com/Phlya/adjustText An example of the process can be seen here:

Here is the example image:

import matplotlib.pyplot as plt
from adjustText import adjust_text
import numpy as np
together = [(0, 1.0, 0.4), (25, 1.0127692669427917, 0.41), (50, 1.016404709797609, 0.41), (75, 1.1043426359673716, 0.42), (100, 1.1610446924342996, 0.44), (125, 1.1685687930691457, 0.43), (150, 1.3486407784550272, 0.45), (250, 1.4013999168008104, 0.45)]
together.sort()

text = [x for (x,y,z) in together]
eucs = [y for (x,y,z) in together]
covers = [z for (x,y,z) in together]

p1 = plt.plot(eucs,covers,color="black", alpha=0.5)
texts = []
for x, y, s in zip(eucs, covers, text):
    texts.append(plt.text(x, y, s))

plt.xlabel("Proportional Euclidean Distance")
plt.ylabel("Percentage Timewindows Attended")
plt.title("Test plot")
adjust_text(texts, only_move={'points':'y', 'texts':'y'}, arrowprops=dict(arrowstyle="->", color='r', lw=0.5))
plt.show()

If you want a perfect figure, you can fiddle around a little. First, let's also make text repel the lines - for that we just create lots of virtual points along them using scipy.interpolate.interp1d.

We want to avoid moving the labels along the x-axis, because, well, why not do it for illustrative purposes. For that we use the parameter only_move={'points':'y', 'text':'y'}. If we want to move them along x axis only in the case that they are overlapping with text, use move_only={'points':'y', 'text':'xy'}. Also in the beginning the function chooses optimal alignment of texts relative to their original points, so we only want that to happen along the y axis too, hence autoalign='y'. We also reduce the repelling force from points to avoid text flying too far away due to our artificial avoidance of lines. All together:

from scipy import interpolate
p1 = plt.plot(eucs,covers,color="black", alpha=0.5)
texts = []
for x, y, s in zip(eucs, covers, text):
    texts.append(plt.text(x, y, s))

f = interpolate.interp1d(eucs, covers)
x = np.arange(min(eucs), max(eucs), 0.0005)
y = f(x)    
    
plt.xlabel("Proportional Euclidean Distance")
plt.ylabel("Percentage Timewindows Attended")
plt.title("Test plot")
adjust_text(texts, x=x, y=y, autoalign='y',
            only_move={'points':'y', 'text':'y'}, force_points=0.15,
            arrowprops=dict(arrowstyle="->", color='r', lw=0.5))
plt.show()