Arrows with an inflexion point in matplotlib

Creating arrows in matplotlib can quickly becomes a nightmare, especially when you want to add an inflexion point.

This post explains how to simplify this process by creating our own dedicated function. Then we'll go over how to use it in practice with a real plot and how to play with the parameters.

Libraries & Data

For creating this chart, we will need to load the following libraries:

matplotlib for creating the chart and the arrows
pandas for loading the data
pypalettes: for the color palette

import matplotlib.pyplot as plt
import pandas as pd
from pypalettes import load_cmap

# set a higher resolution
plt.rcParams['figure.dpi'] = 250

# load the gapminder dataset
df = pd.read_csv('https://raw.githubusercontent.com/holtzy/The-Python-Graph-Gallery/master/static/data/gapminderData.csv')
df = df[df['year']==df['year'].max()]
df.head()

	country	year	pop	continent	lifeExp	gdpPercap
11	Afghanistan	2007	31889923.0	Asia	43.828	974.580338
23	Albania	2007	3600523.0	Europe	76.423	5937.029526
35	Algeria	2007	33333216.0	Africa	72.301	6223.367465
47	Angola	2007	12420476.0	Africa	42.731	4797.231267
59	Argentina	2007	40301927.0	Americas	75.320	12779.379640

Simple bubble chart

This code uses the ax.scatter() function from matplotlib.

The aim of this post is to show how arrows with inflexion points can be used to improve this kind of chart.

# initialize the figure
fig, ax = plt.subplots(figsize=(14,7))
ax.set_xlim(-1500, 50000)
ax.spines[['top', 'right']].set_visible(False)

# create a bubble chart
ax.scatter(
    x = df['gdpPercap'],
    y = df['lifeExp'],
    s = df['pop']/100000,
    c = pd.Categorical(df['continent']).codes,
    cmap = load_cmap('Acadia'),
    alpha = 0.8,
    edgecolors="white",
    linewidth=2
)

# display the plot
plt.show()

Simple arrow with an inflexion point

In order to make our code easier to read, we will create a function called arrow_inflection() that will receive the following parameters:

an ax:
a start and end point for the arrow (tuple with x and y values)
the angleA and angleB for the arrow
the radius of the inflexion point
the color of the arrow (default is black)
the transform for custom coordinates (default is None)

def arrow_inflexion(
   ax,
   start, end,
   angleA, angleB,
   radius=0,
   color="black",
   transform=None
):
   
   # get the coordinates
   x1, y1 = end
   x2, y2 = start
   
   # avoid division by zero
   epsilon = 1e-6
   if x2 == x1:
      x2 += epsilon
   if y2 == y1:
      y2 += epsilon
   
   # select right coordinates
   if transform is None:
      transform = ax.transData
   
   # add the arrow
   connectionstyle = f"angle,angleA={angleA},angleB={angleB},rad={radius}"
   ax.annotate(
      "",
      xy=(x1, y1), xycoords=transform,
      xytext=(x2, y2), textcoords=transform,
      arrowprops=dict(
         color=color, arrowstyle="->",
         shrinkA=5, shrinkB=5,
         patchA=None, patchB=None,
         connectionstyle=connectionstyle,
      ),
   )

The function can be a bit complex at first since it uses lots of different matplotlib tools. Here are the main ones that we explain how to use in the gallery:

the transform argument for choosing the coordinate system
how to create a simple arrows
how to create a curved arrows

Otherwise you can just use the above function like in the examples below and it will work just fine:

# initialize the figure with 4 subplots
fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(10,10))

# top left arrow
arrow_inflexion(ax=axs[0,0], start=(0.1, 0.2), end=(0.4, 0.5), angleA=0, angleB=90, radius=0)
axs[0,0].text(x=0.1, y=0.6, s="angleA=0, angleB=90, radius=0", fontsize=12, ha='left')

# top right arrow
arrow_inflexion(ax=axs[0,1], start=(0.1, 0.2), end=(0.4, 0.5), angleA=0, angleB=50, radius=0)
axs[0,1].text(x=0.1, y=0.6, s="angleA=0, angleB=50, radius=0", fontsize=12, ha='left')

# bottom left arrow
arrow_inflexion(ax=axs[1,0], start=(0.1, 0.2), end=(0.4, 0.5), angleA=-15, angleB=90, radius=100)
axs[1,0].text(x=0.1, y=0.6, s="angleA=-15, angleB=90, radius=100", fontsize=12, ha='left')

# bottom right arrow
arrow_inflexion(ax=axs[1,1], start=(0.1, 0.2), end=(0.4, 0.5), angleA=90, angleB=10, radius=0)
axs[1,1].text(x=0.1, y=0.6, s="angleA=90, angleB=30, radius=0", fontsize=12, ha='left')

# display the plot
plt.show()

Combined bubble chart with arrows

The following code is based on our previous bubble chart with the use of our arrow_inflection() function.

The only real complexity is to find the right values for the start and end points of the arrows. Since there is no magic method for this, you will have to go through a trial and error process to find the right values.

# initialize the figure
fig, ax = plt.subplots(figsize=(14,7))
ax.set_xlim(-1500, 50000)
ax.spines[['top', 'right']].set_visible(False)
cmap = load_cmap('Acadia')

# create a bubble chart
bubble = ax.scatter(
    x = df['gdpPercap'],
    y = df['lifeExp'],
    s = df['pop']/100000,
    c = pd.Categorical(df['continent']).codes,
    cmap = cmap,
    alpha = 0.8,
    edgecolors="white",
    linewidth=2
)

# add an arrow
arrow_inflexion(ax=ax, start=(10000, 49), end=(15000, 60), angleA=20, angleB=70)
arrow_inflexion(ax=ax, start=(43000, 75), end=(30000, 60), angleA=60, angleB=-30)
arrow_inflexion(ax=ax, start=(15300, 76.5), end=(17000, 83), angleA=90, angleB=10)
arrow_inflexion(ax=ax, start=(800, 70), end=(4000, 83), angleA=90, angleB=45)

# simple annotation at the end of each arrow
ax.text(x=15000, y=60, s="Africa", fontsize=12, ha='center', fontweight='bold', color=cmap(0))
ax.text(x=28000, y=59.5, s="Americas", fontsize=12, ha='center', fontweight='bold', color=cmap(1))
ax.text(x=18500, y=82.5, s="Europe", fontsize=12, ha='center', fontweight='bold', color=cmap(4))
ax.text(x=4000, y=83.5, s="Asia", fontsize=12, ha='center', fontweight='bold', color=cmap(3))

# display the plot
plt.show()

Going further

Contact & Edit

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