Arrows with an inflexion point in matplotlib

logo of a chart:Colours

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.


This plot is a stacked area chart. It show the evolution of natural disasters, separated by type of events.

The chart was made by Joseph Barbier. Thanks to him for accepting sharing his work here!

Let's see what the final picture will look like:

stacked area chart

Libraries & Data

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

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('')
df = df[df['year']==df['year'].max()]
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
    x = df['gdpPercap'],
    y = df['lifeExp'],
    s = df['pop']/100000,
    c = pd.Categorical(df['continent']).codes,
    cmap = load_cmap('Acadia'),
    alpha = 0.8,

# display the plot

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(
   start, end,
   angleA, angleB,

   # 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}"
      xy=(x1, y1), xycoords=transform,
      xytext=(x2, y2), textcoords=transform,
         color=color, arrowstyle="->",
         shrinkA=5, shrinkB=5,
         patchA=None, patchB=None,

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:

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

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,

# 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