Geographic hulls by Mark Seemann
Seven lines of Python code.
Can you tell what this is?
I showed this to both my wife and my son, and they immediately recognized it for what it is. On the other hand, they're also both culturally primed for it.
After all, it's a map of Denmark, although I've transformed each of the major islands, as well as the peninsula of Jutland to their convex hulls.
Here's the original map I used for the transformation:
I had a reason to do this, having to do with the coastline paradox, but my underlying motivation isn't really that important for this article, since I rather want to discuss how I did it.
The short answer is that I used Python. You have to admit that Python has a fabulous ecosystem for all kinds of data crunching, including visualizations. I'd actually geared up to implementing a Graham scan myself, but that turned out not to be necessary.
GeoPandas to the rescue #
I'm a novice Python programmer, but I've used Matplotlib before to visualize data, so I found it natural to start with a few web searches to figure out how to get to grips with the problem.
I quickly found GeoPandas, which works on top of Matplotlib to render and visualize geographical data.
My next problem was to find a data set for Denmark, which I found on SimpleMaps. I chose to download and work with the GeoJSON format.
Originally, I'd envisioned implementing a Graham scan myself. After all, I'd done that before in F#, and it's a compelling exercise. It turned out, however, that this function is already available in the GeoPandas API.
I had trouble separating the data file's multi-part geometry into multiple single geometries. This meant that when I tried to find the convex hull, I got the hull of the entire map, instead of each island individually. The solution was to use the explode function.
Once I figured that out, it turned out that all I needed was seven lines of Python code, including imports and a blank line:
import geopandas as gpd import matplotlib.pyplot as plt map = gpd.read_file('dk.json') map.explode().boundary.plot(edgecolor='green').set_axis_off() map.explode().convex_hull.boundary.plot().set_axis_off() plt.show()
In this script, I display the unmodified map before the convex hulls. This is only an artefact of my process. As I've already admitted, this is new ground for me, and I initially wanted to verify that I could even read in and display a GeoJSON file.
For both maps I use the boundary property to draw only the outline of the map, rather than filled polygons.
Enveloping the map parts #
Mostly for fun, but also to illustrate what a convex hull is, we can layer the two visualizations in a single image. In order to do that, a few changes to the code are required.
import geopandas as gpd import matplotlib.pyplot as plt map = gpd.read_file('dk.json') _, ax = plt.subplots() map.explode().boundary.plot(ax=ax, edgecolor='green').set_axis_off() map.explode().convex_hull.boundary.plot(ax=ax).set_axis_off() plt.show()
This little script now produces this image:
Those readers who know Danish geography may wonder what's going on with Falster. Since it's the sixth-largest Island in Denmark, shouldn't it have its own convex hull? Yes, it should, yet here it's connected to Zealand. Granted, two bridges connect the two, but that's hardly sufficient to consider them one island. There are plenty of bridges in Denmark, so according to that criterion, most of Denmark is connected. In fact, on the above map, only Bornholm, Samsø, Læsø, Ærø, Fanø, and Anholt would then remain as islands.
Rather, this only highlights the quality, or lack thereof, of the data set. I don't want to complain about a free resource, and the data set has served my purposes well enough. I mostly point this out in case readers were puzzled about this. In fact, a similar case applies to Nørrejyske Ø, which in the GeoJSON map is connected to Jutland at Aalborg. Yes, there's a bridge there. No, that shouldn't qualify as a land connection.
Other countries #
As you may have noticed, apart from the hard-coded file name, nothing in the code is specific to Denmark. This means that you can play around with other countries. Here I've downloaded various GeoJSON data sets from GeoJSON Maps of the globe, which seems to be using the same source data set that the Danish data set is also based on. In other words, if I download the file for Denmark from that site, it looks exactly as above.
Can you guess which country this is?
Or this one?
While this is all good fun, not all countries have interesting convex hull:
While I'll let you have a bit of fun guessing, you can hover your cursor over each image to reveal which country it is.
Conclusion #
Your default position when working with Python should probably be: There's already a library for that.
In this article, I've described how I wanted to show Denmark, but only the convex hull of each of the larger islands, as well as the Jutland peninsula. Of course, there was already a library for that, so that I only needed to write seven lines of code to produce the figures I wanted.
Granted, it took a few hours of research to put those seven lines together, but I'm only a novice Python programmer, and I'm sure an old hand could do it much faster.
