A Voronoi diagram is a partition of a plane into regions close to a given set of points (tessellation). For my mother's birthday, I decided to make her some Voronoi art of a map of Ireland and where her siblings lived.
The first thing I needed was to plot an outline of the island of Ireland. I had never used R before, but knew that it was well suited to graphical plotting. Installation to Windows was very straightforward. To plot a an outline in R, I needed a corresponding shapefile. This is easier said than done. Many of the shapefiles I found did not have a high enough level of detail, or contained additional unncessary information (for example the CSO site). In the end, I used the Republic of Ireland file from geoboundaries.org and the Northern Island file from OSNI. Once I had the correct shapefiles, plotting them together and cleaning up the output was relatively straight forward using the R documentation and cursory searches. I did use ChatGPT at one point to write a function to remove the holes in the output (e.g. lakes). I opted for a minimal R theme as I really just wanted the country border to stand out against a plain background. Adding the individual co-ordinates to represent her siblings is a simple matter of including a dataframe in the plot. The code I used is available on github.com.
A local art print store printed it out for me on some good quality paper. The border came out a lot more detailed than the digital version in reality and looked very well.
The construction of the Voronoi cells for a small number of points is straightforward by bisecting the correct lines between the points. For 4 points, there are only 2 possible triangulations, it's just a matter of knowing in advance which one of them is the Delaunay triangulation.
All that was left was to find a suitable frame, of which a local craft store carried a wide range. The black frame made the country outline and the cell walls stand out against the background. A sign of a thoughtful present is that you're looking forward to giving it and I think my mother really enjoyed the finished product as something to display in her home.
