Drawing Voronoi Diagrams in Haskell

Click here to go straight to the nice pictures

This is an assignment in the Functional Programming class I took at Willamette University in the Fall of 2018. Our task was to use a basic bmp image creator that the Professor provided and extend it to create some of our own art in Haskell! Having recently taken a Discrete and Computational Geometry course (from the wonderful Josh Laison) and falling in love with Voronoi Diagrams I decided to try and create these in Haskell. Here are the results!

This functional programming class was taught by the wonderful (notice a trend here :) I don't think I ever had one non-wonderful Professor at Willamette) Fritz Ruehr. He provided us with the RenderBMP.hs file and the first half of the code located in Voronoi.hs. My code starts after the -- Voronoi Diagrams comment in the Voronoi.hs file.

How to draw some Voronoi Diagrams:

I generated these on my computer running Windows 10 and using the Glasgow Haskell Compiler.

1. Clone the repository onto your machine.
2. From the command prompt you can load the program using ghci Voronoi.hs.
3. Things are drawn by using try <diagram>. For example, I have defined a voronoi function and a Voronoi diagram can be drawn by using the command try (voronoi 10) (this draws a Voronoi diagram with 10 random points).
4. Look in your directory for the resulting testy.bmp image file (this name can be changed in the RenderBMP.hs file).

From here you can just look through the Voronoi.hs file and see the comments where I indicate how to use the function. I just tried to have some fun thinking about what I could create. There are certainly many more possibilities out there. I also left in some of Professor Ruehr's examples (Fritz's examples) and you can try those also: try mickey, try galaxy, etc.

Note that drawing the Voronoi diagrams is very slow. Right now it is just a brute force algorithm that for each pixel calculates how far that pixel is away from each circle to determine which one is closest. Do not worry though, I did NOT get through Professor Laison's class without learning about all of the efficient algorithms for drawing Voronoi diagrams that are out there :) but to use this image creator as Professor Ruehr created it I had to use the brute force algorithm.