MHB What Type of Math is Used in Fortune's Algorithm?

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Fortune's Algorithm is recognized as one of the fastest methods for generating Voronoi diagrams, which are essential in procedural generation. To understand this algorithm, familiarity with computational geometry is crucial. Key mathematical concepts include geometry, algorithms, and possibly some aspects of calculus. Exploring the sweep line algorithm can provide foundational knowledge that aids in grasping how Voronoi diagrams are constructed. Additionally, attempting to create a simple algorithm based on visual examples, such as those found in GIFs on Wikipedia, can enhance understanding and practical skills in this area.
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I've heard that Fortune's Algorithm is the fastest algorithm yet found to generate a voronoi diagram. I am far from being able to understand it, but I got interested in it because I want to learn about procedural generation. My question is, what sort of mathematics would I have to be familiar with to understand it?

In case you are unfamiliar with it, there is a pseudocode version here.
I can't copy/paste it because it has unusual characters that don't seem to translate on this forum.
 
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You could look into the sweep line algorithm first, and then go back to how the diagram is generated. This algorithms hail from the realm of "computational geometry". It might be useful to look at a text on this topic.

Another thing I would try to do is just try come up with an algorithm yourself from looking at the gif in the wiki page.
 

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