Can someone please explain it to me? Reading about it and my brain cannot compute
In: Mathematics
You are given a bunch of dots, often in the plane. Give each of them its own color, then color every other point according to which of the given points is closest. If there are several at the same distance, just use black.
This divides everything into cells around the respective dots. It has a kind of crystalline structure and is indeed something that can arise when crystals grow, as well as when cells multiply to fill skin or space.
A Voroni diagram is a graphical representation of a specific partition of the plane. Let’s walk through an example.
Take a piece of paper, that will be our finite plane. Then put N dots on it, perhaps randomly. The concept is to divide the paper into N pieces where every spot on the paper is closer to one dot than all the others. This partition can be drawn, with lines where the cuts would be, to produce a Voroni diagram.
The simplest example is just two dots, A and B. For every point, you just measure the distance to A and the distance to B and it goes into the partition with the dot that’s closest. If you start near A and go towards B, all the points will be A for a while, and then just past half way they will switch to B. If you explore around the transition you will find there is a line that contains all the points that are an equal distance from each point. This line will be the only line on your 2-dot Voroni diagram.
With more points, it gets more interesting. This makes shapes lke the shape of a giraffe’s spots.
Suppose you have a bunch of fire stations and need to decide which is responsible for which homes. You decide each station should be responsible for the homes that are closer to it than any other fire station, as that’s the fire station that can get there fastest.
So you draw a voronoi diagram. The voronoi diagram breaks up your map into sections. Each section has exactly one fire station in it and every spot in that section is closer to that fire station than it is to any other fire station. This is your map of which fire station is responsible for which homes.
That’s the ELI5 version of what a voronoi diagram does. Is that what you’re looking for or maybe how it’s computed? Or something else?
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