this post was submitted on 13 Mar 2025
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Does this animation help?
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Voronoi_growth_euclidean.gif/440px-Voronoi_growth_euclidean.gif
Oh! It totally does. I guess I've just never had to apply distances in such a way that they'd butt up against one another to become what looks like basic geometry.
Thanks!
I assume part of the confusuion is that the earth is not flat. If one would create a Voronoi diagram on the surface of a globe, the resulting borders would still be straight lines, but, when projected, it depends on the projection, whether they remain straight.
The creator probably started with a Mercator projected map of Europe and then calculated the distance between any point on the map and all capitals. The distance on two points on the spere, however, cannot be obtained by counting the distance in h/v pixels on the map and applying Pythagoras, as Mercator projection exaggerates horizontal, east-west, distances. So one needs to map the pixel coordinates back onto the sphere and calculate the distances there.
It's definitely a nice map though.