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.
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.
I’ve tried to demonstrate it here. You end up with straight lines because it’s always a middle point so it doesn’t curve one way or another between the two points.
If the circles had a set radius then you’d have empty space and more circley-looking spots. But since they basically expand until there’s a middle point you’ll have these straight lines.
For those who don’t know already, this is called a Voronoi diagram.
I think I’m too stupid to understand this. How are they straight lines and not at a diameter / in a circle from any given point? It seems… wrong.
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.
What does the separating line between two circles look like?
More… circles?
I’ve tried to demonstrate it here. You end up with straight lines because it’s always a middle point so it doesn’t curve one way or another between the two points.
If the circles had a set radius then you’d have empty space and more circley-looking spots. But since they basically expand until there’s a middle point you’ll have these straight lines.
I was joking. But +1 for the effort and this looks like art, btw.
Oh dang didn’t realize you weren’t the same person. Thanks for the compliment, I had fun drawing it
Draw it, then consider where the exact middle point would be. Now do the whole line between them. I think that’s the best way to figure it out.