I know it’s not obvious from the title, but I’m pretty sure this idea could be used to create topologically-correct rectangular cartograms for arbitrary geographies and values. https://arxiv.org/pdf/1505.05785.pdf …
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Replying to @robinhouston
The tiles in the rectangular cartogram correspond to edges of a resistor network, right? Is there an easy way to see how to go from an arbitrary "geography" to the resistor network?
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Replying to @blockspins
Hmm. Yeah. Maybe it’s harder than I naively thought. There’s a distinction between horizontal and vertical adjacency, and maybe you can only guarantee to preserve one or the other, not both.
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Replying to @robinhouston @blockspins
Actually I don’t think that’s a problem, because the horizontal and vertical adjacencies are related by planar duality. You would have to decide, for each border, whether you wanted it to be horizontal or vertical on the cartogram.
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Thanks, that makes sense. A full set of horizontal / vertical choices is an interesting set of extra data associated to the graph. I wonder how these are related to their compatible orientations.
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