Question: Cartogram scale and area_error meaning

[ktrinko]

The scale value is calculated for non-contiguous cartograms (Olson) and the area_error is calculated for contiguous cartograms (Dougenik et al. and Gastner et al.) But what do these values exactly mean?

[mthh]

The scale value of Olson/non-contiguous cartograms is by how much we apply the scale transformation to each feature (a scale of 2 would make the object 200% larger). Regarding how it is computed, I believe we follow the description of Olson's paper. I've broken down the calculation in this comment, if you're interested: #208 (comment).

The area_error of cartograms by Gatsner et al. seems to me that it refers to the error between the calculated area and the target area (to determine how closely the calculated size of an entity matches what it should be if it had been resized perfectly; we display it in Magrit because it informs us about how "good" the resizing is). This value is also used as a "stop condition" internally to control when the algorithm should stop. I admit I don’t know the internal details of all this, and it seems to me that the reference paper discusses it: https://www.pnas.org/doi/full/10.1073/pnas.1712674115.

The area_error of cartograms by Dougenik et al. (I’m a bit more familiar with how the algorithm works) corresponds to the ratio between the desired target area for a polygon (proportional to the statistical value) and its current area. It is also used as an indicator of the algorithm’s convergence (and we also display it in Magrit because it informs us about how "good" the resizing is), but not as a stopping condition in our implementation, since the user manually selects the number of iterations. The final value that you get in the area_error field is computed here: https://github.com/riatelab/magrit/blob/master/src/helpers/cartograms.ts#L342.

Hope this helps !

BTW, I plan to go through the various issues tagged as "question" soon, in order to compile some useful information for the documentation so that it can benefit as many people as possible!

[ktrinko]

Thank you for your Kind Support!