Are the proportional circles calculated using area or radius?

[almccon]

On twitter someone asks if we're calculating our circle sizes correctly: https://twitter.com/mxfh/status/676939990169952256

Compare Mexico and Central America in 2000: http://dsl.richmond.edu/panorama/foreignborn/#decade=2000

Mexico is 9,177,487, and Central America is 2.026,150.

If they were scaled linearly by radius, Mexico's circle would be 4.52 times wider.

However, on the map the circle is only 3 times wider (~300px vs ~100px).

So I think we're doing it right. The radius is calculated on this line: https://github.com/americanpanorama/panorama-foreignborn/blob/master/app/components/DisjointedWorldLayout.jsx#L501, but it's using a function defined here https://github.com/americanpanorama/panorama-foreignborn/blob/master/app/stores/scales.js#L19-L21 which shows that we're using a sqrt function. So I think we're good.

[mxfh]

https://github.com/americanpanorama/panorama-foreignborn/blob/04f413aa8b59e2ce31cd69eb3d0296a796898ebe/app/stores/scales.js#L19 looks indeed alright, but the legend does something else:

[mxfh]

d3.scales.sqrt() does not behave well with ranges and domains length >2

var radius = d3.scale.sqrt()
  .domain([500000, 1000000, 1500000, 2000000])
  .range([12, 24, 36, 48]);

should be more like

var radius = d3.scale.sqrt()
  .domain([0, 2000000])
  .range([0, 48]);

and labels/breaks added via ticks, see http://bl.ocks.org/mxfh/6285470954cf4d207fd0

[mxfh]

This scale behaves not continuously as a square root function, the input domain between 500k and 2m is mapped linearly to the output range:

var testScale = d3.scale.sqrt().range([]).domain([500000, 1000000, 1500000, 2000000]).range([12, 24, 36, 48]);

testScale(0) // -16.970562748477143
testScale(172000) // 0.02111068445544717
testScale(500000) // 12 start of linear part
testScale(1000000) // 24
testScale(1500000) // 36
testScale(2000000) // 48 end of linear part
testScale(2500000) // 58.57221223283089
testScale(5000000) // 100.05215136300797
testScale(9000000) // 148.4357878494041

[sconnelley]

When specifying >2 values in the domain, the scale becomes a polypower scale as in "multiple piecewise power scales that divide a continuous domain and range". More documentation over here. Irregardless, I think I agree that the domain and range would be better set to a length of 2.

[rnelson2]

changed to the following so it's both accurate and has the breakpoints to render four circles in the legend.

var radius = d3.scale.sqrt() .domain([500000, 1000000, 1500000, 2000000]) .range([12, 26.91, 38.35, 48]);

[mxfh]

Polypowered wizardy.

[mxfh]

How are these breaks calculated? I get different values when applying the unit area ratios to a factor of 48.

https://docs.google.com/spreadsheets/d/1rSxd3rfVgnQVxnDNdbTW2GBqNMbIc5OIBL9PbGpTrbk/edit#gid=0

resulting in

d3.scale.sqrt()
  .domain([0, 500000, 1000000, 1500000, 2000000])
  .range([0, 24, 33.9 , 41.6, 48]); 

comparing the scales: http://codepen.io/mxfh/full/pggXoW/

grey: old implementation red: current, blue: proposed new version, overlayed with simple non polypower version (orange)

for reference with sqrt x-axis (makes sqrt-curve a straight line starting from origin, if it is one):

[almccon]

Here's @rnelson2's change, now pushed to the public repo: efec7e986b314922e414a4afff4d67f7e74dc2a7

[almccon]

Sorry @mxfh, I won't have time to think more deeply about those charts until January.

[emilyhobson]

To @almccon for consideration