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2018

I wanted to fully understand how map projections work, so I created my own:

Humbly called The Bogner-Projection™

Humbly called The Bogner-Projection™

Map projections are essentially math formulas that convert polar coordinates (longitude & latitude) into “normal” cartesian coordinates (x & y).

Below you can find the code for my projection as well as Mercator↗, which is the one most maps use.

```
function mercatorProjection(lon, lat) {
const x = lon
const y = Math.log(Math.tan(Math.PI / 4 + lat / 2))
return [x, y]
}
function bognerProjection(lon, lat) {
lon = lon * 180 / Math.PI
lat = lat * 180 / Math.PI
const amplitude = Math.abs(lat/180) - 1
const maxX = 0.5 + 0.6 * Math.abs(Math.sqrt(1 - amplitude*amplitude))
const normalizedLon = ((lon / 180) + 1) / 2
const y = lat / 90
const x = -1 + normalizedLon * maxX
return [x, y]
}
```

Map projections shape our view of the world↗, but few people think or even know about them. I am surprised they didn't appear in George Orwell's 1984.

There is a saying that “All maps lie” because it's mathematically impossible to convert a sphere into a 2d picture without distorting parts of it.

The egocentric joke aside this was a great exercise to understand map projections on their lowest level.

I could also harness the power of d3.js↗ thanks to Mike Bostock's work↗.