Cave Painter

While searching for a method to draw geodata right into the terminal, Mike Schilli discovers the wondrous world of map projections.

- Mike Schilli

While I was working on hike-find, a command‑line pro‑ gram that chooses a trail from a collection of GPX files with track points, for a recent issue [1], I got the idea of drawing the trail contours the program found in a terminal window. Unfortunately, a GPX file generated by an app such as Komoot or a Garmin tracker only contains geocoordinates as floating‑point numbers. They refer to the points of the globe through which the trail passes.

These geopoints on a spherical sur‑ face now need to be converted to a two‑dimensional coordinate system so that they look as natural as possible on a flat map. This problem was solved centuries ago. Any map, whether paper or digital, is based on the genius idea of projecting geopoints on the globe, which are available as latitude and longitude values, onto an XY coordinate system on a plane.

Back to the Year 1569 

As early as 1569, Gerhard Merca‑ tor, a cartographer from Flanders, set out to flatten the spherical data determined by early sea navigators. To do this, he simply projected the spherical surface of the Earth onto a cylinder wound around it (Figure 2). The outer layer of the cylinder, in turn, can be easily unrolled and viewed as a flat map. However, this projection (with a vertical winding cylinder) is only 100 percent correct at the equator and suffers from distortions to the north or south of it, until – finally – grotesquely inflated land masses appear in the polar regions.