Episode 5: The Art of Compromise in Cartography.

Projections that keep their distance.

In the family of projections, I'd like… aphylactic projections! That's the cute, poetic name given by the "Vazi-je-tente-un-truc" team, whom we discussed in this article. These projections attempt to compensate for both angle and area distortions, which are inevitable when moving from the terrestrial globe to a flat surface.

While maintaining a sense of proportion regarding the notion of celebrity, the stars in this team are equidistant projections, which preserve distances from a given point.

Equidistant Cylindrical Projection, from NASA's Earth Observatory “Blue Marble” series.

Just as no projection can preserve the value of all angles or all areas, these projections cannot preserve the value of all distances.

And yes, yet another projection system that only shows us the truth at a given point!

Below is the Plate Carrée Equidistant Cylindrical Projection, so named because the parallels and meridians form equal squares.

Visualization of cartographic distortions induced by the Plate Carrée Equidistant Cylindrical Projection with Tissot's indicatrix (after Sting - CC BY-SA).

In the case of the equidistant conic projection, meridians and parallels are equally spaced.

Visualization of cartographic distortions induced by the equidistant conic projection with Tissot's indicatrix (after Justin Kunimune - CC BY-SA).

Equidistant projections are used whenever knowing precise distances from a point or along lines is important. For example, in navigation, when knowing the actual distance will determine whether it's a day trip or a week-long journey, or for mapping a network like subway lines to determine if a station every 700 meters is sufficient or not.

And when they are not equidistant?

In school textbooks, the Robinson projection is often found. This is an aphylactic projection but not an equidistant one, because, although the meridians are regularly spaced, the parallels are not.

The latter are regularly spaced between the 38th parallel north and the 38th parallel south (which frame the equator) and then, the closer one gets to the poles, the smaller the gap between them becomes.

Robinson Projection, from NASA's Earth Observatory “Blue Marble” series.

Another world is possible.

The three families of projections we've seen in this series allow for classifying projections based on their distortions: angles, areas, or a bit of both.

But projections can also be classified based on their geometric properties. This is what we're referring to when we talk about a cylindrical Mercator projection or a conic Lambert projection. Here too, the representation possibilities are numerous!

But that’s another story…