November 20, 2014

Get To Know a Map Projection: Azimuthal Orthographic


A globe on a two-dimensional screen seems pretty dull compared to map projections that look like armadillos, butterflies, or deconstructed polygons. The azimuthal orthographic (as it’s formally known) is hardly more than a snapshot of Earth from some distant point in space, right?

Sure, except it was invented thousands of years before we had anything capable of flying into space to send back eyewitness accounts of our planet’s shape. Before then, the only way to see Earth from an interstellar point of view was by combining math with crap-load of imagination.

Most map projections bend and stretch the globe until it’s flat enough to show the whole world at once. In other words, most map projections show you so much that they lose their perspective. 
  The azimuthal orthographic is all about perspective. It also has geometric distortions, but only for tricking your brain into believing that the continents really are wrapping themselves realistically around the horizon. It is so good at doing this that it makes us see the world as if we were hundreds of thousands of miles away in space, and write the experience off as mundane.

Or maybe the experience is mundane because it is so familiar. The azimuthal orthographic is thousands of years old. In the first century, Ptolemy described how a geographer named Hipparchus used the projection, which he called the analemma, to map the globe. (Thanks to the jerks who burned down the Library of Alexandria, we don’t have Hipparchus’ original maps.)

Over the years, geographers toyed with the projection, but it was always overshadowed by other methods. It didn’t get much attention until 1613, when a Belgian cartographer named Francois d’Aiguilon reintroduced the projection, and gave it the overwrought moniker we know it by today.

D’Aiguilon was obsessed with the behavior of light. In his six volume treatise on optics, he presented the azimuthal orthographic as an extreme exercise in point of view. Imagining the azimuthal orthographic as looking down at Earth from a floating eye, d’Aiguilon figured that moving the eye up or down would change the distance to the horizon. In other words, the further you pull back, the more of the earth behind the horizon’s curve you can see, to a maximum of exactly half of the planet (even d’Aiguilon couldn’t see around corners, mon ami). This was an extension of his work coming up with equations to measure how much a person could see from a given viewpoint.

Carlos Furuti, a Brazilian cartographer whose website is an awesome resource for projections, shows how azimuthal orthographic projections can be used to calculate how much of Earth you can see at any altitude. For example, looking down from an airplane at 32,000 feet, you would be able to see about 221 miles in any direction. If you head up to the International Space Station, your view is increased to 1,250 miles. Impressive, but this is still only about 5 percent of Earth’s total surface at a time. In order to get anywhere close to an entire hemisphere, our camera eye must retreat past the moon, over 230,000 miles away.
But remember, Hipparchus, Ptolemy, and d’Aiguilon didn’t need to know about airplanes, space stations, or even the distance to the moon in order to imagine how Earth’s visible horizon would grow according to altitude. This is because they had imagination (ok, trigonometry too). And their imaginations weren’t limited to flying into the depths of space. The azimuthal orthographic has two sister projections that look at the earth in ways nature never intended.

The first, called the gnomonic, has the imaginary viewing eye looking outward from the center of the earth. It has some cool navigational properties, but is perhaps most useful if you’re trying to explain what the world looks like after smoking salvia.

The second, called the azimuthal stereographic, also looks at the planet, but from an eye placed on the far side of the globe looking through it. Where the orthographic causes the continents to fall away, and the gnomonic stretches them into infinity, the stereographic moderately stretches them towards the edges. Their sizes are slightly off, but their shapes and arrangement stay true to life. As such, it’s the most practical of the three, and is useful for teaching geography or plotting sea voyages. Not only does it make a pretty classy looking world map, Hipparchus also used it to map the stars.

Nowadays, we tend to think of maps as tools for flattening the world and making its dimensions manageable. The azimuthal orthographic looked at the earth another way, by giving dimensions to the world’s perceived flatness. The map might not tell us much about Earth that we don’t already know, but it’s an important reminder that only a few hundred people in all of history have every seen the earth’s shape to confirm that it is, in fact, a globe.

Special thanks to Carlos Furuti for his great website of map projections.

By Nick Stockton

Picture above: Joan Blaeu’s 1664 shows how the azimuthal stereographic makes a fairly accurate world map, even when made with incomplete knowledge of geography. Joop Rotte/Wikipedia

With thanks to Wired

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