3 ms·

Regardless of what the eye sees, the brain perceives three dimensions. This projection happens to be the one that the brain can automatically unpack into an acc

Regardless of what the eye sees, the brain perceives three dimensions. This projection happens to be the one that the brain can automatically unpack into an accurate 3D representation. Technically, things near the edges are squished and distorted, but that gets undone in the wetware.

jacobolus 8y ago
You really can’t get an accurate sense of angles/shapes, areas, distances, or directions with an orthographic projection except by moving the view around. Even when you do, it is very difficult to accurately compare attributes of regions which are far away on the globe, and easy to mislead yourself. (This is a problem with physical globes as well.) For many types of mapping use cases, orthographic projections are substantially worse than other possible choices. Sometimes physical spheres (or virtual representations of spheres as dynamic orthographic or perspective projections) are nice. That’s why I spent a whole bunch of time building myself a spherical chalkboard, for example. But they aren’t the best choice for any purpose. Personally I don’t think they make a very good choice for a general-purpose world map. They are better as a supplement to flat maps.
jacobolus 8y ago
Let me give you a concrete example. Here is what North America looks like on this new map: https://i.imgur.com/lCI8DjY.jpg https://i.imgur.com/lCI8DjY.jpg This is not a good projection to use if you want to see all of North America. There is dramatically more distortion than necessary, and shapes near the edges get very squished (the west coast of the US is okay), but it is not at all obvious to a naïve viewer what kind of distortions are involved, and past experience looking at soccer balls or whatever isn’t going to fix it. (Note: a Mercator projection is also not a good choice for this. On a Mercator projection sizes are dramatically bloated as you go north.)
- mikeash 8y ago
  I'm not convinced it isn't still the best option. The naive viewer may not properly perceive the distortions, but I bet they'll get closer than with anything else, for general purposes. What projection would you say would be good for that view?
  - jacobolus 8y ago
    For North America per se you could e.g. pick the conformal projection with roughly constant scale around the boundary of the continent (one world atlas does this), or you could pick a projection which minimized distance errors (there are several possible ways of quantifying those, which will yield different maps), or you could pick among several equal-area projections (especially useful if you want to make a choropleth map), or for something dynamic you could use an azimuthal equidistant projection or some conic projection (e.g. Lambert conformal conic, Albers equal-area conic), or .... https://pubs.er.usgs.gov/publication/pp1395 https://pubs.er.usgs.gov/publication/pp1395 There are many choices. An orthographic projection is generally one of the worst except insofar as it gives the impression of a physical sphere when you zoom all the way out.

jacobolus 8y ago

You really can’t get an accurate sense of angles/shapes, areas, distances, or directions with an orthographic projection except by moving the view around. Even when you do, it is very difficult to accurately compare attributes of regions which are far away on the globe, and easy to mislead yourself. (This is a problem with physical globes as well.) For many types of mapping use cases, orthographic projections are substantially worse than other possible choices. Sometimes physical spheres (or virtual representations of spheres as dynamic orthographic or perspective projections) are nice. That’s why I spent a whole bunch of time building myself a spherical chalkboard, for example. But they aren’t the best choice for any purpose. Personally I don’t think they make a very good choice for a general-purpose world map. They are better as a supplement to flat maps.

jacobolus 8y ago

Let me give you a concrete example. Here is what North America looks like on this new map: https://i.imgur.com/lCI8DjY.jpg https://i.imgur.com/lCI8DjY.jpg This is not a good projection to use if you want to see all of North America. There is dramatically more distortion than necessary, and shapes near the edges get very squished (the west coast of the US is okay), but it is not at all obvious to a naïve viewer what kind of distortions are involved, and past experience looking at soccer balls or whatever isn’t going to fix it. (Note: a Mercator projection is also not a good choice for this. On a Mercator projection sizes are dramatically bloated as you go north.)

mikeash 8y ago
I'm not convinced it isn't still the best option. The naive viewer may not properly perceive the distortions, but I bet they'll get closer than with anything else, for general purposes. What projection would you say would be good for that view?
- jacobolus 8y ago
  For North America per se you could e.g. pick the conformal projection with roughly constant scale around the boundary of the continent (one world atlas does this), or you could pick a projection which minimized distance errors (there are several possible ways of quantifying those, which will yield different maps), or you could pick among several equal-area projections (especially useful if you want to make a choropleth map), or for something dynamic you could use an azimuthal equidistant projection or some conic projection (e.g. Lambert conformal conic, Albers equal-area conic), or .... https://pubs.er.usgs.gov/publication/pp1395 https://pubs.er.usgs.gov/publication/pp1395 There are many choices. An orthographic projection is generally one of the worst except insofar as it gives the impression of a physical sphere when you zoom all the way out.