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jacobolus

Here’s my suggested alternative, also conformal, http://i.imgur.com/Y6ki0l9.jpg

Inspired by http://www.genekeyes.com/Cahill-desk-maps/Cahill-1918-rotate...

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Transverse Peirce Quincuncial also makes a nice global conformal projection:

http://frammish.org/tpq.jpg

Conformally squishing a hemisphere into a square (or if you like, squishing a 90°–90°–90° triangle on the sphere into a 45°–45°–90° triangle on the plane) causes very extreme distortion near the corners. Can be fun from an aesthetic perspective, but it’s not the most practical for most uses as a working map.

That seems nice for paper.

I'd like to see actual spheres used for computers. We don't have to stick with fixed 2D projections for electronics. Render the Earth as a sphere centered on the center of the viewport. When zoomed in, it'll look flat (just as the Earth itself looks flat up close) but without the size distortions you get when you scroll e.g. Google Maps far north and south. Zoomed out, you'll see how everything actually relates in 3D space.

By “actual spheres” what you presumably mean is an orthographic projection (or maybe some kind of perspective projection). But such projections are almost never the best choice for any purpose, unless you’re trying to make a game about flying a little rocket around the solar system or something. As maps, they both hide significant parts of the globe and dramatically distort the rest. The point of a map is usually not to just be a stand-in for a hand-held globe, but to help a viewer understand and answer questions about geography. The zoomed out views of Google Earth etc. are mostly gimmicks.

I know these projections would have big problems if they were static, but it seems to me that the whole game changes when it's dynamic. The fact that half the globe is hidden from view is much less important when a flick of a finger can bring it into view.

I admit I don't quite get that bit about not just being a stand-in for a globe. I thought the main reasons maps aren't globes is just because maps are much easier to store, and because maps can be zoomed in to an arbitrary degree. Computer displays eliminate both of those reasons.

Globes are nice for teaching people the relation between a map and a spherical planet. They’re not necessarily the best at quickly answering geography questions, because you need to spin them around to make comparisons, and only the middle part of the globe (from any particular perspective) has low distortion. For e.g. data displays, they’re often quite misleading.

It’s difficult to follow rhumb lines on a globe, and it can also be difficult to follow great circle arcs (depending on how the globe is allowed to spin). Making arbitrary 3-dimensional rotations works pretty well for an unattached ball, but is very annoying to do using existing mouse + multitouch UIs. Comparing shapes, distances, and coordinates of places far apart on the globe is a pain. Globes (and computer displays) are difficult to blow up to very large size, and hard to annotate.

I think spheres are great (to the point that I made myself a spherical chalkboard), but having a sphere (or an interactive orthographic projection) doesn’t replace most uses of other maps.

> made a spherical chalkboard

Interesting. How? Chalkboard paint on a globe? Does it ride in/on a globe carriage?

Chalkboard paint on a stainless steel “gazing ball”; construction of the stand still pending. Picture: http://i.imgur.com/pLiHA61.jpg

Would this work for a digital map, or just paper? Is there a way to handle the problem of North not always pointing up?

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