I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...
To make it less distorted, you will have to make more cuts, seriously increasing the risk that the map does not accurately show the distance between points P and Q because the shortest path between them on the globe goes through a cut on your map.
I've thought about trying to build an app that does what that animation on the Wikipedia page does [0], but I'm not sure where I'd find spherical (or near enough) textures of the world map to experiment with.
Comments
I was hoping to see someone post that. :-)
I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...
To make it less distorted, you will have to make more cuts, seriously increasing the risk that the map does not accurately show the distance between points P and Q because the shortest path between them on the globe goes through a cut on your map.
In the limit, you could get something like http://en.wikipedia.org/wiki/Goode_homolosine_projection, but with infinitely many lobes. And that is a _could_: you can add branches like in Dymaxion wherever you feel like it.
Thank you! :-)
I've thought about trying to build an app that does what that animation on the Wikipedia page does [0], but I'm not sure where I'd find spherical (or near enough) textures of the world map to experiment with.
[0] http://en.wikipedia.org/wiki/File:Dymaxion_2003_animation_sm...
You could "unproject" another projection for which you have texture back to your sphere and then do the isocahedron projection.
Also, maybe you can find a database of the countries border as lat/lng polygons and just draw the countries.
Natural Earth has lots of that kind of databases: http://www.naturalearthdata.com/downloads/