How do I make a projection with easy connectivity?

[waldronate]

Dave Allen wrote the original tec and clim programs back around 1990. http://markjstock.org/pages/builder.html has copies of this software. He had an upgraded, gui version a while after that called World Builder, but it seems to have disappeared.

After looking at the World Builder projection code in Wilbur, it turns out that I had misremembered the projection. His projection was an octagonal implementation on a square with north pole at center top and south pole at center bottom. The connectivity wasn't that simple, either.

The projection I described was from a compromise that I came to later. It is similar to the symmetric Collignon projection, but squashed and racked to get the poles in the corners of a square. http://www.progonos.com/furuti/MapPr...C/cartTOC.html has a good description of map projections; the Collignon is discussed under pseudocylindrical projections.

Most games don't use a spherical projection because the math isn't partcularly cheap to evaluate and it's rarely relevant to the story. Many games opt for a toroidal world (go off the top and end up on the bottom, go off the left and end up on the right, etc.) or cylindrical (go off the right or left edge and get to the other edge; top and bottom don't allow exit or come back in on the same edge halfway across the grid) because they are easy to evaluate. Users want north/south to be up/down in my experience rather than at at 45 degree angle.