Posted by **Joseph Fatula**
on 21:47 4/1/02

In reply to: (none)

I like the Historical Atlas on your site very much.

On the page comparing Europe and Erelae, you refer to both being in the same projection. Is your map of Almea made based on any map projection, or are you just making it flat and not worrying about it? If it is by some projection from a curved surface, I'd really like to know what you're doing to make this happen.

Thanks for any info!

Joe Fatula

It's a cheap, by-eye adaptation of a sinusoidal projection.

An example of a proper sinusoidal projection is my map of Almea. The secret of this projection is that the n-degree latitudes are simply cos n times the length of the equator. That's true of the actual latitudes on the globe as well, which makes this projection one of the least distorting. The individual segments properly narrow as you get to the poles, and don't expand or flatten the polar regions as on a rectangular map.

The disadvantage is that if you simply draw each latitude as one straight line, the whole map looks like a big squat diamond, and the areas round the sides still get distorted. The solution is to divide the map into sections, as I did with the planetary map. Each section is relatively undistorted.

The Ereláe map follows the same proportions, but not really mathematically. Basically, I drew each 15-degree latitude line as a sweeping arc, about equidistant, but getting narrower as you head toward the poles. I drew a straight line down the center of the map, which represents the 7.5-degree longitude. Now, on each latitude, I marked off 15-degree segments, using the cos n rule.

E.g., the 15-degree latitude lines are about 5 cm apart. That means that the 15-degree longitude lines should be 5 cm apart at the equator, (5 * cos 15 ) cm apart at 15 degrees, (5 * cos 30) cm apart at 30 degrees, and so on.

Then I just connected the longitude lines, using curved lines.

There are other ways to go, but this one has the advantage that it's pretty accurate and pretty easy. If you map a very large area, it does result in distortions of north/south; but I'd rather have the less-distorted areas.

*These days there's probably software that will give you any projection
you like... I don't know of any such, though.
*