question about Mercator and loxodromes

[vorropohaiah]

Hey all,

I was wondering about the mercator projection, and how (to simplify things) it was used to straighten loxodromes, preserving angles, to aid navigational purposes. since im a dolt at these technical aspects of cartography, and as i cant be bothered to try it out myself, I was wondering if the mercator projection would work as intended with worlds of different sizes (bigger) than earth?

thanks

[Jaxilon]

Check out Hai-Etlik, he seems to be a guru about such stuff. I know he's posted some details about projections in another thread some months back. I'm not sure exactly when but if you look him up you might be able to look up posts he's made. That or you can just try a search for Mercator.

[waldronate]

Projections deal with transforming one surface to another. In the case of common map projections, it's projecting the surface of a globe (sphere or ellipsoid, depending on your accuracy needs) onto a flat plane. The size is irrelevant, that's just the scaling factor; what's important is the shapes involved. We can easily draw a Mercator projection of the Moon, Earth, Jupiter, the Sun, or the entire apparent globe of the heavens with equal ease.

[vorropohaiah]

question answered, thanks

[Hai-Etlik]

Yes, it works for any approximately spherical surface regardless of size. The way it works can be thought of this way:

In a normal cylindrical projection (Which Mercator is), the length of one matching pair of parallels (or the equator by itself) sets the width of the map, and all the other parallels are stretched or squashed to the same length. The poles, both of which are just single points, also get "stretched" into lines this length. If you leave the north-south distance alone, you get a projection called "Equidistant Cylindrical" or "Equirectangular". If you want to preserve angles though, you need to compensate for the east-west stretching which you can do by also stretching north-south by the same amount. This has been compared to inflating a balloon inside a cardboard tube coated with glue. This is the Mercator projection. It turns out which pair of parallels you choose to start from aren't important in Mercator as it does nothing but scale the map up and down without altering the shape. (This is not the case for other cylindrical projections.) Since no finite amount of scaling will stretch a point to a line, the poles get pushed to infinity which is why Mercator maps never include the poles.

[Midgardsormr]

Thank you; that was the best explanation of a cylindrical projection I've ever heard.

[vorropohaiah]

thanks Hai-etlik. was hoping you'd see the thread