How do I find the scale of maps?

[The King of Nipples]

So I'm working on a map and I messed up the scale and need some help. How would I find how big 1 pixel is on a 4000x4000 pixel map that is the exact size of Earth?

[waldronate]

It depends on the projection of your image. For some projections and in some locations on the image, the size would be 40000km/4000pixel = 10km/pixel.

[The King of Nipples]

It depends on the projection of your image. For some projections and in some locations on the image, the size would be 40000km/4000pixel = 10km/pixel.

So if I just go with 10km per pixel for the whole map will this be good enough? I'm okay if it comes out a little bigger than Earth.

[waldronate]

The problem is that a map projection (a mathematical construct that converts points on the sphere to points on the plane) always distorts some quantity such as area or shape. Consider flattening out an orange peel: if you take the peel and press it flat on a table, it will distort and break as you flatten it. The same thing happens with maps, but the map usually doesn't break, it only distorts. For the common Equirectangular projection, the distortion is proportional to 1/cos(latitude), which gives infinite distortion at the pole because a single point is stretched out into a line segment (it is also about twice the area as that of the surface of the corresponding sphere). Different projections have different tradeoffs of distortion.

Many people just don't worry about map projection because it's not terribly important to the use for which they will put the map or because they are mapping a relatively small area where the projection distortions aren't too severe.

Is assuming 10km per pixel for all pixels of an earth-sized world on a 4000x4000 map? The answer is that it depends entirely on what you're doing with the map.

[Gidde]

To add to what Waldronate just said (which is all true) I have played with this exact problem a ton.

If you really want scale to be correct, go with either a Mollweide (preserves area, so each pixel is a square 10km on a side) or if you're ok with some fudging and want it to look nice, Winkel Triple looks fantastic without distorting too much anywhere, but is never going to be exactly accurate anywhere either.

Mercator, which preserves shape (so you'll see it alot around here since it's pretty), will distort your scale all to hades.

My personal favorite for keeping area constant without the map looking like crap is an interrupted Mollweide (basically lets you break the peel in slices instead of smushing it). GProjector lets you interrupt it wherever you want to which is really handy.

[The King of Nipples]

The problem is that a map projection (a mathematical construct that converts points on the sphere to points on the plane) always distorts some quantity such as area or shape. Consider flattening out an orange peel: if you take the peel and press it flat on a table, it will distort and break as you flatten it. The same thing happens with maps, but the map usually doesn't break, it only distorts. For the common Equirectangular projection, the distortion is proportional to 1/cos(latitude), which gives infinite distortion at the pole because a single point is stretched out into a line segment (it is also about twice the area as that of the surface of the corresponding sphere). Different projections have different tradeoffs of distortion.

Many people just don't worry about map projection because it's not terribly important to the use for which they will put the map or because they are mapping a relatively small area where the projection distortions aren't too severe.

Is assuming 10km per pixel for all pixels of an earth-sized world on a 4000x4000 map? The answer is that it depends entirely on what you're doing with the map.

Well, I want an atlas of my world, but I also want to accurately display distances. I wanted this because I want to see how far apart things are easily I was using equirectangular, I think, because of the ease of use and didn't think the distortion would be a problem for measuring distance just make it look weird. I was also told equirectangular looks the best on a globe which would be cool to have.

[The King of Nipples]

To add to what Waldronate just said (which is all true) I have played with this exact problem a ton.

If you really want scale to be correct, go with either a Mollweide (preserves area, so each pixel is a square 10km on a side) or if you're ok with some fudging and want it to look nice, Winkel Triple looks fantastic without distorting too much anywhere, but is never going to be exactly accurate anywhere either.

Mercator, which preserves shape (so you'll see it alot around here since it's pretty), will distort your scale all to hades.

My personal favorite for keeping area constant without the map looking like crap is an interrupted Mollweide (basically lets you break the peel in slices instead of smushing it). GProjector lets you interrupt it wherever you want to which is really handy.

What is the difference between Mercator and Equiangular? Also is there a kind of projection that is rounder/rectangular that will keep the scale similar to interrupted Mollweide, if so do you know of a program that would help me make my map like that?

[Gidde]

GProjector will take a map in equirectangular and project it into whichever projection you choose. I usually do a world's land/ocean in (seas) black and (land) white in equirectangular and then project that in several different ways from the get-go in order to do different things.

If you do the *whole* map in equirectangular, it's very hard to draw on it (because you have to simulate the crazy stretching).

The best way to see the differences is to take a pic in equirectangular (for instance, the Blue Marble pics), run it through GProjector and see what all the different projections look like.

[The King of Nipples]

GProjector will take a map in equirectangular and project it into whichever projection you choose. I usually do a world's land/ocean in (seas) black and (land) white in equirectangular and then project that in several different ways from the get-go in order to do different things.

If you do the *whole* map in equirectangular, it's very hard to draw on it (because you have to simulate the crazy stretching).

The best way to see the differences is to take a pic in equirectangular (for instance, the Blue Marble pics), run it through GProjector and see what all the different projections look like.

Oh I see what you mean with Mollweide it does not look bad is there any reason to go with interrupted Mollweide vs uninterrupted Mollweide? I like the way uninterrupted Mollweide looks more. If there is a reason to use what interruption would you recommend? I'm fine if it is mostly accurate with distance it doesn't need to be 100% but I'd like that.

[waldronate]

http://www.geo.hunter.cuny.edu/~joch...projection.htm might offer some assistance.