SH3 Globe: Mercator or Gall Peters projection

[Captain Nemo]

I was reading another topic about the SH3 globe where it was stated that it is based on the Mercator Projection. However, from looking at the SH3 globe I would have to disagree with this statement. Looking at the shape of Iceland in SH3 I would say it is more likely based on the Gall-Peters projection. I believe the Gall-Peters projection tries to keep the size of land masses in perspective whereas the Mercator projection distorts land masses quite considerably e.g. Greenland bigger than Australia. In the Gall-Peters projection most distortion takes place above 45 degrees north and 45 degrees south. Probably doesn't make much difference to SH3 players but thought I would share anyway.

Mercator Projection


Gall-Peters Projection


Nemo

[Hitman]

Good observation. I have been myself wondering for a long time if there would be a way to modify SH3 map to make it be in-game a mercator projection. I really hate seeing the grids and the land masses become distorted near the poles, it is quite the contrary of what you see in real charts.

[Pisces]

I am positively sure it is neither of them. It's just a linear relationship between longitude and latitudes degrees on the real world vs. distances in kilometers against the SH(3) equator and GM-line. 1 degree equals 120 km. Measure it, you'll see.

This Gall-Peters projection (wiki) uses the sin-function for the vertical coordinate. The Mercator projection (wiki) uses a combination of natural logarithm and the tan or sin function. Both would make the relationship between RL latitude degrees and SH3 vertical kilometers non-linear. Those do not match up with the linear measurements I made. Besides, likely game-developers avoid these kind of functions if they can. As they are far to computationally intensive. An extra divide or multiply they don't have problems with these days.

Just looking at the shape of land features can be deceiving. I think screen resolution and aspect-ratio (wide-screen) issues might come into play. And to me neither look fitting the Sh3 map.

My proof:

In the game the north tip of the small island north of Iceland (Grimsey) is 7988.8 kilometers from the equator. It is in Google Earth at latitude 66d33m58.55s. Dividing 7988.8 (km) by 120 (km)=66.573333 in decimal notation. In dms-notation this is 66d34m24s The difference is about 850 meters in Google Earth. And 0.01% in relative terms.

Distances near the equator are just as linear, which I leave for you to test.

[Pisces]

p.s. If you still don't believe, try the coordinate display in the mission editor.

[Captain Nemo]

Pisces thanks for your input which I found most interesting. If I understand you correctly, are you saying that the difference between Google Earth and the SH3 map is only 0.01%?

Forgive me if I have completely misunderstood what you were saying.

Nemo

[Luno]

This Gall-Peters projection (wiki) uses the sin-function for the vertical coordinate. The Mercator projection (wiki) uses a combination of natural logarithm and the tan or sin function. Both would make the relationship between RL latitude degrees and SH3 vertical kilometers non-linear. Those do not match up with the linear measurements I made. Besides, likely game-developers avoid these kind of functions if they can. As they are far to computationally intensive. An extra divide or multiply they don't have problems with these days.

Isn't the SH3 world flat anyway? I don't understand why it should be computationally difficult to pinpoint the sub on a flat surface no matter what projection it was based from.

If I understand you correctly, are you saying that the difference between Google Earth and the SH3 map is only 0.01%?

Only in the vertical. However, it is stretched horizontally at higher latitudes.

At least superficially, it looks like an "Equirectangular" projection so that lines of latitude and longitude are equally spaced.

(not my images)

[Pisces]

Originally Posted by Luno

Isn't the SH3 world flat anyway? I don't understand why it should be computationally difficult to pinpoint the sub on a flat surface no matter what projection it was based from.

Yes, that wasn't a very well thought through argument. I was just trying to emphasize that the developers liked to keep it simple. Never mind beyond that.

Originally Posted by Captain Nemo

Pisces thanks for your input which I found most interesting. If I understand you correctly, are you saying that the difference between Google Earth and the SH3 map is only 0.01%?

Forgive me if I have completely misunderstood what you were saying.

Nemo

I can't vouch that percentage for all other places on the map. But in that particular part the Google Earth latitude is 66.56626389 degrees, while the ruler in the game measured it to 66.573333 'degrees'. The difference being 0.00707 degrees, which comes down to 0.01% of 66.56626yadayada. The SH3 map is a bit blocky, so it won't be exactly like the Google Earth satellite and aerial-photography images. The position error would probably be larger nearer the equator, but that is because latitudes are smaller numbers, while the blocks are of fixed size. But I wouldn't worry about it.

When sailing near land you shouldn't be browsing Google Earth anyway.

Originally Posted by Luno

Only in the vertical. However, it is stretched horizontally at higher latitudes.

No, the same holds for horizontal distances in the SH3 map to the Greenwich Meridian. Don't confuse what I wrote with actual kilometers or nautical miles in the real world. Real World degrees are 120 SH3-kilometers tall and wide!!! So on average it would hold horizontally also.

At least superficially, it looks like an "Equirectangular" projection so that lines of latitude and longitude are equally spaced.

"Equirectangular" (wiki)sounds about right.

[Luno]

No, the same holds for horizontal distances in the SH3 map to the Greenwich Meridian. Don't confuse what I wrote with actual kilometers or nautical miles in the real world. Real World degrees are 120 SH3-kilometers tall and wide!!! So on average it would hold horizontally also.

I guess the way you worded it is confusing. Let me attempt to clarify what I mean: In the real world, one degree longitude is ~120 km at the equator. At 30 degrees latitude, one degree of longitude is ~96 km, and at 60 degrees it's only ~55 km.

In SH, the degrees of longitude are always the same at 120 km. So a feature which is 55km long becomes stretched to 120 km long at 60 degrees latitude on the game map.

It would be nice if the SHIII world was actually round (like in the Microsoft flight sims). It would be a little more complicated to transfer a dot on the globe onto the flat map, but it would be well worth it: real distances and continent shapes/sizes and the possibility for real navigating using the sun and stars (with sun, moon, and planetary positions accurate for 1939-1945).

[Pisces]

Originally Posted by Luno

I guess the way you worded it is confusing. Let me attempt to clarify what I mean: In the real world, one degree longitude is ~120 km at the equator. At 30 degrees latitude, one degree of longitude is ~96 km, and at 60 degrees it's only ~55 km.

In SH, the degrees of longitude are always the same at 120 km. So a feature which is 55km long becomes stretched to 120 km long at 60 degrees latitude on the game map.

It would be nice if the SHIII world was actually round (like in the Microsoft flight sims). It would be a little more complicated to transfer a dot on the globe onto the flat map, but it would be well worth it: real distances and continent shapes/sizes and the possibility for real navigating using the sun and stars (with sun, moon, and planetary positions accurate for 1939-1945).

Well, I did my best attempt to speak only of 'Real World' degrees, and 'SH3 or game' kilometers. I never mentioned 'Real World'-kilometers in this thread.

But I guess I'm not the most eloquent these days.

[Luno]

Nah, maybe I'm just too tired. It's been a long week (and it only just started )

[Captain Nemo]

Thanks for all the replies.

Luno appears to have identified the type of map projection used by SH3 which is equirectangular. This is reinforced by what Wiki has to say "In particular, the plate carrée has become a de-facto standard for computer applications that process global maps, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth".

Nemo