Dots in maps

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lmviterbo
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Dots in maps

Post by lmviterbo » Sun Jan 30, 2005 4:11 am

avij on [url=http://forum.eurobilltracker.eu/viewtopic.php?p=32289#32289]Fri 17 Oct, 2003 14:10[/url] wrote:The map is a grid of 150x150 cells, where each cell is 0,44 degrees longitude wide and 0,28 degrees latitude tall. There are no "kilometer" measures at all in the map, just the coordinates. The dots are drawn using the coordinate positions, almost like the dots found on hit reports.
On May 2004 EBT started using a new map, the one everybody has now on their account details page. (The small rotated dots that won the May poll are seen only on hit maps, I think.)

I wonder if the same grid is used on the new maps. Here's the grid on my notes map (I've drawn a grid with some guessed lines):

Image

Is the grid an irregular "De Stijl"ish thing because of rounding numbers for coordinates? And, if so, shouldn't it be possible (and easy) to have another rounding system so that the grid becomes a regular one? Or would that need a different projection instead of Mercator? On my map, I'm not even sure on how many dots I have (21, sure?). In fact, I wonder how it is possible to know exactly how many dots there are on anyone's map.

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Re: Dots in maps

Post by avij » Sun Jan 30, 2005 9:42 am

Hi, the same 150x150 grid is indeed still in use. You got the grid mostly right, but there's one extra vertical line in your picture. You should have used the map of all Portuguese notes as a base for your drawing, it can clearly be seen from that picture that the "irregular" cells are wider than the rest. If you have a look at the whole European map, you'll see that approximately every 7th or 8th cell is one pixel wider, so we could fix the irregularities by increasing the horizontal resolution by about 20 cells, that way the cells would always be 3 pixels wide.

However, that's only for the X axis which is quite a lot easier. The Y axis is more difficult, and as can be seen from the European map the vertical resolution varies between 2 pixels (in the south) to 6 pixels (in the north). What kind of rounding would fix that problem? Or what kind of projection would be immune to this kind of problems?
Last edited by avij on Sun Jan 30, 2005 2:55 pm, edited 1 time in total.
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Re: Dots in maps

Post by Gauss » Sun Jan 30, 2005 1:43 pm

avij wrote:The Y axis is more difficult, and as can be seen from the European map the vertical resolution varies between 2 pixels (in the south) to 6 pixels (in the north). What kind of rounding would fix that problem? Or what kind of projection would be immune to this kind of problems?
Pretty much no projection because, well, the earth is a ball (more or less) and the screen is flat (more or less).

Mercator projection, however, is not quite optimal for maps which raise to higher geographic latitudes. Wikipedia has (section "controversy", at the moment) a good illustration of the area distortion which is the larger the closer you get to the poles. This applies for the standard Mercator projection whose reference line is the equator (basically, everything is projected onto a cylinder which encompasses the earth/ball, and the cylinder touches the ball at the equator). Now the Transverse Mercator projection could use a different meridian as reference line, probably some meridian that runs through central Europe. Then Portugal and Turkey would appear larger than they are now, Belgium smaller and Finland a bit smaller as well. In summary, it wouldn't help too much.

The main structural problem with Mercator is that it is not area-preserving. This is typical for cylindrical projections.

There is an extensive overview of various projection methods at the website of the USGS and a more instructive overview here.

Generally very good results are obtained with either of the two Lambert projections. The Lambert Conic is, like Mercator, angle-, not area-preserving but still much better than the former. The Lambert Azimuthal is area-preserving which comes at the expense that shapes get distorted, but still in a very acceptable manner.

A significant problem with the Lambert methods is to work out the mathematics they use: They are much more messy than Standard Mercator. Plus: Once we had that, and implemented that, we shall need a new map, and already the creation of the last map was quite an effort. And yes, we almost surely can't just simply download some map because of
1) copyright
2) quite specific needs (just coastlines and borders)
3) the parameters used during the creation of that other map have to be the same as in our projection which draws dots, but these parameters are normally not indicated on a downloadable map (parameters: reference meridian for Mercator, tangential point(s) for Lambert)

I feel that we are doing quite well with the current projection despite its known problems and, for the moment, focus on other issues of site development. In any case (as to my knowledge), we are the only tracking site which provides maps at all. Maybe the text above gives some hints, why.

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Post by avij » Sun Jan 30, 2005 5:04 pm

Thanks Gauss for your support, my point was indeed that no projection is perfect for all needs. The Lambert projection would be unsuitable for our world map, for example.

I'd rather concentrate on some of the more pressing issues, but as an easy fix to reduce the irregularities we could change the grid size a bit, from 150x150 to 157x150. This way the cell would always be 3 pixels wide. I drew some calibration maps, 150x150 (the original) and 157x150. On closer inspection it looks like the dot near Moscow is 4 pixels wide, but I feel this would be an insignificant error. The note map would look like this. How do you feel about this change?
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Re: Dots in maps

Post by lmviterbo » Sun Jan 30, 2005 6:00 pm

Thank you for the enlightment! I had been wondering about this for a loooong time.
avij wrote:You should have used the map of all Portuguese notes as a base for your drawing, it can clearly be seen from that picture that the "irregular" cells are wider than the rest.
Of course... One of the reasons for me to put these questions was that I was planning to help filling the map. Now the task will be easier :) (If you tell me the starting and ending longitudes of the map, it will be even easier.)
avij wrote:If you have a look at the whole European map, you'll see that approximately every 7th or 8th cell is one pixel wider, so we could fix the irregularities by increasing the horizontal resolution by about 20 cells, that way the cells would always be 3 pixels wide.
That would really be neat! I think you should do it in spite of the vertical resolution.
avij wrote:The Y axis is more difficult, and as can be seen from the European map the vertical resolution varies between 2 pixels (in the south) to 6 pixels (in the north). What kind of rounding would fix that problem? Or what kind of projection would be immune to this kind of problems?
Contrary to what Gauss answers, there could indeed be such a "projection". Just compute the vertical lines of a Mercator so that it becomes equidistant on the vertical scale. Shapes, distances and directions overall would probably look weird after the correction, though. I am aware of the load of work Gauss and others had to make the new wonderful map, so I'm not asking for any change.

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Post by lmviterbo » Sun Jan 30, 2005 6:07 pm

Sorry, I hadn't read your last post, avij.
avij wrote:I'd rather concentrate on some of the more pressing issues, but as an easy fix to reduce the irregularities we could change the grid size a bit, from 150x150 to 157x150. This way the cell would always be 3 pixels wide. The note map would look like this. How do you feel about this change?
GREAT!!! :D:D:D

(Maybe I'm missing something, but shouldn't the total amount of horizontal cells in the grid be the total width divided by 3, 487/3 = 162. In fact it's 162.̇3, but you could either trim the whole map to 486 pixels wide, or round the number of cells to 162.)
Last edited by lmviterbo on Sun Jan 30, 2005 6:08 pm, edited 1 time in total.

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Post by airis » Sun Jan 30, 2005 6:08 pm

avij wrote:...we could change the grid size a bit, from 150x150 to 157x150. ...How do you feel about this change?
So there will be 7 more dots (east-west)?
I think it looks good. For example the dot of Menorca island is visible. Previously it dissapeared among the dots of Mallorca. So many dots will change place, but I think they will be more correct.

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Post by bocky » Sun Jan 30, 2005 10:21 pm

Yeah, that would be a nice change :)
lmviterbo wrote:One of the reasons for me to put these questions was that I was planning to help filling the map.
I also thought about filling my map when I saw yours :P

EDIT: Here are my "before" and "after" note maps:
Image :arrow: Image
(grey lines mean it is impossible to get a dot there)

No changes in dot number, but now the two dots on the water (west of Lisbon) merged with those in Lisbon. :)
Last edited by bocky on Sun Jan 30, 2005 11:50 pm, edited 2 times in total.

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Re: Dots in maps

Post by androl » Sun Jan 30, 2005 10:54 pm

lmviterbo wrote:
avij on [url=http://forum.eurobilltracker.eu/viewtopic.php?p=32289#32289]Fri 17 Oct, 2003 14:10[/url] wrote:The map is a grid of 150x150 cells, where each cell is 0,44 degrees longitude wide and 0,28 degrees latitude tall. There are no "kilometer" measures at all in the map, just the coordinates. The dots are drawn using the coordinate positions, almost like the dots found on hit reports.
:) :oops: I should have found that, then I would have known it before I did some great Excel calculating. So now I can finally know the exact coordinates of the dots!

... :cry: avij, you took away 2 of my dots!!!
Image

so what is the exact width of a dot now? 0,44 degrees *150/157 = 0,42038216... degrees?

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Re: Dots in maps

Post by avij » Sun Jan 30, 2005 11:45 pm

androl wrote:... :cry: avij, you took away 2 of my dots!!!
Sorry about that, but for the most of you the amount of dots increased because of this change (I got an extra dot in Belgium from Zaventem, whee).

For reference, here are the current parameters for the grid:
Europe:
- minimum latitude: 29
- maximum latitude: 71
- minimum longitude: -12
- maximum longitude: 54
- grid size: 157 x 150 (up from 150x150)

world:
- minimum latitude: -57
- maximum latitude: 83
- minimum longitude: -180
- maximum longitude: 180
- grid size: 366 x 200 (up from 280x200)

The grid doesn't cover 100% of the map, for example southern Kuwait is not on the grid. I wanted to have nice round numbers for the grid borders, that's why there is some margin in the map :wink: The grid on the world map was changed quite a bit, now the cells are always (apart from one cell at the meridian) 2 pixels wide. The current 2.5 (approx) and 3 pixel widths were deemed too large in a quick poll that I conducted in #ebt.fi, thus the new 2 pixel width.

Androl is correct, the width of a dot on the European map is now indeed (12+54)/157 = 0.42038216560509554140 degrees.
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Re: Dots in maps

Post by lmviterbo » Mon Jan 31, 2005 12:06 am

avij wrote:for the most of you the amount of dots increased because of this change
Yay! I've got 3 extra dots! And they're quite easy to count, too!

The map now looks overall better, indeed. Less dots are on water now (I still have 2, one of them being the second most important town in Portugal, Porto; I wonder if the map's border would need some extra dot here and there).

avij wrote:The grid doesn't cover 100% of the map. [...]
Androl is correct, the width of a dot on the European map is now indeed (12+54)/157 = 0.42038216560509554140 degrees.
I guess the only way for us to know where to go hunt for notes and new dots would be to know exactly what are the full map limits. avij, could you give us those details?


Still another thing: why does the world map have fuzzy borders (in shades of gray) instead of the precise ones on the Europe map?

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Re: Dots in maps

Post by Gauss » Mon Jan 31, 2005 1:25 am

lmviterbo wrote:I guess the only way for us to know where to go hunt for notes and new dots would be to know exactly what are the full map limits. avij, could you give us those details?
If I were him I wouldn't. Reasoning: If you want to fill the whole map (at least of Portugal) and don't know exactly where you have to enter the bills - then you will have to do it with trial and error. This means: You'll probably have to enter more notes because you'll probably sometimes enter a note at a new place without getting a new dot. This means: More notes. (And every tracker is happy about that, right?)

And you should also see it from this side: Whenever you come to a new place and enter a note there you have not only the chance to get a hit with that note, but also the chance to get a new dot. Makes tracking even more attractive!

:wink:

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Post by airis » Mon Jan 31, 2005 2:08 am

Yes, there were some changes. I lost one dot in Helsinki. It seems that Länsisatama (western boat harbour) and Helsinki-Vantaa airport are now in the same dot. I might have got more dots too, but I am not sure.

One thing I noticed: The dot of Ylitornio-Aavasaksa area in south-western Lapland is now clearly in Sweden. I did draw that border again as done previously and it was in okay. The coordinates seemed to be correct too. That Menorca dot east of Mallorca is also a bit too west. Well these are only two dots.

Btw some people who have tried to fill the map might have got some new empty dots to fill. :wink:

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Post by lmviterbo » Mon Jan 31, 2005 2:18 am

Just for the records: 9 dots are still lying on the Atlantic off the Portuguese shore now. Maybe some Portuguese coordinates lie on Spain (on the map), but I don't have a way of telling this.

@avij, Gauss, airis and the whole team that drew the map: if you're still able to correct the borders (so that even less dots lie outside their own countries or on the sea), just tell me. Last April, I was working like crazy and couldn't find the time to contribute but I will gladly do it now if needed, at least with precise Portugal coordinates up to whatever resolution you want (0,42 x 0.28 degrees or more).

If that implies a lot of programming work, just forget it: it's already pretty good.

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Re: Dots in maps

Post by avij » Mon Jan 31, 2005 3:57 am

lmviterbo wrote:Still another thing: why does the world map have fuzzy borders (in shades of gray) instead of the precise ones on the Europe map?
Because only the European map was redrawn, the world map was left intact and it had those funny fuzzy borders.
Gauss wrote:If I were him I wouldn't.
As a matter of fact, the coordinates for the grid can already be calculated from the information I posted above, so it's too late to deny such requests.
airis wrote:The dot of Ylitornio-Aavasaksa area in south-western Lapland is now clearly in Sweden.
Hm, I've now moved all the dots very slightly to the east. Now your dot at least touches the border, so if your note was found at the border it should be okay. This change will affect the Portuguese coast as well. Reports from other countries are welcome.

As for dot hunting, this page may be useful. By clicking on the map you'll get a list of all the cities in that dot. Please note that this information is obtained from tens of thousands of EBT users, so there will be incorrect entries, such as Tampere being in Estonia instead of Finland. That page is not designed to be used for locating incorrect entries from the database. If that page is used for such purposes, the page will be removed. Any other feedback is welcome, just don't bitch about the incorrect city names etc found from the results.
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