MAP PROJECTIONS (Full Version)

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Curtis Lemay -> MAP PROJECTIONS (9/5/2009 8:43:42 PM)

Frustrated with the absence of any decent TOAW Article section anywhere since the one at GameSquad went AWOL, I've decided to just post re-prints of them as threads here on this board. This one has received a bit of a re-write.




Curtis Lemay -> RE: MAP PROJECTIONS (9/5/2009 8:46:59 PM)

MAP PROJECTIONS


By Bob Cross


Here’s an important point on map-making that can get overlooked – projections. Remember that the Earth is a sphere but we have to make a flat map.

[image]local://upfiles/14086/0302BF60E2E84E51A7A39105049DAA6D.jpg[/image]




Curtis Lemay -> RE: MAP PROJECTIONS (9/5/2009 8:49:03 PM)

How we project the sphere onto that flat surface can make a difference. There are a vast number of ways to do that, but the most common types are cylindrical, sinusoidal, conic, and plane projections. Each has its properties and proper applications. Map properties are:

Conformal – figures retain their true shapes at the expense of relative area.
Equal-area – figures retain their true relative area at the expense of shape.
Azimuthal – angles retain their true values upon projection.
Equidistant – distances retain their true values upon projection.

For wargaming, the greatest needs are that the map be equal-area and equidistant. It is critical that the hexes all be the same size. Not only does this affect combat but it affects whether the distance from one point to another will be true all over the map. The need for hex-columns to be North-South or for hex-rows to be East-West is not so important. Similarly, the need for areas to retain their shapes, while desirable, is not critical.

[image]local://upfiles/14086/45344F5208A24D03A610960DCB1546C6.jpg[/image]




Curtis Lemay -> Cylindrical projections (9/5/2009 8:51:02 PM)

Cylindrical projections tend to be conformal. Parallels are horizontal and meridians are vertical. We’re all familiar with the Mercator projection in which Greenland is the same size as South America. Unless you are doing a map of a very small area or one that is restricted to an equatorial area, avoid cylindrical projections. Use this for a large northern map and you may find yourself with 5-km hexes at the top and 20-km hexes at the bottom.

[image]local://upfiles/14086/1D4C76B531234674A78E907B0DA99A43.gif[/image]




Curtis Lemay -> RE: Cylindrical projections (9/5/2009 8:52:47 PM)

There are equal-area cylindrical projections, but they are definitely not equidistant.

[image]local://upfiles/14086/DE648F767FCF46F7823E4B3CB1934017.jpg[/image]




Curtis Lemay -> Sinusoidal projections (9/5/2009 8:54:34 PM)

Sinusoidal projections are equal-area. Parallels are horizontal, like in cylindrical projections, but meridians are sinusoidally curved, except for the central meridian, which is straight. They are not equidistant, but there is not much distortion of distances. For my money, this is a very good projection for wargaming, provided the area covered is smaller than continent-sized. It’s the one I’ve used for the CFNA, France 1944, Okinawa 1945, Germany 1945, and Soviet Union 1941 maps. Plus, it was very easy to implement into the “latlong” program I made to calculate the latitudes and longitudes of each map hex.

[image]local://upfiles/14086/9E7C9E4BA02F4FA8BECEBE707197AD0A.jpg[/image]




Curtis Lemay -> RE: Sinusoidal projections (9/5/2009 8:55:58 PM)

I managed to find this sinusoidal projection of South America. It’s not the best example of the benefits, since it straddles the equator. But even with this case, you can see some benefit at the bottom, where the Falklands no longer appear as far from the coast as the Galapagos (as they do in the Mercator projection, above). You can clearly see the increasing curvature of the meridians towards the left and right sides. But the real benefit of this projection occurs when the map ventures closer to the poles – as Northern Europe does. (But, unfortunately, I couldn’t find a sinusoidal projection of Europe).

[image]local://upfiles/14086/E8CB02C40E4F4CD48A1A5663CE444F20.jpg[/image]




Curtis Lemay -> Conic projections (9/5/2009 8:58:48 PM)

Conic projections are described as compromise projections in that they do a good job on most map properties but are not perfect at any. Parallels are curved, equally spaced, and concentric. Meridians are straight and converging. The scale is correct at the meridians and at the two standard parallels. Elsewhere the scale varies.

[image]local://upfiles/14086/8A3981C9551B493EA156228AFEBED791.jpg[/image]




Curtis Lemay -> RE: Conic projections (9/5/2009 9:00:51 PM)

Again, we’re all familiar with the Lambert Conformal Conic projection of the US where the northern boundary with Canada is curved. This isn’t a bad projection for wargaming, especially if the map covers a lot of east-west longitude (continent-sized).

[image]local://upfiles/14086/3D914C9E8B8144B0AEB4242166B55A60.gif[/image]




Curtis Lemay -> Planar projections (9/5/2009 9:02:22 PM)

Planar (also called azimuthial) projections are probably only of interest if you are doing the Pacific War. We should all be familiar with polar projections, showing the Earth from either of the poles. But this can also be centered on any other point

[image]local://upfiles/14086/26399E0A65FC4AF1887078A77E75BD71.gif[/image]




Curtis Lemay -> RE: Planar projections (9/5/2009 9:03:50 PM)

You can get an equal-area projection (or equidistant) but both parallels and meridians will be curves. I’ve seen a few Pacific wargames that used this type of projection. It’s good for hemisphere-sized maps.

[image]local://upfiles/14086/B9AF8F6EEE924F90A72EB2761C2BE85A.jpg[/image]




Curtis Lemay -> MAP PROJECTIONS (9/5/2009 9:04:46 PM)

Having said all that, I now will admit that there is one feature of cylindrical projections that is superior to all the others – they are easy to expand. All the other projections require some foresight in where on the Earth the projection is to be centered. If you come back later and wish to extend it, it’s going to be less than ideal. For example, my France 1944 map has its central meridian on the middle hex-column (the one going through Boulogne-sur-Mer). That’s the only hex-column that runs true North-South. All the other hex-columns have a slight sinusoidal slant to them which increases with their distances from that central hex-column. If I now decide that I want to extend the map to Poland, each hex-column added will have more and more slant until it becomes jarringly obvious. Had I started out expecting to extend to Poland, I would have put the central meridian much further east – but that can’t be done after the fact without starting over.




Curtis Lemay -> RE: MAP PROJECTIONS (9/5/2009 9:06:24 PM)

Note that I'd like this thread to be treated like an Article rather than a discussion. So I'm going to try to get the monitors to lock it. Until then, I'd appreciate that no one post here. If you want to post about the Article, please make a new thread to do so.

Thanks.




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