A radical new map concept

[el cid again]

This is a way out - and may not be possible - but Cobra and I are exploring the concept of a no range error map. It would look funny on the edges. North is really up only in the middle - the Carolines area.
But we think it may be possible to do the art. IF it is, I will do the (awful) task of coding every hex side. But if no one wants it, we won't do it.

[herwin]

ORIGINAL: el cid again

This is a way out - and may not be possible - but Cobra and I are exploring the concept of a no range error map. It would look funny on the edges. North is really up only in the middle - the Carolines area.
But we think it may be possible to do the art. IF it is, I will do the (awful) task of coding every hex side. But if no one wants it, we won't do it.

Er, what do you mean by "no range error map". I have some expertise in map projections.

[el cid again]

ORIGINAL: herwin

ORIGINAL: el cid again

This is a way out - and may not be possible - but Cobra and I are exploring the concept of a no range error map. It would look funny on the edges. North is really up only in the middle - the Carolines area.
But we think it may be possible to do the art. IF it is, I will do the (awful) task of coding every hex side. But if no one wants it, we won't do it.

Er, what do you mean by "no range error map". I have some expertise in map projections.

I actually mean an equal area projection. We allow other things to be distorted - like shape and direction. The most common form of this is an equal area cylindrical projection. But I am thinking in terms of an equal area spherical projection. This is really only possible in the age of computers - in the sense we can play with the map and do more than could be done with an optical projection. We should be able to extend the projection at the corners so that we can show a path of the correct length all the way to the Cape of Good Hope and to Cape Horn. Not sure - this is barely past brainstorming - and it is not yet confirmed what we can do within the structural limits of the game map system (144 x 144 hexes, 60 sm per hex means theoretically a square 8640 miles on a side = 12,219 miles diagonal measure - just where we put the edges and corners is not cast in stone - but it cannot be farther apart than that).

The problem, of course, is that the Earth is not flat, but our screens are!
I once solved this problem with back to back circles 13 feet in diameter - each side had a hemisphere - and the center (poles) had a pipe mounted so the whole wheel rotated - meaning any part of the Earth could come before your eyes. This allowed 5,000,000 one aeronautical charts to be used - except their conical projections do not 'meet' properly - so we had to do hand created adjustment wedge sections to make them meet. On this scale one nautical mile is visible - and we were able to get errors to about half that size. But it took a long time to assemble - and a gigantic room to hold it!

What I want to do is take a composite satellite image of the Earth - you can see about a third of it - washed so there are no clouds - and then use software to put that in the form it would have if it were projected on a spherical globe from the inside - and plot the resulting positions - and then "peel" the image and "lay it flat" - as it were. There are other possibilities - and a couple of programs that may allow enough distortion to achieve the desired effects. In this case, we don't care as much about true north or shape of land mass - particularly not near the center - as we do about every time you move a hex it is the same distance. This should be possible to do - although no one may like what it looks like. Regardless of what it looks like, it should be a good tool, and I have other reasons to want to see this done. [I regret to say it may be we will be contesting this same area again, possibly not as far in the future as WWII is in the past. I have material indicating that Kodiac Alaska is supposed to be "controlled" by a specific target date by a less than friendly power. It is the end of what they call "the second island chain." And Hawaii is the end of "the third island chain" - to be annexed later.]

[herwin]

The problem is that equal-area does not imply *correct* distances. In fact, any flat map of the globe has to distort distances. Curvature is measured from that distortion. If you want relatively undistorted distances, you have to shove the severe distortions off the map or into areas nobody cares about.

[herwin]

You *could* do everything correctly (like air traffic control systems do) and use the map graphics simply as a projection. The hexes would not all be the same size, and you would travel along great circles or rhumb lines.

[Montbrun]

Distortion at the edges will be normal:

[el cid again]

ORIGINAL: herwin

You *could* do everything correctly (like air traffic control systems do) and use the map graphics simply as a projection. The hexes would not all be the same size, and you would travel along great circles or rhumb lines.

This sounds like the opposite of what I have in mind. How can range be correct if hexes are different size?

[el cid again]

That looks an awful lot like a Mercatur Projection - with gross distortions as you move towards the poles. This is not going to work well.

[herwin]

ORIGINAL: el cid again

ORIGINAL: herwin

You *could* do everything correctly (like air traffic control systems do) and use the map graphics simply as a projection. The hexes would not all be the same size, and you would travel along great circles or rhumb lines.

This sounds like the opposite of what I have in mind. How can range be correct if hexes are different size?

Because range can be calculated from actual position on the globe and the hexes are just for show. Range is then defined in miles/kilometers/nautical miles, and not in terms of hexes. If you insist on hexes being accurate, you're working with a flat earth, since they make up a flat surface. It doesn't matter locally, but it does at longer ranges.

[el cid again]

I do not see how hexes are different from any other unit of measure - except of course they are areas in fact but when using them to measure range they are simply units of distance. Latitude never changes - so plotting latitude is not a big problem in terms of hexes -

if I had my way each hex would be half a degree or 30 nautical miles - and I could work the navigation in my head - but we have a slightly different system at the moment - it is just over 50 nautical miles per hex (and exactly 60 statute miles).

As I see it, the thing that changes in terms of geographic position is longitude. At the equator it is exactly the same as latitude - 1 nautical mile is one minute of arc - or 1/60 of a degree (and 1/30 of a 30 nautical mile hex). As you move away from the equator in latitude, longitiude changes, so that the meridians converge, and the distance represented by a minute of arc declines. What I do is take the real position on the globe in latitude and longitude, and plot it on a flat surface, using the exact change in longitude for that latitude. I am not sure what you should call this kind of plotting - but it works perfectly for plane and ship navigation purposes. If you put all - say - bases on a map plotted in this way - the map becomes a mechanical computer for range between those bases - and you can count hexes to get the true range. I call that a "zero range error map."

[bradfordkay]

The only way to have a non-distorted map of the size of WITPS is to place it on a sphere. Somehow, I don't believe that the WITP engine will handle this. I hope that I'm wrong on this latter statement.


EDIT: there is another method. If you were to make the actual, visual, size of the hexes larger as you reach into the edge areas (in WITPS case, this would be the southern, eastern and western edges) where each hex has the same map distance but looks twice to three times as large...

[el cid again]

ORIGINAL: bradfordkay

The only way to have a non-distorted map of the size of WITPS is to place it on a sphere. Somehow, I don't believe that the WITP engine will handle this. I hope that I'm wrong on this latter statement.


EDIT: there is another method. If you were to make the actual, visual, size of the hexes larger as you reach into the edge areas (in WITPS case, this would be the southern, eastern and western edges) where each hex has the same map distance but looks twice to three times as large...

Why can we not have the area of the map not be "square" - even though the area we see is square? That is, as we move south, more and more longitude appears on the map. This is a system I use with hand made maps. IF the map were big enough it would at some point be too big - and the "corners" would overlap. I want to have shipping run in from Cape of Good Hope and/or Cape Horn anyway - or as close as we can get - to permit some LOC warfare (if Japan gets smart - and in the Indian Ocean German and Japanese subs DID run an LOC war - with effect) - but not the little bit of it we have - it is the middle). The hexes represent the right area - but ever more degrees of longitude as you proceed South.
Same in the north of course - but only on the NW side do we care - and it won't seem quite right direction wise. The compass won't be right at the "corners" of the map (in the sense north is not up). But right now due West is almost due north in Russia - and no one complains.

[m10bob]

Most accurate global map most of us have seen looks like a peeled orange, but game-wise, I don't think it would be visually appealing,(no pun intended.)

[el cid again]

This is true. I don't think it will work though, so it is moot. The game wants hexes "beside" each other - and "edges" in a traditional rectangle sense. . But our rectangle should be able to represent a sort of variable presentation - if we just squish longitude as it really does squish. We lose direction (except at center) - but that is worth it in my view. Our sense of what "shape" things are is distorted by the maps we are used to - Mercatur in particular - and the world really does have "tilting" continents as you go toward the poles. What we think of as North is NOT the same direction in fact - it is a different direction from every different point. If you face a globe and consider this, you will see that - over on the right - "north" is different than it is directly in front of you. No reason a map can't show that - it is more right than "north is always up" anyway. North is the direction of the pole from a particular location. The question is, can an area about 8640 miles on a side be done with ranges more accurately than we now have?
[Some of my point to point plots are 50% off - although the average error is only 5% - this is an AVERAGE - not the same thing as saying the map is withing 5% of true; Andrew increased this to an average of half a per cent - but STILL has 50% errors at points! In fact - Andrew's map has MORE places with 30-50% errors than stock does - although on the average it is more accurate.] I hate those big errors - can we do something about it that is practical? I usually don't map an area quite this large.

[herwin]

ORIGINAL: el cid again

I do not see how hexes are different from any other unit of measure - except of course they are areas in fact but when using them to measure range they are simply units of distance. Latitude never changes - so plotting latitude is not a big problem in terms of hexes -

if I had my way each hex would be half a degree or 30 nautical miles - and I could work the navigation in my head - but we have a slightly different system at the moment - it is just over 50 nautical miles per hex (and exactly 60 statute miles).

As I see it, the thing that changes in terms of geographic position is longitude. At the equator it is exactly the same as latitude - 1 nautical mile is one minute of arc - or 1/60 of a degree (and 1/30 of a 30 nautical mile hex). As you move away from the equator in latitude, longitiude changes, so that the meridians converge, and the distance represented by a minute of arc declines. What I do is take the real position on the globe in latitude and longitude, and plot it on a flat surface, using the exact change in longitude for that latitude. I am not sure what you should call this kind of plotting - but it works perfectly for plane and ship navigation purposes. If you put all - say - bases on a map plotted in this way - the map becomes a mechanical computer for range between those bases - and you can count hexes to get the true range. I call that a "zero range error map."

To help your intuition, the real problem is that a 60-mile diameter circle on the surface of the earth has a circumference a bit less than pi*60 nm. The area is greater than you would expect from the *measured* circumference because it sticks out a bit in the middle, but less than pi*30*30 square nm, which is what you would expect from the linear distance (range). If you were to lay the circle out on a table, the center would be raised a bit. Zero area error map projections produce errors in range, and you simply can't get a zero range error projection on a flat map. You have to do your best, which is what Andrew has been doing.

[bradfordkay]

"That is, as we move south, more and more longitude appears on the map."


No, as you move towards the equator you have more and more longitude. As you move further south towards the antarctic you will have less, just as you will moving towards the arctic. One minute of longitude at the equator equals one minute of latitude, but that is the only latitude where they are equal. This is why the map for WITP is so difficult to create, both visually and factually. If the game were based on vectors instead of hexes, it would be much easier...

[el cid again]

We have got cought up in a classic terminology problem:

when I say "more longitude" I mean more meridians per unit of distance (e.g. a hex)

when you say "more longitude" you mean the distance between meridians is greater

and we are both right - in the sense we mean it.

For me, a higher number is "more" - for you a bigger distance is "more" - and there is no great problem with either idea - so long as it is defined so it is understood.

I do navigation in my head (survival training) - and longitude is (as you probably know) much harder to do than latitude. I can measure latitude with a string and a block of wood - or anything like that - cutting a notch in the block - to make a primitive astrolobe. I may not know the value of my string - but I always know if it is more or less - and time was a knot on a string meant "the latitude of Lisbon" or whatever. I can correct to get back to my latitude, and sail east or west until I reach the right longitude. There are also ways to measure - and estimate - longitude. But when plotting (say dead rekoning in a plane) you need to remember the meridians get closer together as you proceed north or south - more lines per actual linear distance unit. That is why I think it is "more" - more degrees but not as much more distance as it would be at the Equator. Near the equator you can pretend a minute of longitude equals a minute of latitude - that is the easy place.

Our problem is that the area is so big the "rise" in the "middle" of the map matters a lot. I begin to fear it cannot be done without going over to a projection of a sphere. But what is wrong with that? Why NOT have the image of the globe as our map - and you just zoom in on it?

[bradfordkay]

I would dearly love to have the map as a global sphere. However, I am not sure that it can be done with hexes... it'll take a better mathematician than I to figure out if that is possible.

[el cid again]

We call the center of the map 74,74 (half of 148,148).

We take a paper and cut a wedge out of it - two of them - fat end north and south - pointy end at 74,74. We cut each wedge in half - and put them on the sides of the paper. We place the paper on a globe and mark the edges where (say) ten degree lines cross the edge of the paper - both latitude and longitude. We draw these lines on the paper. We then plot all locations in latitude and longitude - and put them on the paper. This then we give to Cobra and say - "we want art with these places in these locations". Since we use 144 blocks - we can tell the hex ID of every location.

[CobraAus]

A sugestion all these type of game are hex based but the art work is pixel based - the map panel is 6301 pixels wide x 5715 pixels deep so ok using the center of 74,74 to the pixel
work out how may pixels = a line of longitude and latitude I can set up a grid based on thos zie size's - also if the longitude and latitude lines need to stretch do the stretch by pixel
so many per Lon/Lat line - once thats done the hex base can be layed in resizing the hex's
as we move out to the sides - again once thats done I can start placing Art where needed
I am only thinking out loud here and needed to get down on paper so to speak
An Art layer showing just lines of LOB/LAT should not be to hard to produce either, numbered at the edges as guide
I am weak at the knees just thinking about the work involved in this

Cobra Aus