Tuesday, February 23, 2010

Mapping Design

I've talked about this before, in passing ... but for my own records I wanted to write a single post on the subject, that I might refer back to it later.

When deciding to map the world as a hex map (all my previous world maps had been open maps without the hex design), I decided not to do what most every standardized map does - I did not wish to treat the world as though it were a flat plank, such as:


Does this map's dimensional quality bother anyone other than me?  How exactly do the longitudinal lines draw together at the top of the map's center, in order to meet at the north pole?  Answer: they don't.  This map is based on the same principle that graced every schoolroom when the makers of the above map were in grade three - you recognize it, of course.  It's the Mercator Projection:


Generally acknowledged to be among one of the silliest map projections ever designed (making Greenland the size of the United States, and convincing two generations of people that planes from New York fly over the middle of the Atlantic in order to reach Europe), this map was everywhere up until about thirty years ago.  It was originally designed as an aid to sea navigators (to calculate compass directions), it became popular due to geographically illiterate publishers appreciating the manner in which the projection makes it appear that the civilized northern states are physically comparable to their colonial equatorial counterparts.

The problem, of course, is that the verticle lines on the map are anything but ... they converge together towards a North Pole that cannot be reconciled with the map's appearance.  But sea navigators didn't need to navigate the north pole in the 16th century, so it was fine for them.  For a modern world, it is a sad, disposable artifact.

But in the 1960's, as I say, the projection was standard.  So have a look again at the Greyhawk map and tell me - how wide are one of those hexes at the top of the map, compared with those at the bottom?  Since the top of the map is arctic in character, and the bottom is tropical, the assumption is that this represents the pole to the equator ... in which case, every hex on the map must be a different diameter.  This just bugs me.

So when planning my world, I envisioned a globe, not a plank - and ran smack into the limitations of depicting a curved surface on a two-dimensional plane.

It has to be understood, NO map projection can be accurate, for just that reason.  The question couldn't be, what design will be flawless - it would have to be, what sort of flaw would least annoy my sensibilities.  I spent a lot of time contemplating dodecahedrons or the 20-sided die - even the 30-sided - for at least these represented orbs.  The 20-sided is really the only one that can be reconciled with a hex map, but it did require a considerable number of 'bends', at each change between faces.  Of course the 20-sided can be laid out flat:


But I considered the breaks in the above form to be, well, annoying.

So after much thought and brain-bending, I settled on the following system.  I am happy with it, although it does moderately warp the world map ... a necessary evil.

Starting with the following (albeit simple) diagram:

Starting with a 20-mile diameter hex at the North Pole, with the pole at its center, it is then 10 miles to the edge of the first hex, which works out to be at a latitude of approximately 89.86 degrees N.  Each concentric circle moving outward then extends near to 0.28 degrees latitude, the equivalent of 20 miles (if I've done my math correctly - if I haven't, it's a mistake I made five years ago and its too late to fix it now).  The first ring around the polar hex is 'Ring 1', the next is 'Ring 2' and so on.

To simplify the matter for me, the 360 degree circle at that latitude was then divided by the number of hexes in the given ring ... so that for Ring 1, each hex is 60 degrees in longitude in diameter; for Ring 2, 30 degrees in longitude and progressively less and less as one approaches the equator (which would be Ring 311, but is instead called the 'Equatorial Ring' in order to allow me to designate the rings south of Equator 311, 312, 313 and so on.  This made bookkeeping easier for me.

As such, this depiction of the Earth's surface creates two duplicate concentric plates, folded together at the Equator, and remarkably easy to lay out.  The lack of breaks, bends and so on allows for large expanses of the map to be seen at one time.  At 1 inch per hex, either hemisphere would be 51.83 feet across.  For me, it is a small dream that one day both finished maps could be laid out on a large gymnasium floor ... if ever I could finish them.

Travel between two places according to this map can lead persons far to the north, following 'the curve of the earth' ... which is why Marco Polo's route to China seems perplexingly indirect on a typical flat map (there's a high hump in the middle that describes Polo travelling north in order to travel east).  We experience the same situation casually when flying across Greenland to travel from North America to Europe.

It does, however, force the maps I draw to make a 'turn' of 60 degrees at six points along whatever line of latitude.  The distortion is quite obvious in some places, and less so in others, depending on how uniform the land or the sea is at that particular point.  You can see from my diagram that those points are along the following longitudes: 30 E, 90 E, 150 E, 150 W, 90 W and 30 W ... I chose those particular meridians both for their round numbers, and so that most would follow lines that were mostly water.  I didn't want to warp England in the middle, or indeed any part of Europe ... but it did wind up having some trouble with the western shore of Turkey.  Ah well.

That's about it, I guess.  I recommend to others that they consider a globe, when designing their worlds ... it will help draw together a unity that a 'plank map' won't provide.




9 comments:

Zzarchov said...

I actually (twisted sense of pleasure) like the flat map. I often go with flat worlds (with an edge to fall off of). If it is a round world I will draw the map ON a globe (styrofoam sphere) and give the players faulty maps. Maps themselves are treasures in the time period I run games and good maps make epic gifts to appease foreign kings and earn favours.

Geoffrey said...

I wish that BLANK GLOBES were sold, with surfaces that could easily be written upon. Some of the blank globes would be completely blank, while others would have lines of latitude and of longitude written upon them.

PatrickW said...

So, would I be correct in guessing you are using CC2 as your mapping software?

Also, the distortion you mentioned in this map (the "2 Giant Pie Plates" version) comes from flattening the curve from the pole to the Equator, correct?

Finally, would it be possible for you to post an example of the warping issue at the six "bends" (e.g., the issue with the western shore of Turkey)?

Thanks! I started a new game world with just the local map, but want to get a larger scale map done before they have to start really travelling for level appropriate challenges.

rmckee78 said...

A great scene on the subject (some politics mixed in) from The West Wing:
http://www.youtube.com/watch?v=n8zBC2dvERM

Welleran said...

I've had "Make a globe" on my campaign world's To Do list for about 15 years now!

Alexis said...

Zzarchov,

I have no words.

Geoffrey,

A blank globe is interesting, but we’re talking about a globe that’s 52 feet across. That somehow needs to fit in my living room, so I can use it during a game.

Patrick,

That is precisely the distortion ... it tends to stretch out the image of regions from left to right. But I remind myself that most maps stretch out the image of regions from top to bottom (from familiarity, we really don’t realize that this happens).

I plan to publish a map of Norway in a day or two, but I’ll try to publish the map you ask for sooner. It just so happens that was the first ‘bending’ area I mapped ... but I’m quite used to how it looks now.

Regarding the comment you left on “How It’s Done Rejoiner,” the numbers on river sizes refers to water volume. I haven’t worked it out precisely, but generally 1 point would be equivalent to the amount of ebbing groundwater from an area of approximately 52 sq.mi. (one sixth of a 20-mile hex). Green colors lighten in shades (microsoft fill option) from 70% (less than 500 ft below sea level to 20% (1500-1999 ft above sea level). Orange colors darken from 40% (2000-2499 ft) to 100% (5000-5999 ft). Then one odd color that is dark orange/red without brown, for 6000-6999 ft. Steel blue begins at 30% (7000-7999 ft), ascends by 1000s in shade until 10000 feet, then ascends by 2000s in shade until, well, I’m not certain. The highest altitude I’ve yet found is 18000+ feet, which has a 100% shade.

Probably more information than you needed.

Rmckee78,

I had that scene in my head as I wrote the post. Hah.

PatrickW said...

Actually, that was exactly the information I was looking for - thank you. I may have more questions on that when I get a chance to fiddle about with Publisher and try out this method of mapmaking.

I've been back-reading your map posts and I now know that you are using Publisher (not CC2) to make your maps. That seems very inspired and I would never have thought to use it as such. I am very impressed with the quality of maps you are making.

You state you are creating the maps on a 35x30 hex grid. What size hexes are you using (or put another way, what size paper are you formatting to)? I've done some hex maps in Paint on 11x17" (A3) paper using rather small hexes, which limits the information I can instill to the map (usually terrain type and maybe a settlement of some sort). I have the impression your hexes are an inch or so in size.

Thank you again for sharing - you are very inspiring.

Strix said...

You could spray paint a globe white and go nuts. Heck, you can even get a can of white board paint and go nuts repeatedly ;)

Steve L. said...

It would be useful to have software that would print a map onto a piece of paper sized to fit a globe, with lines indicating where to make the cuts in order to have the paper map fit the curving surface of the globe (and which would conform to the projection used, I think). My globe (from the 1970s) was made in a similar way; you can see the seams in the paper.