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.