Topology - Update 1

[Singularity24601]

Wraparound maps solve the strategic serendipity of map borders, but I dislike them because I find them hard to visualize. On a spherical world, if you head far enough east, you reach the west, but you don't reach south if you head far enough north - that would only be true if you were on a torus (a doughnut). On a sphere, if you're on the eastern hemisphere and head far enough north, you reach the north side of the western hemisphere, now heading south. I propose two methods of simulating spherical worlds:

1) Modified tesselation
I believe it should be possible to achieve a closer approximation to a sphere by rotating each "row" of iterations by 180 degrees (ie, vertically and horizontally flipping). I have attached diagrams to demonstrate:
Image 1: Torus tesselation
Image 2: Incorrect sphere tesselation
Image 3: Correct sphere tesselation

2) Cylindrical projection
Simply neighbour the eastern and western edges (with or without tesselation), provided 2 conditions are met:
- All provinces of the northernmost and southernmost latitudes must be neighbours with each other (equivalent to dividing arctica/antarctica like a pie).
- The number of provinces per latitude must be a maximum in the equatorial latitude, decreasing roughly trigonometrically to minimums at the northernmost and southernmost latitudes (eg, 1-3).

To achieve these conditions will result in some distortion:
- As one approaches the polar extremes, the shape of the provinces are preserved, but the area of the provinces become progressively larger (Mercator projection).
- As one approaches the polar extremes, the area of the provinces are preserved, but the shape of the provinces become progressively flatter (eg, Gall-Peters projection).
- A compromise between the two extremes (eg, equidistant cylindrical projection).

[Gandalf Parker]

I worked on a couple of more realistic maps. I wrapped east to west normally. Then I "pinched" the north and south by making them just a few provinces that stretched across the top and bottom of the map which all lead to each other. All of the north provinces led to each other and all of the south ones led to each other.

I was also working on creating "modules"
http://host.dom3minions.com/maps/modules/_index.jpg
which are all exactly 100 provinces. The way that Dom3 numbers provinces, I should be able to stack 3 modules and just renumber the provinces from 1-100 to being 101-200 and 201-300

I figured that doing it as modules would increase the chance of getting an interesting map rather than continually watching for some large map to come out interesting. And Im hoping for ones that have a white polar region that I can tack onto a big middle temperate looking one.

[PDF]

I don't like wraparound maps due to the fact that indeed doughnut-shaped world is rather hard to visualize, as you point out...
I don't understand your method 1 , but the 2 is ok for me In Dominions a province surface does not play any role, so I've no problem with big polar regions.
Anyway the map drawing can put the provinces into a circle so that provinces are not deformed, the only trick then is to link east and west provinces.
The only drawback is that you can't "change" the map view as is possible with a wraparound.
The best solution would be that IW give us a "East/West wraparound" option

[paradoxharbinger]

single direction wrapping maps are planned for my map generator, just ring-world type of thing at the moment, but there is a possibility that the 'modified tesselation' techniquue could be implemented as well. here is my thread on it