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Peirce Quincuncial Projection Map 2023-03-24

This generates random quincuncial maps. I hadn't heard of them either until, @f1rpo mentioned,
A world map based on some funky map projection that places one of the poles in the center (example) might combine well with the Toroidal world-wrap setting. But Globe view is not going to translate that properly into a sphere.
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Main points about a quincuncial map are:
* one pole is in the centre of the map and the other pole is in the four corners (like the dots for the 5 on a dice)
* the equator is the diagonal lines joining the midpoint of the edges
* the area of greatest map distortion is at the midpoint of the edges
* standard wrapping will not work with it

The script allows for generation of the following maps:
Pangaea - super continent wrapping around central(north) pole and extending out to the associated three corners
2 N-S Continents - Two continents on opposite diagonals, extending almost from pole to pole
3 N-S Continents - Continents on three diagonals
4 N-S Continents - Continents on four diagonals
E-W Continent - This generates a northern continent almost wrapping around the central (north) pole and then a southern continent in 3 corners. Without the mapping, the "southern continent" is effectively split into three continents. The ocean divides the continents along the equator.

A true quincuncial map is tilable with no overlapping. That's not quite true on this map. There's a frame, two tiles wide around the main playing area. The outermost tiles is impassable peaks most of the way around, with oceans in the corner. This links the southern continent areas. The ring of tiles one in from this duplicates the (plot and terrain) tiles from the adjacent corner, i.e. where the wrapping, if working would have led to.

I abandoned my hopes to do a proper quincuncial specific wrap as I could not get the path finding to work. My hopes for that wrap are in the spoiler. Toroidal map has been enabled which should be relatively interesting for Pangaea and E-W continents. When the toroidal map option is active there are bands of ice in the middle section of each edge to prevent travel across the edge of the map in the area of greatest distortion.
Wrapping plans
Spoiler :

For wrapping the map into a globe shape, imagine the central playing area as divided into 16 equal squares.
The four central squares are most of the northern hemisphere. The four corner tiles are the most of the southern hemisphere.
Along any given edge, the tiles in the corner squares link together. For example if you head in a left direction off a tile on the edge of the playing are, e.g. (2,y), the wrap would have the unit move to the tile (2,n-y), where n = mapwidth - 1.
For the squares on the centre of the edges, the wrapping would be different. This is where there's the greatest distortion on the Peirce Projection map, so the mapscript should make sure that all of the tiles in this area are ocean tiles. This means that when the wrapping works, there'll be inland seas on the Pangaea continent. To represent this distortion, imagine circles drawn with its centre in the centre of a corner quadrant. Any tiles within the two squares along the middle of the edge, which are outside of the area of the circles drawn from the centre of the associated quadrants will be ocean tiles and regarded as within the "crease" when the map is wrapped to form a globe. Imagine these tiles being folded inside the globe when the map is being wrapped into a globe. The way the wrap should work at these creases is that when a unit (probably naval) moves into the tile on the edge of the crease it is moved vertically or horizontally, depending on which edge is closest, to the next tile that is outside the crease.


ColdPangaea.PNG

TemperatePangaea.PNG
TropicalPangaea.PNG
Temperate2NS.PNG
3NS.PNG
4NS.PNG
EW.PNG
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LPlate2
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