#### orthoceros

##### Chieftain

- Joined
- Aug 14, 2007

- Messages
- 45

*since then*. So let’s try to finally realize it:

**Goals**

**Make it possible to play Civilization on a**Get rid of the unrealistic cylindrical or donut maps and open a new strategic dimension by allowing units to move over the poles.*really spherical planet.*- All map locations will be
*locally strategically identical*, i.e. each tile will have the same number of direct neighbours. - Most algorithms of the game engine for 2D hexagonal maps can be
*reused 1:1*on the spherical map. Only exception: The path finding algorithm and the distance-in-tiles algorithm need to be adapted for an octahedron base geometry. With these exceptions and from a coding perspective, the only necessary*changes are of purely graphical nature*. - The distance-in-tiles around the equator will be the same as for the circle through the North and South Pole. On the Earth map,
*all local artifacts will be placed either in ice (at the poles) or in the oceans*.

**Problems**

- The Civilization game mechanics require that the map is discrete, i.e. consisting of a finite number of
*tiles*. A continuous distance/area tile-less Civilization engine is not available today. - All tiles must be equal and have the
*same amount of neighboring tiles*, because else not all locations would be strategically identical, which would be weird from a player’s perspective. - Even if one allowed for e.g. a few pentagons in a map otherwise consisting of hexagons (which has been discussed in other threads on this forum), it would be complicated to adapt all algorithms of the game engine so that they can cope with these irregularities.
- The central problem is: It is
to tessellate the surface of a sphere with only hexagonal tiles (or with only n-gons for arbitrary n≥4). For more information on this, have a look at http://en.wikipedia.org/wiki/Tessellation and http://en.wikipedia.org/wiki/Platonic_solid.**mathematically impossible**

**Solution**

- From a mathematical perspective the solution is to
*allow some tiles to slightly*. (“It is not possible to tessellate the sphere with only hexagons, but a bit more than just the sphere is again possible.”**overlap** - Using an
*octahedron as base geometry*, we will only need overlapping tiles at the North and the South Pole and at four equidistant locations around the equator. On the earth all of these artifacts can be*placed either in ice (at the two poles) or in the oceans*. - At each of these locations 4 hexagons overlap a bit, but the centers of these four tiles are still free of any overlapping. Thus the units on these tiles can be displayed just fine as on any other tile. The terrain of these tiles will need graphical blending. (The Civ V screenshots already show graphical blending for the non-overlapping tiles, so not
*much additional development effort is required*here).