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Topic: Completion of a map by symmetry

gnarfk
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Joined: 2015-01-05, 16:18
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Posted at: 2015-01-21, 16:02

Hello. i'm new to the forum and i apologize for my approximative english, but i have a suggestion for the map editor.

When someone try to build a fair map, and want the chances of winning for any player to be equal, he tries to build something that's looks the same in both sides. But , maybe he miscounted the number of trees or of any ressource at a starting position, or the distance from a player to his closest sea ....

A thing that could help, is a tool that'll allow the editor to build only a part of a map, and to finish the job using a symmetry (axial or central) or a rotation (by half a turn , or 1/3 , 1/4 , 1/6 of a turn) or a translation (by half the size of the map or the third or ...).... This way, all starting positions would have equal chances ...

Edited: 2015-01-21, 16:06

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tuggyne
Joined: 2011-07-22, 00:27
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Posted at: 2015-01-21, 16:20

It's been mentioned before, but I don't think much has come of it yet. Would be nice, though.


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wl-zocker
Joined: 2011-12-30, 17:37
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Posted at: 2015-01-21, 16:26

Welcome to the forum and thank you for this idea. Have a look at https://bugs.launchpad.net/widelands/+bug/647447. There are already ideas on how that can be done, but nobody has found the time to implement that feature face-sad.png

A general note on symmetric maps: Due to the fact that a building's flag always has to be south of it, a perfectly symmetric map is not perfectly fair: The player who has to expand northwards (e.g. to reach gold) can do that faster than the player on the other side (who is expanding southwards). There is not yet a good solution for that problem, so some finetuning will always be needed.

I personally also like non-symmetric maps (e.g. Riverlands), which do not tend to get boring so fast. Of course such maps are not suitable for multiplayer games or tournaments, but as long as they are balanced, they are still fun to play.


"Only few people know how much one has to know in order to know how little one knows." - Werner Heisenberg

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gnarfk
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Posted at: 2015-01-21, 16:29

Thank you for your answers . I'll look at your links face-smile.png


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gnarfk
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Posted at: 2015-01-21, 16:39

In the report bug , there is only mention of the symmetry , but not of the rotations .... (the rotations might help to build 3 or 6 players maps , while the translations could help building maps for any number of players, and combinations of transformations can also be done)

i had the same thought about flags from buildings, and i have no good answer to it. But at least , the symmetry axle which follows the same direction of the road from a building to its flag could create a symmetry that keeps things fair.

I think neither the symmetry nor the rotations (or translations) are hard to "algebrize" . this could definitly help people to create new maps (you said that playing on symmetric maps is boring , but if you have lots of different maps to play ... that might not be the case)


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wl-zocker
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Posted at: 2015-01-21, 17:32

In the report bug , there is only mention of the symmetry , but not of the rotations

I can think of the following symmetry operations (point group C6v, if you know group theory face-wink.png ):

  • mirroring at one plane (for me, it is easier to think of the map as a 3D object with heights): creates maps for 2 players
  • mirroring at three planes (in the main directions west-east, NW-SE,NE-SW): for 6 players
    • (it is also possible to use the orthogonal planes (north-south and so on), but probably more difficult to implement
  • mirroring at two orthogonal planes (e.g. W-E and N-S) (I am not sure whether that is possible): for 4 players
  • rotation by 180°: for 2 players
  • rotation by 120°: for 3 players
  • rotation by 60°: for 6 players

Of course you can use multiples of the indicated player numbers, but the map is then not completely fair.

But at least , the symmetry axle which follows the same direction of the road from a building to its flag could create a symmetry that keeps things fair.

I have never thought of that, but you are right! However, I assume that the most natural mirror plane would be east-west, so that way would be a bit strange.

I think neither the symmetry nor the rotations (or translations) are hard to "algebrize"

Since the map internally works with Cartesian coordinates, rotation by 60°/120° are not that easy. Furthermore, you have to think about what you do at the borders (to use the symmetry operations, you have to cut the map somewhere, and then it is rectangular, which does not fit to rotation by 60°/120°.


"Only few people know how much one has to know in order to know how little one knows." - Werner Heisenberg

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gnarfk
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Posted at: 2015-01-21, 17:43

i know group theory, i'm math teacher. if you need help to find formulae for rotations or anything , i can do that.

For some numbers of players , we have the problem of borders , but if we stop considering the world as what topologist call "donuts" , we can do the 120° rotations , and the only remaining problem is some "useless land" in the corners ....


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wl-zocker
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Posted at: 2015-01-21, 18:05

i know group theory

I did not expect that face-grin.png

if you need help to find formulae for rotations or anything , i can do that.

There is a section about geometry in our Wiki, maybe that helps you.
Since it might take some time until someone works on this, there is no urgent need to do it. Feel free though.

but if we stop considering the world as what topologist call "donuts" , we can do the 120° rotations , and the only remaining problem is some "useless land" in the corners

I do not know how to cleverly combine the symmetry of a torus with the triangles of Widelands. My idea was therefore cutting the map at its internal borders (where the x or y coordinates are 0) and to work on the emerging rectangle. Ignoring the "useless land" might be the best approach then.


"Only few people know how much one has to know in order to know how little one knows." - Werner Heisenberg

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gnarfk
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Joined: 2015-01-05, 16:18
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Posted at: 2015-01-21, 18:28

wl-zocker wrote:

There is a section about geometry in our Wiki, maybe that helps you.
Since it might take some time until someone works on this, there is no urgent need to do it. Feel free though.

i'm looking at this section.

I do not know how to cleverly combine the symmetry of a torus with the triangles of Widelands.

that's how it is done actually i think ... (and maybe it would be possible to change that to other type of topology, but that's not the point here)

My idea was therefore cutting the map at its internal borders (where the x or y coordinates are 0) and to work on the emerging rectangle. Ignoring the "useless land" might be the best approach then.

it is also possible to fill the useless land with desert or swomp or any unusable terrain type.


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einstein13
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Posted at: 2015-01-22, 10:11

My idea was therefore cutting the map at its internal borders (where the x or y coordinates are 0) and to work on the emerging rectangle. Ignoring the "useless land" might be the best approach then.

it is also possible to fill the useless land with desert or swomp or any unusable terrain type.

I'm not a mathematician, but physycist. I know that rotations aren't very hard for computer: there is only rotation matrix with sin and cos functions. Of course the implementation will be a bit harder, but still possible. But in my opinion the blank spaces should be filled by "background" type of terrain. You should have a possibility to create all the map with one type of terrain and keep it as "background". face-smile.png That would help a lot.


einstein13
calculations & maps packages: http://wuatek.no-ip.org/~rak/widelands/

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