[Freeciv-Dev] Re: (PR#3936) introducing native coordinates

[Jason Dorje Short <vze49r5w@xxxxxxxxxxx>]

Raimar Falke wrote:
> To understand native coordinates it is necessary to understand
> iso-maps. And the latter is the problem. I did never understood
> them. Please be gentle with me.
Understanding iso-native coordinates does require understanding iso-maps.

> This is what I think iso-maps are: they are a normal map rotated by
> 45° (pi/4). I think that you also need to rotate the directions (enum
> direction8) for this.
The rotation is -pi/4.  That way when the iso-view GUI rotates things by 
pi/4 it looks flat.
The directions *are* rotated, yes.  Note that the DIR_D[XY] arrays would 
have to be changed for native coordinates, and they would be different 
between iso and non-iso maps.  The conclusion is that native coordinates 
are not good for local operations like moving in a single direction, and 
these are best done in map coordinates.

Side note: other projects use isometric coordinates as their *only* 
coordinate system.  For instance Freecol does this, and I've read 
several articles about it.  The disadvantage of this is:
  - Even for an iso-map, isometric coordinates as not good for some 
things.  Look at freecol's implementation of the map_distance() 
function, for instance.
  - This would not work for non-iso maps, which freeciv uses (and wants 
to continue to use).
> How far is this from the truth? If this is near the truth why can't we
> just leave the storage the same of the tile and just change all the
> other operations (direction to dir_dx/dir_dy offset and so on)?
>
> Also can you help me with these:
Very close.

> Normal map (with non-iso tileset):
>  012
>  345
>  678
>
> Normal map (with iso tileset):
>    0
>   3 1
>  6 4 2
>   7 5
>    8
>
> Iso-map (with non-iso tileset): is this possible at all?  It should
> look like this:
>
>    0
>   3 1
>  6 4 2
>   7 5
>    8
Not quite - the rotation is -pi/4, and the coordinates are not sparse. 
So it is
   25
  148
 037
  6

Remember, this is non-iso view so each tile is oriented cardinally.

> but how can this be mapped to a compact grid? Both of
>
>    0
>    31
> ...
> and
>    0
>   31
> look wrong.
See below.

> Iso-map (with iso tileset): ??
>   0 1 2
>    3 4 5
>   6 7 8
Yep, this is the natural iso-view (as used by the GUI) of the isometric 
map I wrote above.
From here, it is easy to map into a compact grid just by dividing the X 
(or Y) dimension by 2.  So we get
  012
  345
  678

Which is the "native" representation.  It is "native" not because it is 
the most intuitive, but because it is the easiest system to work with 
for most (non-local) low-level operations.
jason