Query for "surrounding hex tiles" based on axial coordinates - sql

Question

After reading Red Blob Games' excellent article on heaxgon tile maps and their coordinates.
I am wondering how one would write a SQL-query that returns the tiles surrounding a centered tile up to a range of X. (assuming the "axial coordinates" covered in the article)
A simple idea I first had was
WHERE x BETWEEN tile_x - 1 AND tile_x + 1 AND y BETWEEN tile_y - 1 AND tile_y + 1
But this will return too many tiles, in a way that creates a shape more like a rhombus rather than a circle, which is what I need.
Unfortunately, I haven't found a conclusive answer to this, maybe someone here can give me a hint.
I already thought about some tricks on the sum of the coordinates and wether they are larger of lower than the range, but this won't work with the axial coordinates.

Answer 1

From the diagrams in the linked article, it seems that something like
where (x between tile_x and tile_x + 1) and (y between tile_y - 1 and tile_y + 1)
or (x = tile_x - 1) and (y = tile_y)
should work
If you want to find the tiles (tile_x, tile_y) within a distance n from a given tile (x, y), it will be easier if the x coordinate is modified by adding 0.5 to the x coordinate of each row having an odd distance from the given tile, such that the symmetry is increased:
-1.5 -0.5 0.5 1.5
-2 -1 0 1 2
-2.5 -1.5 -0.5 0.5 1.5 2.5
-3 -2 -1 0 1 2 3
-2.5 -1.5 -0.5 0.5 1.5 2.5
-2 -1 0 1 2
-1.5 -0.5 0.5 1.5
This can be achieved using the expression tile_x + 0.5 * tile_y%2
As the number of tiles within the given distance is reduced by one
from row to row, the limits of (modified) x coordinates in a given
row is n - abs(tile_y - y)/2.
Then the tiles is within a distance n if
abs(tile_y - y) <= n
and abs(tile_x - x + 0.5 * (tile_y-y)%2) <= n - abs(tile_y - y)/2
In sql:
SELECT tile_x, tile_y
FROM tiles
WHERE ABS(tile_y - y) <= n
AND ABS(tile_x - x +0.5*(tile_y-y)%2) + ABS(tile_y - y) / 2 <= n

Answer 2

After some more reading, I found that the article I linked actually alread solves that problem, although somewhat hidden, so here is a more "straight forward" answer.
(Nonetheless, Terje D.'s answer works fine, I just post this because I feel it's a little easier to understand than the "sorcery" of his answer)
In the article from Red Blob Games, he actually describes the formula that calculates the distance between two given hexes:
function hex_distance(Hex(q1, r1), Hex(q2, r2)) {
return (abs(q1 - q2) + abs(r1 - r2)
+ abs(q1 + r1 - q2 - r2)) / 2;
}
I translated this into a function in MySQL
CREATE FUNCTION `rangeBetweenTiles`(tile1q int, tile1r int, tile2q int, tile2r int) RETURNS int(11)
DETERMINISTIC
BEGIN
RETURN (abs(tile1q - tile2q) + abs(tile1r - tile2r)
+ abs(tile1q + tile1r - tile2q - tile2r)) / 2;
END
And use this in another function:
CREATE FUNCTION `isInRange`(tile1q int, tile1r int, tile2q int, tile2r int, `range` Int) RETURNS tinyint(1)
DETERMINISTIC
BEGIN
RETURN rangeBetweenTiles(tile1q, tile1r, tile2q, tile2r) <= `range`;
END
Which can then be used very easily in a select statement:
select *
from tiles
where isInRange(:tile_q, :tile_r, positionQ, positionR, :n)
And it works perfectly fine for any :n