Distance between 2 hexagons on hexagon grid

Question

I have a hexagon grid:

with template type coordinates T. How I can calculate distance between two hexagons?

For example:

dist((3,3), (5,5)) = 3

dist((1,2), (1,4)) = 2

Answer 1

Posting here after I saw a blog post of mine had gotten referral traffic from another answer here. It got voted down, rightly so, because it was incorrect; but it was a mischaracterization of the solution put forth in my post.

Your 'squiggly' axis - in terms of your x coordinate being displaced every other row - is going to cause you all sorts of headaches with trying to determine distances or doing pathfinding later on, if this is for a game of some sort. Hexagon grids lend themselves to three axes naturally, and a 'squared off' grid of hexagons will optimally have some negative coordinates, which allows for simpler math around distances.

Here's a grid with (x,y) mapped out, with x increasing to the lower right, and y increasing upwards.

By straightening things out, the third axis becomes obvious.

The neat thing about this, is that the three coordinates become interlinked - the sum of all three coordinates will always be 0.

With such a consistent coordinate system, the atomic distance between any two hexes is the largest change between the three coordinates, or:

d = max( abs(x1 - x2), abs(y1 -y2), abs( (-x1 + -y1) - (-x2 + -y2) )

Pretty straightforward. But you must fix your grid first!