Hexagonal Grids, how do you find which hexagon a point is in?

Question

I have a map made up of rows and columns of hexagons

This isn\'t an actual image of the hex-map I am using,

Answer 1

I've had another look at http://playtechs.blogspot.co.uk/2007/04/hex-grids.html and it is very tidy mathematically.

However Sebastian's approach does seem to cut to the chase, and accomplish the task in remarkably few lines of code.

If you read through the comments section you can find that someone has written a Python implementation at http://gist.github.com/583180

I will repaste that here for posterity:

# copyright 2010 Eric Gradman
# free to use for any purpose, with or without attribution
# from an algorithm by James McNeill at
# http://playtechs.blogspot.com/2007/04/hex-grids.html

# the center of hex (0,0) is located at cartesian coordinates (0,0)

import numpy as np

# R ~ center of hex to edge
# S ~ edge length, also center to vertex
# T ~ "height of triangle"

real_R = 75. # in my application, a hex is 2*75 pixels wide
R = 2.
S = 2.*R/np.sqrt(3.)
T = S/2.
SCALE = real_R/R

# XM*X = I
# XM = Xinv
X = np.array([
    [ 0, R],
    [-S, S/2.]
])
XM = np.array([
    [1./(2.*R),  -1./S],
    [1./R,        0.  ]
])
# YM*Y = I
# YM = Yinv
Y = np.array([
    [R,    -R],
    [S/2.,  S/2.]
])
YM = np.array([
    [ 1./(2.*R), 1./S],
    [-1./(2.*R), 1./S],
])

def cartesian2hex(cp):
    """convert cartesian point cp to hex coord hp"""
    cp = np.multiply(cp, 1./SCALE)
    Mi = np.floor(np.dot(XM, cp))
    xi, yi = Mi
    i = np.floor((xi+yi+2.)/3.)

    Mj = np.floor(np.dot(YM, cp))
    xj, yj = Mj
    j = np.floor((xj+yj+2.)/3.)

    hp = i,j
    return hp

def hex2cartesian(hp):
    """convert hex center coordinate hp to cartesian centerpoint cp"""
    i,j = hp
    cp = np.array([
        i*(2*R) + j*R,
        j*(S+T)
    ])
    cp = np.multiply(cp, SCALE)

return cp