Path: utzoo!attcan!uunet!nih-csl!lhc!mimsy!haven!uflorida!rex!wuarchive!usc!rutgers!rochester!pt.cs.cmu.edu!sei!firth
From: firth@sei.cmu.edu (Robert Firth)
Newsgroups: comp.sys.mac.games
Subject: Re: Hex distances
Message-ID: <9593@fy.sei.cmu.edu>
Date: 19 Nov 90 13:05:40 GMT
References: <1990Nov17.111429.6250@wuarchive.wustl.edu>
Reply-To: firth@sei.cmu.edu (Robert Firth)
Organization: Software Engineering Institute, Pittsburgh, PA
Lines: 25

Distances on hexagonal tesselations.

Let the distance between the centre of a hex and the centre
of an adjacent hex be 1.  Consider the hexes to be laid out
in successive horizontal rows, so each successive row is
displaced a half unit.

Let the coordinate axes be horizontal and upward right sloping diagonal.
These coordinate axes are at an angle of pi/3, or 60 degrees.

Given two hexes whose coordinates differ by H (horizontal) and
D (diagonal), then we have:

delta_x  =  H + D cos pi/3  =  H + D/2
delta_y  =      D sin pi/3  =  D sqrt(3)/2

Hence the total distance is given by

dist  =  sqrt(delta_x^2 + delta_y^2)

which simplifies to

dist  =  sqrt(H^2 + D^2 + HD)

Hope that helps.