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<H1>[MUD-Dev] Re: Hex-grid mapping</H1>
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<LI><em>To</em>: <A HREF="mailto:mud-dev#kanga,nu">mud-dev#kanga,nu</A></LI>
<LI><em>Subject</em>: [MUD-Dev] Re: Hex-grid mapping</LI>
<LI><em>From</em>: James Wilson <<A HREF="mailto:jwilson#rochester,rr.com">jwilson#rochester,rr.com</A>></LI>
<LI><em>Date</em>: Tue, 1 Dec 1998 22:54:38 -0500</LI>
<LI><em>Reply-To</em>: <A HREF="mailto:mud-dev#kanga,nu">mud-dev#kanga,nu</A></LI>
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<PRE>
On Tue, 01 Dec 1998, Jon Leonard wrote:
>On Tue, Dec 01, 1998 at 07:51:24PM -0500, James Wilson wrote:
>> this isn't a hex grid. It's a warped square grid. A hex grid has the useful
>> property that any cell has six neighbors, which is often a better fit for
>> tactical simulations than the square grid's four-with-four-diagonals neigbors.
>> For instance, diagonal motion makes a lot more sense in hexes than in squares
>> (assuming one move equals the traversal of one border).
>>
>> You can't tweak your equation to give them six neigbors, so don't try. (The
>> number of neighbors of each cell is a topological invariant, i.e. you can warp
>> space in any smooth way and each square will still have
>> four-with-four-diagonals neighbors.)
>
>Would you have been happier if I'd drawn my hexes like this?
>
> / \ / \ / \ / \
> / \ / \ / \ / \
> | 0,2 | 1,2 | 2,2 | 3,2 |
> | | | | |
> / \ / \ / \ / \ /
> / \ / \ / \ / \ /
> | 0,1 | 1,1 | 2,1 | 3,1 |
> | | | | |
> / \ / \ / \ / \ /
> / \ / \ / \ / \ /
>| 0,0 | 1,0 | 2,0 | 3,0 |
>| | | | |
> \ / \ / \ / \ /
> \ / \ / \ / \ /
>
>Those are really hexagons... And the six neighbors have the coordinate
>deltas I specified. The fact that they don't look pretty in ASCII graphics
>says little about the math.
>
>That they're best stored in memory as a two dimensional array doesn't change
>how the geometry works. Two of the "corner" diagonals are as adjacent as the
>"sides", and the other two diagonals are farther away than with a square
>geometry.
>
>The underlying mathematics are that if you try to do coordinate geometry with
>axes 60 degrees apart, the distance function changes to d=sqrt(x*x-x*y+y*y),
>and the lattice points wind up being the centers of packed hexagons.
nevertheless there are eight neighbors of each node, not six. perhaps he doesn't
care about that.
James
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<li><strong><A NAME="00890" HREF="msg00890.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>
<ul compact><li><em>From:</em> Nathan F Yospe <yospe#hawaii,edu></li></ul>
<li><strong><A NAME="00887" HREF="msg00887.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>
<ul compact><li><em>From:</em> Par Winzell <zell#alyx,com></li></ul>
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<UL><LI><EM>From:</EM> Jon Leonard <jleonard#divcom,slimy.com></LI></UL></LI>
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<ul><li>Thread context:
<BLOCKQUOTE><UL>
<LI><strong><A NAME="00878" HREF="msg00878.html">[MUD-Dev] Hex-grid mapping</A></strong>,
Matthew R. Sheahan <a href="mailto:chaos#crystal,palace.net">chaos#crystal,palace.net</a>, Tue 01 Dec 1998, 07:43 GMT
<UL>
<LI><strong><A NAME="00879" HREF="msg00879.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Jon Leonard <a href="mailto:jleonard#divcom,slimy.com">jleonard#divcom,slimy.com</a>, Tue 01 Dec 1998, 08:16 GMT
<UL>
<LI><strong><A NAME="00882" HREF="msg00882.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
James Wilson <a href="mailto:jwilson#rochester,rr.com">jwilson#rochester,rr.com</a>, Wed 02 Dec 1998, 01:08 GMT
<UL>
<LI><strong><A NAME="00883" HREF="msg00883.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Jon Leonard <a href="mailto:jleonard#divcom,slimy.com">jleonard#divcom,slimy.com</a>, Wed 02 Dec 1998, 01:53 GMT
<UL>
<LI><strong><A NAME="00884" HREF="msg00884.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
James Wilson <a href="mailto:jwilson#rochester,rr.com">jwilson#rochester,rr.com</a>, Wed 02 Dec 1998, 04:07 GMT
<UL>
<LI><strong><A NAME="00887" HREF="msg00887.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Par Winzell <a href="mailto:zell#alyx,com">zell#alyx,com</a>, Wed 02 Dec 1998, 06:48 GMT
</LI>
<LI><strong><A NAME="00890" HREF="msg00890.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Nathan F Yospe <a href="mailto:yospe#hawaii,edu">yospe#hawaii,edu</a>, Wed 02 Dec 1998, 21:45 GMT
</LI>
</UL>
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</LI>
<LI><strong><A NAME="00880" HREF="msg00880.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Ling <a href="mailto:K.L.Lo-94#student,lboro.ac.uk">K.L.Lo-94#student,lboro.ac.uk</a>, Tue 01 Dec 1998, 22:14 GMT
<UL>
<LI><strong><A NAME="00885" HREF="msg00885.html">[MUD-Dev] Re: Hex-grid mapping</A></strong>,
Jon A. Lambert <a href="mailto:jlsysinc#ix,netcom.com">jlsysinc#ix,netcom.com</a>, Wed 02 Dec 1998, 06:02 GMT
</LI>
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