<!-- MHonArc v2.4.4 --> <!--X-Subject: [MUD-Dev] Re: Hex-grid mapping --> <!--X-From-R13: Xnzrf Ivyfba <wjvyfbaNebpurfgre.ee.pbz> --> <!--X-Date: Tue, 1 Dec 1998 20:07:39 -0800 --> <!--X-Message-Id: 9812012258380A.09289@d185d1e96 --> <!--X-Content-Type: text/plain --> <!--X-Reference: 19981201174930.B8275#divcom,slimy.com --> <!--X-Head-End--> <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> <html> <head> <title>MUD-Dev message, [MUD-Dev] Re: Hex-grid mapping</title> <!-- meta name="robots" content="noindex,nofollow" --> <link rev="made" href="mailto:jwilson#rochester,rr.com"> </head> <body background="/backgrounds/paperback.gif" bgcolor="#ffffff" text="#000000" link="#0000FF" alink="#FF0000" vlink="#006000"> <font size="+4" color="#804040"> <strong><em>MUD-Dev<br>mailing list archive</em></strong> </font> <br> [ <a href="../">Other Periods</a> | <a href="../../">Other mailing lists</a> | <a href="/search.php3">Search</a> ] <br clear=all><hr> <!--X-Body-Begin--> <!--X-User-Header--> <!--X-User-Header-End--> <!--X-TopPNI--> Date: [ <a href="msg00883.html">Previous</a> | <a href="msg00885.html">Next</a> ] Thread: [ <a href="msg00883.html">Previous</a> | <a href="msg00887.html">Next</a> ] Index: [ <A HREF="author.html#00884">Author</A> | <A HREF="#00884">Date</A> | <A HREF="thread.html#00884">Thread</A> ] <!--X-TopPNI-End--> <!--X-MsgBody--> <!--X-Subject-Header-Begin--> <H1>[MUD-Dev] Re: Hex-grid mapping</H1> <HR> <!--X-Subject-Header-End--> <!--X-Head-of-Message--> <UL> <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> </UL> <!--X-Head-of-Message-End--> <!--X-Head-Body-Sep-Begin--> <HR> <!--X-Head-Body-Sep-End--> <!--X-Body-of-Message--> <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 </PRE> <!--X-Body-of-Message-End--> <!--X-MsgBody-End--> <!--X-Follow-Ups--> <HR> <ul compact><li><strong>Follow-Ups</strong>: <ul> <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> </UL></LI></UL> <!--X-Follow-Ups-End--> <!--X-References--> <UL><LI><STRONG>References</STRONG>: <UL> <LI><STRONG><A NAME="00883" HREF="msg00883.html">[MUD-Dev] Re: Hex-grid mapping</A></STRONG> <UL><LI><EM>From:</EM> Jon Leonard <jleonard#divcom,slimy.com></LI></UL></LI> </UL></LI></UL> <!--X-References-End--> <!--X-BotPNI--> <UL> <LI>Prev by Date: <STRONG><A HREF="msg00883.html">[MUD-Dev] Re: Hex-grid mapping</A></STRONG> </LI> <LI>Next by Date: <STRONG><A HREF="msg00885.html">[MUD-Dev] Re: Hex-grid mapping</A></STRONG> </LI> <LI>Prev by thread: <STRONG><A HREF="msg00883.html">[MUD-Dev] Re: Hex-grid mapping</A></STRONG> </LI> <LI>Next by thread: <STRONG><A HREF="msg00887.html">[MUD-Dev] Re: Hex-grid mapping</A></STRONG> </LI> <LI>Index(es): <UL> <LI><A HREF="index.html#00884"><STRONG>Date</STRONG></A></LI> <LI><A HREF="thread.html#00884"><STRONG>Thread</STRONG></A></LI> </UL> </LI> </UL> <!--X-BotPNI-End--> <!--X-User-Footer--> <!--X-User-Footer-End--> <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> </LI> </UL> </LI> </UL> </LI> </UL> </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> </UL> </LI> </UL> </LI> </UL></BLOCKQUOTE> </ul> <hr> <center> [ <a href="../">Other Periods</a> | <a href="../../">Other mailing lists</a> | <a href="/search.php3">Search</a> ] </center> <hr> </body> </html>