From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 21500 invoked by alias); 16 Jul 2004 01:34:32 -0000 Mailing-List: contact xconq7-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: xconq7-owner@sources.redhat.com Received: (qmail 21493 invoked from network); 16 Jul 2004 01:34:31 -0000 Received: from unknown (HELO mail3.panix.com) (166.84.1.74) by sourceware.org with SMTP; 16 Jul 2004 01:34:31 -0000 Received: from panix5.panix.com (panix5.panix.com [166.84.1.5]) by mail3.panix.com (Postfix) with ESMTP id 69988981C2; Thu, 15 Jul 2004 21:34:31 -0400 (EDT) Received: (from kingdon@localhost) by panix5.panix.com (8.11.6p2-a/8.8.8/PanixN1.1) id i6G1YV527251; Thu, 15 Jul 2004 21:34:31 -0400 (EDT) Date: Fri, 16 Jul 2004 03:07:00 -0000 Message-Id: <200407160134.i6G1YV527251@panix5.panix.com> From: Jim Kingdon To: mcdonald@phy.cmich.edu Cc: xconq7@sources.redhat.com In-reply-to: (message from Eric McDonald on Thu, 15 Jul 2004 12:21:56 -0400 (EDT)) Subject: Re: possibility of emulation References: X-SW-Source: 2004/txt/msg00748.txt.bz2 > Xconq on a Klein Bottle map, anyone? Oh, that's different from hex vs non-hex (and probably easier). We all know flat maps (edges on left, right, top and bottom) - the xconq default. xconq has the start of a cylindrical map (edges on top and bottom, but if you go off the left edge you appear on the right with the same y coordinate). There are plenty of computer games with a doughnut-shaped map (like cylindrical, but wrap around top/bottom as well). (Mathematicians call this one a torus). Now, let's try the Moebius strip. Make it like the cylindrical map, but when you go off the left edge you appear on the right with a y coordinate of "size - origY". So imagine following the top edge to the right (east). As you go off the right, you get to the bottom left corner, and if you keep going east, you follow the bottom edge, and then appear at the top left. Note that you are following the edge, and without moving to the other edge, there is only one edge. Ready for the Klein bottle? Join both edges (as we did with the doughnut). But twist one of the joins as we did for the Moebius strip. Actually, it is probably easier to implement in xconq than it is to visualize. There are some nice pictures at http://www.jcu.edu/math/vignettes/Mobius.htm Looking at the pictures of rectangles with arrows on them should show how it would look on the xconq screen. What all this does for gameplay, I don't know. Might have a big effect, given how easy it is to sneak past the AI at the edge of the map. But maybe the AI would just have another weak spot - I'm not sure whether this weakness of the AI is a matter of geometry or just of the AI not protecting its flanks/rear in general. > local plane approximations of multi-dimensional saddle curves or > spheroidal pieces. (There probably couldn't be any decent, > comprehensible representation beyond a certain zoom factor, so there > would be no world map.) That would be interesting too (in mathematical terms, it is a question of changing the geometry, not just the topology).