From - Tue Oct 5 18:22:08 2004 Return-Path: Received: from mail1.cc.huji.ac.il (real-outmail.cc.huji.ac.il [132.64.1.17]) by nef.ens.fr (8.12.11/1.01.28121999) with ESMTP id i95GM4W9012647 for ; Tue, 5 Oct 2004 18:22:04 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by mail1.cc.huji.ac.il (Postfix) with ESMTP id 70931C5415; Tue, 5 Oct 2004 18:22:04 +0200 (IST) Received: from mail1.cc.huji.ac.il (localhost [127.0.0.1]) by localhost (VaMailArmor-2.0.1.16) id 17809-350D1458; Tue, 05 Oct 2004 18:22:04 +0200 Received: by mail1.cc.huji.ac.il (Postfix, from userid 31998) id 63279CAF0A; Tue, 5 Oct 2004 18:22:04 +0200 (IST) Received: from VMS.HUJI.AC.IL (vms.huji.ac.il [128.139.4.12]) by mail1.cc.huji.ac.il (Postfix) with SMTP id 3F47AC5415 for ; Tue, 5 Oct 2004 18:22:04 +0200 (IST) Received: by HUJIVMS via BMAIL (HUyMail-V7f2); Tue, 05 Oct 2004 18:22:04 +0200 Received: by HUJIVMS via BMAIL (HUyMail-V7f2); Tue, 05 Oct 2004 18:21:58 +0200 Date: Tue, 5 Oct 2004 18:21 +0200 Message-id: <05102004182158@HUJIVMS> From: To: metafont@ens.fr MIME-version: 1.0 Content-type: Text/plain; charset=US-ASCII Content-Transfer-Encoding: 7BIT Subject: How to draw a Hex Board? X-Spam-Level: X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.3.3 (nef.ens.fr [129.199.96.32]); Tue, 05 Oct 2004 18:22:05 +0200 (CEST) Hello, I need to draw a HeX board made of 100 hexagons glued together on a romboical board. Some of the hexagons are shaded black and others -- gray. I will appreciate any advice you can provide how to go about it. Thanks in advance, Michael Maschler From - Wed Oct 6 08:51:34 2004 Return-Path: Received: from post-24.mail.nl.demon.net (post-24.mail.nl.demon.net [194.159.73.194]) by nef.ens.fr (8.12.11/1.01.28121999) with ESMTP id i966pWN2037823 for ; Wed, 6 Oct 2004 08:51:33 +0200 (CEST) Received: from boo.demon.nl ([82.161.175.147]:34624 helo=hal.chatalicious.net) by post-24.mail.nl.demon.net with smtp (Exim 4.34) id 1CF5e3-00031b-OP for metafont@ens.fr; Wed, 06 Oct 2004 06:51:27 +0000 Date: Wed, 6 Oct 2004 08:51:43 +0200 From: Taco Hoekwater To: metafont@ens.fr Subject: Re: [metafont] How to draw a Hex Board? Message-Id: <20041006085143.75f24942.taco@elvenkind.com> In-Reply-To: <05102004182158@HUJIVMS> References: <05102004182158@HUJIVMS> Organization: Elvenkind X-Mailer: Sylpheed version 0.9.5 (GTK+ 1.2.10; i586-mandrake-linux-gnu) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.3.3 (nef.ens.fr [129.199.96.32]); Wed, 06 Oct 2004 08:51:33 +0200 (CEST) Michael, Is this because you want to document Hex games, or do you have something else in mind? On Tue, 5 Oct 2004 18:21 +0200 wrote: > > > Hello, > > I need to draw a HeX board made of 100 hexagons glued together > on a romboical board. Some of the hexagons are shaded black and others > -- gray. > > I will appreciate any advice you can provide how to go about it. > > Thanks in advance, > > Michael Maschler > From - Thu Oct 7 18:17:25 2004 Return-Path: Received: from mailhost.uark.edu (mailhost.uark.edu [130.184.5.66]) by nef.ens.fr (8.12.11/1.01.28121999) with ESMTP id i97GHMba037554 for ; Thu, 7 Oct 2004 18:17:23 +0200 (CEST) Received: from mathfolk.uark.edu ([130.184.197.23]) by mailhost.uark.edu (iPlanet Messaging Server 5.2 HotFix 1.21 (built Sep 8 2003)) with ESMTPSA id <0I5800KQ32KX7P@mailhost.uark.edu> for metafont@ens.fr; Thu, 07 Oct 2004 11:17:21 -0500 (CDT) Date: Thu, 07 Oct 2004 11:17:33 -0500 From: Dan Luecking Subject: Re: [metafont] How to draw a Hex Board? In-reply-to: <05102004182158@HUJIVMS> X-Sender: luecking@mail.uark.edu To: metafont@ens.fr Message-id: <5.2.1.1.0.20041007110239.00bcdc80@mail.uark.edu> MIME-version: 1.0 X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Content-type: text/plain; charset=us-ascii; format=flowed Content-transfer-encoding: 7BIT X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.3.3 (nef.ens.fr [129.199.96.32]); Thu, 07 Oct 2004 18:17:23 +0200 (CEST) At 06:21 PM 10/5/2004 +0200, you wrote: >Hello, > >I need to draw a HeX board made of 100 hexagons glued together >on a romboical board. Some of the hexagons are shaded black and others >-- gray. > >I will appreciate any advice you can provide how to go about it. You need to be a little more precise. It is easy to write a formula for the corners and connect them all in a for loop, but first one needs to know what you mean by a rhombical board. I assume you mean the corner hexagons describe a rhombus, but what size? what orientation? I assuming something symmetrical like this (ascii art, use fixed-width font for viewing): /\ / \ \ / \/ but do you want the 60 degree corners at top and bottom or at the sides? How many do you want, or do you want that to be a parameter? How do you wish to specify which ones to shade gray or black? Do you really want metafont (shading gray is hard), or would you rather have metapost code? Regards, Dan Daniel H. Luecking Department of Mathematical Sciences University of Arkansas From - Thu Oct 7 18:43:49 2004 Return-Path: Received: from post-23.mail.nl.demon.net (post-23.mail.nl.demon.net [194.159.73.193]) by nef.ens.fr (8.12.11/1.01.28121999) with ESMTP id i97Ghh5S049583 for ; Thu, 7 Oct 2004 18:43:43 +0200 (CEST) Received: from boo.demon.nl ([82.161.175.147]:42069 helo=hal.chatalicious.net) by post-23.mail.nl.demon.net with smtp (Exim 4.34) id 1CFbMj-000Pft-61 for metafont@ens.fr; Thu, 07 Oct 2004 16:43:41 +0000 Date: Thu, 7 Oct 2004 18:44:02 +0200 From: Taco Hoekwater To: metafont@ens.fr Subject: Re: [metafont] How to draw a Hex Board? Message-Id: <20041007184402.1a839055.taco@elvenkind.com> In-Reply-To: <5.2.1.1.0.20041007110239.00bcdc80@mail.uark.edu> References: <05102004182158@HUJIVMS> <5.2.1.1.0.20041007110239.00bcdc80@mail.uark.edu> Organization: Elvenkind X-Mailer: Sylpheed version 0.9.5 (GTK+ 1.2.10; i586-mandrake-linux-gnu) Mime-Version: 1.0 Content-Type: multipart/mixed; boundary="Multipart_Thu__7_Oct_2004_18_44_02_+0200_0828a0d0" X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.3.3 (nef.ens.fr [129.199.96.32]); Thu, 07 Oct 2004 18:43:43 +0200 (CEST) This is a multi-part message in MIME format. --Multipart_Thu__7_Oct_2004_18_44_02_+0200_0828a0d0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Hi Dan, Here's what I emailed him (offlist, apparently) earlier. Not a complete solution, but it should give a reasonable starting point (MetaPost input btw, i guessed from the 'gray' that that would be acceptable). I've taken my board shape from http://en.wikipedia.org/wiki/Hex, there is a different orientation possible (lower-left edge horizontal) but the basic shape is fixed by the geometry of the hexes. Greetings, Taco Dan Luecking wrote: > At 06:21 PM 10/5/2004 +0200, you wrote: > > > >Hello, > > > >I need to draw a HeX board made of 100 hexagons glued together > >on a romboical board. Some of the hexagons are shaded black and others > >-- gray. > > > >I will appreciate any advice you can provide how to go about it. > > You need to be a little more precise. It is easy to write a formula > for the corners and connect them all in a for loop, but first one needs > to know what you mean by a rhombical board. I assume you mean > the corner hexagons describe a rhombus, but what size? what orientation? > I assuming something symmetrical like this (ascii art, use fixed-width > font for viewing): > /\ > / \ > \ / > \/ > but do you want the 60 degree corners at top and bottom or at the sides? > How many do you want, or do you want that to be a parameter? How do > you wish to specify which ones to shade gray or black? Do you really want > metafont (shading gray is hard), or would you rather have metapost code? > > Regards, > Dan > > > Daniel H. Luecking > Department of Mathematical Sciences > University of Arkansas --Multipart_Thu__7_Oct_2004_18_44_02_+0200_0828a0d0 Content-Type: application/octet-stream; name="hexboard.mp" Content-Disposition: attachment; filename="hexboard.mp" Content-Transfer-Encoding: base64 JSBoZXhib2FyZC5tcCAtLSBkcmF3cyBhIHNpbXBsZSBlbXB0eSBib2FyZCBm b3IgdGhlIGhleCBnYW1lCiUgCgpwcm9sb2d1ZXMgOj0gMTsKCgolIGhvdyB0 byBpbml0aWFsaXplIGFuIGVtcHR5IGJvYXJkCmRlZiBtYWtlYm9hcmQgKGV4 cHIgZGlhbSwgbnVtdGlsZXMpID0KICBiZWdpbmdyb3VwOwogIHNhdmUgeCx5 LHIsYzsKICAlIHNvbWUgdHJpY2tlcnkgdG8gZGVjaWRlIHRoZSBvZmZzZXQg aW4gdGhlIFggZGlyZWN0aW9uCiAgJSB6MiBpcyB0aGUgaGV4IHBvaW50IHRv IHRoZSByaWdodCBvZiAoMCwwKS4KICAlIHozIGlzIHRoZSByaWdodC10b3Ag b25lLAogICUgejEgaXMgdGhlIG1pZHBvaW50IG9uIHRoYXQgbGluZS4KICAl IAogIHozID0gKC41ZGlhbSwwKTsKICB6MiA9IHozIHJvdGF0ZWRhcm91bmQg KCgwLDApLDYwKTsKICB6MSA9IC41W3oyLHozXTsKICAlIGxlZnRtb3N0IHBv aW50J3MgaW5pdGlhbCB0cmFuc2xhdGlvbjoKICB4LnN0YXJ0ID0gMS8yZGlh bTsKICB5LnN0YXJ0ID0gKG51bXRpbGVzKnkyKTsKICAlIGZpbGwgdGhlIGFy cmF5IG9mIHBvaW50cwogIGZvciByID0gMSB1cHRvIG51bXRpbGVzOgogICAg eG9mZnNldCA6PSAoKHItMSkqMngxKTsgJSBtb3ZlIHJpZ2h0CiAgICB5b2Zm c2V0IDo9IHkyKnI7ICAgICAgICAlIG1vdmUgdXAKICAgIGZvciBjID0gMSB1 cHRvIG51bXRpbGVzOgogICAgICB0aWxlW3JdW2NdIDo9ICgoeC5zdGFydCAr ICgoYy0xKSoyeDEpK3hvZmZzZXQpLCgoeS5zdGFydC15MipjKSt5b2Zmc2V0 KSk7CiAgICBlbmRmb3I7CiAgZW5kZm9yOwogIGVuZGdyb3VwOwplbmRkZWY7 CgolIGhvdyB0byBkcmF3IHRoZSBlbXB0eSBib2FyZCAKZGVmIGRyYXdib2Fy ZCAoZXhwciBkaWFtLG51bXRpbGVzKSA9CiAgYmVnaW5ncm91cDsKICBzYXZl IHIsYzsKICBmb3IgciA9IDEgdXB0byBudW10aWxlczoKICAgIGZvciBjID0g MSB1cHRvIG51bXRpbGVzOgoJICBsYWJlbCgiKCImIGRlY2ltYWwgciAmIiwi ICYgZGVjaW1hbCBjICYgIikiLHRpbGVbcl1bY10pOwoJICBkcmF3aGV4KGRp YW0sdGlsZVtyXVtjXSk7CiAgICBlbmRmb3I7CiAgZW5kZm9yOwogIGVuZGdy b3VwOwplbmRkZWY7CgolIGhvdyB0byBkcmF3IGEgc2luZ2xlIGhleCB0aWxl CmRlZiBkcmF3aGV4IChleHByIGRpYW0sIG1pZHBvaW50KSA9IAoJYmVnaW5n cm91cDsJCglzYXZlIHgseTsKCXoxID0gKHhwYXJ0IG1pZHBvaW50ICsgLjVk aWFtLHlwYXJ0IG1pZHBvaW50KTsKCXoyID0gejEgcm90YXRlZGFyb3VuZCht aWRwb2ludCw2MCk7Cgl6MyA9IHoyIHJvdGF0ZWRhcm91bmQobWlkcG9pbnQs NjApOwoJejQgPSB6MyByb3RhdGVkYXJvdW5kKG1pZHBvaW50LDYwKTsKCXo1 ID0gejQgcm90YXRlZGFyb3VuZChtaWRwb2ludCw2MCk7Cgl6NiA9IHo1IHJv dGF0ZWRhcm91bmQobWlkcG9pbnQsNjApOwoJZHJhdyB6MS0tejItLXozLS16 NC0tejUtLXo2LS1jeWNsZTsKCWVuZGdyb3VwOwplbmRkZWY7CgoKJSBnbG9i YWwgYXJyYXkgZm9yIGFsbCB0aWxlIGNlbnRlcnBvaW50cwpwYWlyIHRpbGVb XVtdOwoKbWFrZWJvYXJkKDUwLDExKTsKCmJlZ2luZmlnKDEpOwpwaWNrdXAg cGVuY2lyY2xlIHNjYWxlZCAyOwpkcmF3Ym9hcmQoNTAsMTEpOwplbmRmaWc7 CgplbmQ7Cg== --Multipart_Thu__7_Oct_2004_18_44_02_+0200_0828a0d0--