From - Wed Nov 2 19:36:53 2005 Return-Path: Received: from mailer.gwdg.de (mailer.gwdg.de [134.76.10.26]) by nef2.ens.fr (8.13.2/1.01.28121999) with ESMTP id jA2IajfC067916 for ; Wed, 2 Nov 2005 19:36:47 +0100 (CET) X-Envelope-To: Received: from gwdu71.gwdg.de ([134.76.8.21]) by mailer.gwdg.de with esmtp (Exim 4.54) id 1EXNTT-0002NZ-Jz; Wed, 02 Nov 2005 19:36:40 +0100 Received: from localhost by gwdu71.gwdg.de (8.11.1/1.1.29.3/16Jun03-0924AM) id jA2Iadw0000251253; Wed, 2 Nov 2005 19:36:39 +0100 (MET) X-Authentication-Warning: gwdu71.gwdg.de: lfinsto1 owned process doing -bs Date: Wed, 2 Nov 2005 19:36:38 +0100 (MET) From: Laurence Finston To: liste metafont , help-3dldf , metapost@tug.org Subject: Constructing ellipse from 4 points Message-ID: MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="352865414-1357351762-1130956598=:250965" X-Virus-Scanned: (clean) by exiscan+sophie X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Wed, 02 Nov 2005 19:36:47 +0100 (CET) X-Spam-Checker-Version: SpamAssassin 3.0.2 (2004-11-16) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.2 This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. Send mail to mime@docserver.cac.washington.edu for more info. --352865414-1357351762-1130956598=:250965 Content-Type: TEXT/PLAIN; charset=X-UNKNOWN Content-Transfer-Encoding: QUOTED-PRINTABLE Hello, I'm a bit stuck and hoping someone here will be able to help me. The attached PostScript file contains illustrations of my attempts to find the intersection of an ellipsoid with a plane. The ellipsoid e: length along the x-axis: 10cm length along the y-axis: 5cm length along the z-axis: 7cm center at the origin, rotated 15=B0 about the y-axis, then shifted -1cm along the x-axis (center (-1, 0, 0)). The square s: center at origin, lying in x-z plane side length: 15cm Then, rotated 15=B0 about the y-axis and 45=B0 about the z= -axis, and shifted 1cm along the x-axis (center (-1, 0, 0)). The points h0, h1, and v0 ... v5 all lie in the plane of s. The points h0 and h1 are on one of the ellipses on e, and the points v0 and v1 are on another one, perpendicular to the first. These four points therefore lie on the ellipse that represents the intersection of the ellipsoid and the plane. In more nicely behaved cases, the polygon "v5, v4, v3, v2" is rectangular, and it seemed that its enclosed ellipse was the one I was looking for. However, in this case (and others), it is not, as can be seen from the projections onto the x-z and z-y planes. It seems to me that it ought to be possible to construct an ellipse from the four points v0, v1, h0, and h1. Does anyone here know how, or know where I could look to find out? Any help would be much appreciated. Laurence Finston --352865414-1357351762-1130956598=:250965 Content-Type: APPLICATION/octet-stream; name="ellppln0.ps.gz" Content-Transfer-Encoding: BASE64 Content-ID: Content-Description: Content-Disposition: attachment; filename="ellppln0.ps.gz" H4sICDMGaUMAA2VsbHBwbG4wLnBzAO29a5PcOJYl+N1/hY/ttJk01gwRBEmQ 1bVp7c+eMuvKri1lV2dPbdlapBSSYipSoQ1J+ZjY/O97zrkACDo9QlJN987Y TlWWwt1BEgQu7hv3XvzNf/jd82rz8va7q6q5qFd/8ze7u6vLD7d3v1q//OH6 3fsnf3667i6G/tV6d/vu57vr128+rJu6duvfX768fnF5sz78fLV+fvvqw4+X d1d4+pvrDzdXv1r7/T/ujx+ufrpAJ2j93eXrq/e/Wrfx6z/dvbzCCzbvX1y9 fYm27e3Hty+v377e3v70q3WN/4a2WTs3Olzb3774+P3V2w+/u3x3dff8+r+x n0uPC4e3L3e33/PS+9Xf7P/wm989/5er79j7r9ZPfvzxx4s7G+DVz1cXL26/ fxrv4SOXb1/+4/XbqzjDdXU7DRc/0/f4wO8u7y6/v/pwdYf3vnx3/b/3df23 a3T47u7q/furl/Gu57cf716gx/U3V9+ubz9+ePdRYOounLuom1+50XMu26vX 129/d3f74vnVh1+t8Y4XF+/ubld/8x9Wz/Dc/vrFh7Wv6/VLfnl59WqdGr/j c8++vkfbL/j3bHv/3fXbl7zll6+fPb9HP2/w5dv756uvf9k+29y//PgOn9/8 /v7D3eXb9zeXH65w+fr9zfv1q8ub91frr5/98B6QBIjXoVl///EGLW/UMlx0 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jA2JAHHU078161 for ; Wed, 2 Nov 2005 20:10:19 +0100 (CET) X-Envelope-To: Received: from gwdu71.gwdg.de ([134.76.8.21]) by mailer.gwdg.de with esmtp (Exim 4.54) id 1EXNzw-0004OV-KC; Wed, 02 Nov 2005 20:10:13 +0100 Received: from localhost by gwdu71.gwdg.de (8.11.1/1.1.29.3/16Jun03-0924AM) id jA2JACH0000251714; Wed, 2 Nov 2005 20:10:12 +0100 (MET) X-Authentication-Warning: gwdu71.gwdg.de: lfinsto1 owned process doing -bs Date: Wed, 2 Nov 2005 20:10:12 +0100 (MET) From: Laurence Finston To: Brooks Moses cc: liste metafont , help-3dldf , metapost@tug.org Subject: Re: [metapost] Constructing ellipse from 4 points In-Reply-To: <4.3.1.2.20051102105319.026518b0@cits1.stanford.edu> Message-ID: References: <4.3.1.2.20051102105319.026518b0@cits1.stanford.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Virus-Scanned: (clean) by exiscan+sophie X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Wed, 02 Nov 2005 20:10:19 +0100 (CET) X-Spam-Checker-Version: SpamAssassin 3.0.2 (2004-11-16) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.2 On Wed, 2 Nov 2005, Brooks Moses wrote: > A Google search on "ellipse construct 'four points'" finds the following links: > > http://steiner.math.nthu.edu.tw/ne01/whw/Ellipse1/part2.htm > http://mathworld.wolfram.com/ConicSection.html > http://mathworld.wolfram.com/Ellipse.html Aha! I just searched for "ellipse constructions" and found a lot of sites that didn't look too promising. Thanks. > > The short form is that, to construct an ellipse, you need either five > points, four points and a tangent line, or four points and knowledge of the > direction of the major and minor axes. I can get more points by finding the intersections of the plane with more of the ellipses on the ellipsoid, and I can get as many of those as I want. > Beyond that, I don't know. My guess is that finding the direction of the > major and minor axes and using that construction is the way to go. Thank you for your quick answer. Laurence From - Mon Nov 28 12:29:38 2005 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.1.0 Received: from macker.loria.fr (macker.loria.fr [152.81.1.70]) by nef2.ens.fr (8.13.2/1.01.28121999) with ESMTP id jARIN1HZ097064 for ; Sun, 27 Nov 2005 19:23:01 +0100 (CET) X-Envelope-To: Received: from localhost.loria.fr (localhost [127.0.0.1]) by localhost (Postfix) with ESMTP id B1A3D5ED65; Sun, 27 Nov 2005 19:23:01 +0100 (CET) X-Amavix: Anti-virus check done by ClamAV X-Amavix: Scanned by Amavix Received: from bar.loria.fr (bar.loria.fr [152.81.2.13]) by macker.loria.fr (Postfix) with ESMTP id EAC865ED65; Sun, 27 Nov 2005 19:23:00 +0100 (CET) Received: (from roegel@localhost) by bar.loria.fr (8.9.3/8.9.3/8.9.3-client/JCG) id TAA13492; Sun, 27 Nov 2005 19:23:00 +0100 (MET) Date: Sun, 27 Nov 2005 19:23:00 +0100 From: Denis Roegel To: metafont@ens.fr Cc: Denis Roegel Subject: metapost font extraction question Message-ID: <20051127192300.B13064@bar.loria.fr> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.1i X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Sun, 27 Nov 2005 19:23:01 +0100 (CET) Hi, I am trying to work through the analysis of fonts in pictures, and I have a problem with the positioning of labels. More specifically, I am not able to reposition a label from the information I get using the xpart, ypart, etc., as indicated in the graph manual. Below is an example showing my problem. I want both `Hello's to appear at the same place. Am I forgetting something or is this a metapost bug? Thanks, Denis def reconstructlabel(expr p)= for i within p: transform T; xpart T=xpart i;ypart T=ypart i; xxpart T=xxpart i;xypart T=xypart i; yxpart T=yxpart i;yypart T=yypart i; draw thelabel(textpart i,origin transformed T) withcolor red; endfor; setbounds currentpicture to pathpart p; enddef; beginfig(1); picture p; z0=origin; label.bot(btex Hello etex,z0); p=currentpicture; currentpicture:=nullpicture; reconstructlabel(p); draw p; endfig; end From - Mon Nov 28 20:05:07 2005 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.1.0 Received: from mail.gmx.net (mail.gmx.de [213.165.64.20]) by nef2.ens.fr (8.13.2/1.01.28121999) with SMTP id jASJ4xvP030345 for ; Mon, 28 Nov 2005 20:05:03 +0100 (CET) X-Envelope-To: Received: (qmail invoked by alias); 28 Nov 2005 19:04:57 -0000 Received: from p54AC2A16.dip0.t-ipconnect.de (EHLO hahepc1.hahe) [84.172.42.22] by mail.gmx.net (mp019) with SMTP; 28 Nov 2005 20:04:57 +0100 X-Authenticated: #6218946 Received: from hahe (helo=localhost) by hahepc1.hahe with local-esmtp (Exim 4.50) id 1EgoIw-0001A0-SX; Mon, 28 Nov 2005 20:04:46 +0100 Date: Mon, 28 Nov 2005 20:04:46 +0100 (CET) From: Hartmut Henkel To: Denis Roegel cc: metafont@ens.fr Subject: Re: [metafont] metapost font extraction question In-Reply-To: <20051127192300.B13064@bar.loria.fr> Message-ID: References: <20051127192300.B13064@bar.loria.fr> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Y-GMX-Trusted: 0 X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Mon, 28 Nov 2005 20:05:05 +0100 (CET) On Sun, 27 Nov 2005, Denis Roegel wrote: > Below is an example showing my problem. I want both `Hello's to appear > at the same place. Am I forgetting something or is this a metapost > bug? > > Thanks, > > Denis > > def reconstructlabel(expr p)= > for i within p: > transform T; > xpart T=xpart i;ypart T=ypart i; > xxpart T=xxpart i;xypart T=xypart i; > yxpart T=yxpart i;yypart T=yypart i; > draw thelabel(textpart i,origin transformed T) withcolor red; draw thelabel.bot(... and it fits. But you know this :-) > endfor; > setbounds currentpicture to pathpart p; > enddef; > > beginfig(1); > picture p; > z0=origin; > label.bot(btex Hello etex,z0); > p=currentpicture; > currentpicture:=nullpicture; > reconstructlabel(p); > draw p; > endfig; > > end Regards, Hartmut From - Mon Nov 28 20:53:56 2005 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.1.0 Received: from macker.loria.fr (macker.loria.fr [152.81.1.70]) by nef2.ens.fr (8.13.2/1.01.28121999) with ESMTP id jASJrnir049689 for ; Mon, 28 Nov 2005 20:53:51 +0100 (CET) X-Envelope-To: Received: from localhost.loria.fr (localhost [127.0.0.1]) by localhost (Postfix) with ESMTP id 9C6815EA42; Mon, 28 Nov 2005 20:53:47 +0100 (CET) X-Amavix: Anti-virus check done by ClamAV X-Amavix: Scanned by Amavix Received: from bar.loria.fr (bar.loria.fr [152.81.2.13]) by macker.loria.fr (Postfix) with ESMTP id C0D985EA42; Mon, 28 Nov 2005 20:53:46 +0100 (CET) Received: (from roegel@localhost) by bar.loria.fr (8.9.3/8.9.3/8.9.3-client/JCG) id UAA24629; Mon, 28 Nov 2005 20:53:46 +0100 (MET) Date: Mon, 28 Nov 2005 20:53:46 +0100 From: Denis Roegel To: Hartmut Henkel Cc: Denis Roegel , metafont@ens.fr Subject: Re: [metafont] metapost font extraction question Message-ID: <20051128205346.D21751@bar.loria.fr> References: <20051127192300.B13064@bar.loria.fr> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.1i In-Reply-To: ; from hartmut_henkel@gmx.de on Mon, Nov 28, 2005 at 08:04:46PM +0100 X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Mon, 28 Nov 2005 20:53:51 +0100 (CET) On Mon, Nov 28, 2005 at 08:04:46PM +0100, Hartmut Henkel wrote: > draw thelabel.bot(... > and it fits. But you know this :-) Yes, but I don't want to use .bot. The .bot information is somehow stored in T. Denis From - Mon Nov 28 21:57:28 2005 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on sophora.ens.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.1.0 Received: from macker.loria.fr (macker.loria.fr [152.81.1.70]) by nef2.ens.fr (8.13.2/1.01.28121999) with ESMTP id jASKvPgu072960 for ; Mon, 28 Nov 2005 21:57:25 +0100 (CET) X-Envelope-To: Received: from localhost.loria.fr (localhost [127.0.0.1]) by localhost (Postfix) with ESMTP id 2927B61126; Mon, 28 Nov 2005 21:57:25 +0100 (CET) X-Amavix: Anti-virus check done by ClamAV X-Amavix: Scanned by Amavix Received: from bar.loria.fr (bar.loria.fr [152.81.2.13]) by macker.loria.fr (Postfix) with ESMTP id 5D99661126; Mon, 28 Nov 2005 21:57:24 +0100 (CET) Received: (from roegel@localhost) by bar.loria.fr (8.9.3/8.9.3/8.9.3-client/JCG) id VAA00799; Mon, 28 Nov 2005 21:57:23 +0100 (MET) Date: Mon, 28 Nov 2005 21:57:23 +0100 From: Denis Roegel To: Hartmut Henkel Cc: Denis Roegel , metafont@ens.fr Subject: Re: [metafont] metapost font extraction question Message-ID: <20051128215723.A321@bar.loria.fr> References: <20051127192300.B13064@bar.loria.fr> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.1i In-Reply-To: ; from hartmut_henkel@gmx.de on Mon, Nov 28, 2005 at 08:04:46PM +0100 X-Greylist: Recipient e-mail whitelisted, not delayed by milter-greylist-1.5.10 (nef2.ens.fr [129.199.96.32]); Mon, 28 Nov 2005 21:57:25 +0100 (CET) Below is the solution provided by John Hobby. It works! Denis def reconstructlabel(expr p)= for i within p: transform T; xpart T =xpart i; ypart T =ypart i; xxpart T=xxpart i;xypart T=xypart i; yxpart T=yxpart i;yypart T=yypart i; draw (textpart i infont fontpart i) transformed T withcolor red; endfor; setbounds currentpicture to pathpart p; enddef; beginfig(1); picture p; z0=origin; label.bot(btex Hello etex,z0); p=currentpicture; currentpicture:=nullpicture; reconstructlabel(p); draw p; endfig; end