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%%%% hyprb_03.ldf |
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%%%% Created by Laurence D. Finston (LDF) Mon Nov 28 16:06:23 CET 2005 |
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%% * (1) Copyright and License. |
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%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. |
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%%%% Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation |
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%%%% GNU 3DLDF is free software; you can redistribute it and/or modify |
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%%%% it under the terms of the GNU General Public License as published by |
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%%%% the Free Software Foundation; either version 3 of the License, or |
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%%%% (at your option) any later version. |
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|
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%%%% GNU 3DLDF is distributed in the hope that it will be useful, |
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%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of |
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%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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%%%% GNU General Public License for more details. |
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|
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%%%% You should have received a copy of the GNU General Public License |
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%%%% along with GNU 3DLDF; if not, write to the Free Software |
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%%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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|
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%%%% GNU 3DLDF is a GNU package. |
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%%%% It is part of the GNU Project of the |
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%%%% Free Software Foundation |
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%%%% and is published under the GNU General Public License. |
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%%%% See the website http://www.gnu.org |
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%%%% for more information. |
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%%%% GNU 3DLDF is available for downloading from |
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%%%% http://www.gnu.org/software/3dldf/LDF.html. |
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|
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%%%% Please send bug reports to Laurence.Finston@gmx.de |
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%%%% The mailing list help-3dldf@gnu.org is available for people to |
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%%%% ask other users for help. |
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%%%% The mailing list info-3dldf@gnu.org is for the maintainer of |
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%%%% GNU 3DLDF to send announcements to users. |
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%%%% To subscribe to these mailing lists, send an |
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%%%% email with ``subscribe <email-address>'' as the subject. |
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|
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%%%% The author can be contacted at: |
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|
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%%%% Laurence D. Finston |
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%%%% c/o The Free Software Foundation, Inc. |
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%%%% 51 Franklin St, Fifth Floor |
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%%%% Boston, MA 02110-1301 |
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%%%% USA |
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%%%% Laurence.Finston@gmx.de |
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%% *** (3) Classifying `points' with respect to a `hyperbola' using |
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%% the `location' operator. |
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%% |
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%% LDF 2005.11.28. |
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verbatim_metapost "verbatimtex \magnification=\magstep5 \font\large=cmr12 etex"; |
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pickup pencircle scaled (.75mm, .75mm); |
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beginfig(1); |
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hyperbola h[]; |
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set h0 with_max_extent 10; |
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set h1 with_max_extent 7; |
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|
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point p[]; |
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numeric L[]; |
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%% **** (4) On hyperbola segment: |
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p0 := get_point 32 h1; |
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L0 := p0 location h1; |
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message "L0:"; |
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show L0; |
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%% **** (4) On hyperbola, but not segment: |
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p1 := get_point 5 h0; |
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L1 := p1 location h1; |
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message "L1:"; |
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show L1; |
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|
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%% **** (4) Between center and one of the foci: |
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p2 := (.5, 0, 3); |
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L2 := p2 location h1; |
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message "L2:"; |
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show L2; |
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|
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%% **** (4) Within the region enclosed by the branches of |
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%% one of the halves of the hyperbola segment. |
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p3 := p0 rotated (180, 0, 180) shifted -1; |
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L3 := p3 location h1; |
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message "L3:"; |
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show L3; |
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%% **** (4) Within the region enclosed by the branches of |
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%% one of the halves of the hyperbola, but not the segment. |
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p4 := p1 rotated (180, 0, 180) shifted -1; |
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L4 := p4 location h1; |
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message "L4:"; |
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show L4; |
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%% **** (4) `point' is coplanar with the hyperbola, but does not lie on the curve, |
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%% within one of the regions enclosed by the branches, or between the branches. |
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%% |
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p5 := p1 rotated 180 shifted -1; |
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L5 := p5 location h1; |
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message "L5:"; |
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show L5; |
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%% **** (4) `point' is not coplanar with the hyperbola. |
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p6 := p0 shifted (-1, 1, -5); |
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L6 := p6 location h1; |
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message "L6:"; |
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show L6; |
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%% **** (4) Drawing commands. |
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pickup pencircle scaled (.75mm, .75mm); |
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draw h0 dashed with_dots; |
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draw h1 with_color blue; |
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%% **** (4) Labels. |
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pickup pencircle scaled (2mm, 2mm); |
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for i = 0 upto 6: |
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drawdot p[i] with_color red; |
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endfor; |
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string s; |
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s := "$p_0$, $l = " & decimal L[0] & "$"; |
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label.rt(s, p0 shifted .25); |
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s := "$p_1$, $l = " & decimal L[1] & "$"; |
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label.lft(s, p1 shifted -.25); |
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s := "\setbox0=\hbox{$l = " & decimal L[2] & "$}\vbox{\hbox to \wd0{\hfil$p_2$,\hfil}\box0}"; |
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label.top(s, p2 shifted (0, 0, .25)); |
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s := "$p_3$, $l = " & decimal L[3] & "$"; |
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label.lft(s, p3 shifted -.25); |
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s := "$p_4$, $l = " & decimal L[4] & "$"; |
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label.lft(s, p4 shifted -.25); |
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s := "$p_5$, $l = " & decimal L[5] & "$"; |
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label.lft(s, p5 shifted -.25); |
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s := "\setbox0=\hbox{$p_6$ ($y \\neq 0$),}\vbox{\copy0\hbox to \wd0{\hfil $l = " |
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& decimal L[6] & "$\hfil}}"; |
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label.bot(s, p6 shifted (0, 0, -.25)); |
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%% **** (4) |
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endfig with_projection parallel_x_z; |
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verbatim_metapost "end"; |
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end; |
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