%%%% hyprb_02.ldf
%%%% Created by Laurence D. Finston (LDF) Sun Nov 27 19:20:53 CET 2005
%% * (1) Copyright and License.
%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.
%%%% Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Free Software Foundation
%%%% GNU 3DLDF is free software; you can redistribute it and/or modify
%%%% it under the terms of the GNU General Public License as published by
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%%%% (at your option) any later version.
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%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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%%%% along with GNU 3DLDF; if not, write to the Free Software
%%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
%%%% GNU 3DLDF is a GNU package.
%%%% It is part of the GNU Project of the
%%%% Free Software Foundation
%%%% and is published under the GNU General Public License.
%%%% See the website http://www.gnu.org
%%%% for more information.
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%%%% Please send bug reports to Laurence.Finston@gmx.de
%%%% The mailing list help-3dldf@gnu.org is available for people to
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%%%% The author can be contacted at:
%%%% Laurence D. Finston
%%%% c/o The Free Software Foundation, Inc.
%%%% 51 Franklin St, Fifth Floor
%%%% Boston, MA 02110-1301
%%%% USA
%%%% Laurence.Finston@gmx.de
%% Run these commands:
%% 3dldf hyprb_02.ldf
%% mpost hyprb_02
%% tex hyprb_02.txt
%% dvips -o hyprb_02.ps hyprb_02.dvi
%% gv hyprb_02.ps &
%% *** (3) The intersection points of a `hyperbola' `h' and a linear `path' `q',
%% such that `h' and `q' are coplanar, and the slope of `q' is infinite.
%%
%% LDF 2005.11.27.
verbatim_metapost "verbatimtex \magnification=\magstep5 \font\large=cmr12 etex";
pickup pencircle scaled (.75mm, .75mm);
focus f;
set f with_position (-5, 10, -20) with_direction (-5, 10, 100) with_distance 15;
beginfig(1);
hyperbola h;
set h with_max_extent 10;
transform t;
t := identity rotated (45, 45);
path q[];
q0 := ((-10, 0) -- (10, 0)) rotated (0, 90) shifted 2;
%q0 *= h *= t;
draw h;
draw q0;
bool_point_vector bpv;
bpv := h intersection_points q0;
pen p;
p := pencircle scaled (1.5mm, 1.5mm);
if true: % false
if size bpv > 0:
point A;
A := bpv0;
drawdot bpv0 with_color red with_pen p;
label.lrt("$i_0$", bpv0); % A shifted (0, 0, .2)
fi;
if size bpv > 1:
drawdot bpv1 with_color red with_pen p;
label.urt("$i_1$", bpv1);
fi;
fi;
endfig with_projection parallel_x_z;
verbatim_metapost "end";
end;