%%%% 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, 2019, 2020, 2021, 2022, 2023 The Free Software Foundation, Inc. %%%% 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 %%%% the Free Software Foundation; either version 3 of the License, or %%%% (at your option) any later version. %%%% GNU 3DLDF is distributed in the hope that it will be useful, %%%% but WITHOUT ANY WARRANTY; without even the implied warranty of %%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %%%% GNU General Public License for more details. %%%% You should have received a copy of the GNU General Public License %%%% 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. %%%% GNU 3DLDF is available for downloading from %%%% http://www.gnu.org/software/3dldf/LDF.html. %%%% Please send bug reports to Laurence.Finston@gmx.de %%%% The mailing list help-3dldf@gnu.org is available for people to %%%% ask other users for help. %%%% The mailing list info-3dldf@gnu.org is for the maintainer of %%%% GNU 3DLDF to send announcements to users. %%%% To subscribe to these mailing lists, send an %%%% email with ``subscribe '' as the subject. %%%% 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;