%%%% prbla_05.ldf %%%% Created by Laurence D. Finston (LDF) Thu Nov 17 22:28:24 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 prbla_05.ldf %% mpost prbla_05 %% tex prbla_05.txt %% dvips -o prbla_05.ps prbla_05.dvi %% gv prbla_05.ps & %% *** (3) The intersection of a `parabola' and a linear `path'. %% So far, I've only programmed the coplanar case. %% LDF 2005.11.17. verbatim_metapost "verbatimtex \magnification=\magstep5 \font\large=cmr12 etex"; focus f; set f with_position (0, 10, -20) with_direction (0, 10, 100) with_distance 15; pickup pencircle scaled (1mm, 1mm); beginfig(1); parabola p; set p with_parameter 3 with_extent 7; path q; q := ((-5, 0, -5) -- (7, 0, 12)) shifted (5, 0, -2); draw p with_color blue; draw q; pickup pencircle scaled (2mm, 2mm); drawdot get_vertex p; drawdot get_focus p; label.lft("$v$", get_vertex p); label.rt("$f$", get_focus p); point_vector pv; pv := p intersection_points q; if size pv > 0: drawdot pv0 with_color red; label.lrt("$i_0$", pv0); fi; if size pv > 1: drawdot pv1 with_color red; label.lft("$i_1$", pv1 shifted -.333); fi; endfig with_projection parallel_x_z; verbatim_metapost "end"; end;