%%%% hyprb_04.ldf
%%%% Created by Laurence D. Finston (LDF) Mon Nov 28 17:37:19 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 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 
%%%% 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. 
%%%% It is also available from 
%%%% http://www.dante.de/software/ctan/, the Dante www-server  
%%%% and from http://wwwuser.gwdg.de/~lfinsto1, 
%%%% the author's website.  

%%%% Please send bug reports to lfinsto1@gwdg.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 <email-address>'' 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 

%%%% lfinsto1@gwdg.de 
%%%% s246794@stud.uni-goettingen.de 


%% *** (3) The intersection points of a `hyperbola' `h' and a linear `path' `q',
%%         such that `h' and `q' are non-coplanar.
%%
%%         LDF 2005.11.28.

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; 

picture save_picture;

beginfig(1); 
hyperbola h;
set h with_max_extent 10;

transform t;

t := identity shifted (0, 0, 3);

path q[];

point p[];
p0 := get_point 30 h;
p1 := p0 shifted (-2, -5, -1);
p2 := mediate(p1, p0, 2);

q0 := p1 -- p2;
q1 := q0 rotated (0, 100) shifted -2;

h *= q0 *= t;

draw h with_color blue;
draw q0;
draw q1;

bool_point_vector bpv;

bpv := h intersection_points q0;

if size bpv > 0:
    p3 := bpv0;
fi;

clear bpv;

bpv := h intersection_points q1;

message "bpv:";
show bpv;

if size bpv > 0:
    p4 := bpv0;
fi;

%% **** (4) Labels.

pickup pencircle scaled (1.5mm, 1.5mm); 

drawdot p3 with_color red;
label.lrt("$i_0$, {\\tt true}", p3 shifted .25);

drawdot p4 with_color red;
label.lft("$i_1$, {\\tt false}", p4 shifted -.25);

label.rt("$q_0$", (get_point 1 q0) shifted (.225, -.75)); 
label.lft("$q_1$", (get_point 1 q1) shifted (-.225, -.75)); 




save_picture := current_picture;


endfig with_focus f no_sort;

verbatim_metapost "end";
end;

beginfig(2);
output save_picture with_projection parallel_x_y;  
endfig;

beginfig(3);
output save_picture with_projection parallel_x_z;  
endfig;

beginfig(4);
output save_picture with_projection parallel_z_y;  
endfig;

verbatim_metapost "end";

end;