%%%% cubd_06.ldf
%%%% Created by Laurence D. Finston (LDF) Fri Dec 16 19:37:47 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 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. 

%%%% 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. 
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%%%% 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 

%%%% Laurence.Finston@gmx.de 
 


%% *** (3) The intersection of a `cuboid' and a `plane'.  It is a `polygon'.
%%         LDF 2005.12.16.

verbatim_metapost "verbatimtex \magnification=\magstep5 etex";

pickup pencircle scaled (.75mm, .75mm);

pen dot_pen;
dot_pen := pencircle scaled (1.5mm, 1.5mm);

focus f;
set f with_position (-10, 15, -30) with_direction (-10, 15, 100) with_distance 20; 

picture save_picture;

beginfig(1); 
cuboid c;

cw := 20;
ch := 16;
cd := 10;

rw := cw + 20;
rd := cd + 14;

c := unit_cuboid scaled (cw, ch, cd);

rectangle r;
r := unit_rectangle scaled (rw, 0, rd) rotated (70, 30)  shifted (4, 1, 4);

transform t;
t := identity rotated (15, 15);

r *= c *= t;

draw c;
draw r with_color red;

plane q;
q := (plane) r;

polygon poly;
poly := c intersection q;
draw poly with_color blue;

point p[];

for i = 0 upto 5:
   p[i] := get_point (i) poly; 
   drawdot p[i] with_color green with_pen dot_pen;
endfor;


label.lrt("$i_0$", p0);  
label.lft("$i_1$",  p1);   
label.lft("$i_2$", p2);   
label.top("$i_3$",  p3);   
label.rt("$i_4$",  p4);   
label.lft("$i_5$",  p5 shifted -.375);   

save_picture := current_picture;

endfig with_focus f no_sort;

point label_pt;
label_pt := (0, -10);


beginfig(2); 
output save_picture with_projection parallel_x_z with_factor .75;
%label("Parallel Projection, X-Z Plane", label_pt shifted 6);
endfig with_projection parallel_x_y;


beginfig(3); 
output save_picture with_projection parallel_x_y with_factor .75;
%label("Parallel Projection, X-Y Plane", label_pt);
endfig with_projection parallel_x_y;

beginfig(4); 
output save_picture with_projection parallel_z_y with_factor .75;
%label("Parallel Projection, Z-Y Plane", label_pt);
endfig with_projection parallel_x_y;

verbatim_metapost "end";
end;