%%%% sphrint_0.ldf
%%%% Created by Laurence D. Finston (LDF) Sun Oct 30 17:47:32 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 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 sending 
%%%% 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 Free Software Foundation, Inc. 
%%%% 51 Franklin St, Fifth Floor 
%%%% Boston, MA  02110-1301  
%%%% USA

%%%% Laurence.Finston@gmx.de


verbatim_metapost "verbatimtex \magnification=\magstep5 etex";


focus f;

set f with_position (-1, 5, -20) with_direction (-1, 5, 10) 
      with_distance 20;

picture frame_picture;
picture axis_picture;

beginfig(0);

pickup pencircle scaled (1mm, 1mm);

axis_x_lft := 9;
axis_x_rt := 9.5;
axis_y_bot := 9;
axis_y_top := 7;
axis_z_front := 13;
axis_z_back := 500;

drawdblarrow (-axis_x_lft, 0) -- (axis_x_rt, 0);
label.bot("x", (axis_x_rt, -.1));

drawdblarrow (0, -axis_y_bot) -- (0, axis_y_top);
label.lft("y", (0, axis_y_top)); 

drawdblarrow (0, 0, -axis_z_front) -- (0, 0, axis_z_back);
label.lft("z", (0, 0, axis_z_back)); 

axis_picture := current_picture;
clear current_picture;
endfig; 

beginfig(0);

h := 14;
v := 11;

draw ((-h, -v) -- (h, -v) -- (h, v) -- (-h, v) -- cycle)
shifted (1, -7);

%; % with_color white;

frame_picture := current_picture;
clear current_picture;
endfig; 

sphere s;
set s with_center (0, -2.75, 0) with_radius 5 with_point_count 64 with_divisions 6;

rotate s (5, 5);

circle c;
rectangle r;
r := unit_rectangle scaled 15;
rotate r (5, 0, 5);
shift r by -.75;

for i = 1 upto 5:
   beginfig(i); 

   output frame_picture with_projection parallel_x_y;

   rotate r (5, 0, 5);

   shift s (0, 1);
   c := s intersection (plane) r;

   filldraw c with_fill_color gray with_draw_color blue;
  
   draw s;

   draw r with_color red;

   output current_picture with_focus f no_sort;   

   clear current_picture;

   output axis_picture with_focus f;   
   
   endfig;
endfor;


%% *** (3) Added parser rule and function for finding the intersection
%%         points of a `sphere' and a linear `path'.

pickup pencircle scaled (1mm, 1mm);

focus f;

set f with_position (-1, 5, -20) with_direction (-1, 5, 10) 
      with_distance 20;

beginfig(5);
drawdot origin;

path p;
p := (-6, -6) -- (10, 10);
rotate p (0, 75);

draw p with_color blue;

sphere s;
set s with_radius 6 with_divisions 10;

rotate s (15, 0, 15);

draw s;

bool_point_vector bpv;

bpv := s intersection_points p;

pickup pencircle scaled (.375cm, .375cm);

drawdot bpv0 with_color red;
drawdot bpv1 with_color red;

point i[];
i0 := bpv0;
i1 := bpv0;
shift i1 (1, 3);;

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

drawarrow i1 -- i0;

i2 := bpv1;
i3 := bpv1;
shift i3 (-1, -1);

drawarrow i3 -- i2;

label.rt("$i_0$",  i1);
label.lft("$i_1$", i3);

endfig with_focus f no_sort;  

verbatim_metapost "end";

end;