%%%% cones01.ldf
%%%% Created by Laurence D. Finston (LDF) Thu Nov  9 21:35:51 CET 2006
%%%% Modified LDF 2006.11.11.

%% * (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) Cones.
%%         The shadow of a double-napped cone.
%%         LDF 2006.11.09.

verbatim_metapost "verbatimtex \magnification=\magstep3 etex";

focus f;
set f with_position (-3, 15, -30) 
   with_direction (-3, 15, 100) with_distance 15; 

picture save_picture;

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

%% **** (4) 

beginfig(1); 

%% ***** (5) 

cone c;

y_value := 12;

set c with_type circular with_type double_napped with_radius 10 with_axis_y y_value
   with_point_count 32 with_divisions 6;

shift c(10, 0, 20);

rectangle r;

r := unit_rectangle scaled (100, 0, 100);
shift r (0, 0, 20);

%% ***** (5) 

point p;
p := (1, 0, 0);
rotate p(0, 0, 32);
rotate p(0, 25);

p *= -1;

%% ***** (5) 

point q[];
path s[];

path proj[];


bool_point_vector bpv;

point apex[];

apex0 := get_apex c;


q0 := apex0;
q0 += p * 10;


s0 := apex0 -- q0;


bpv := s0 intersection_points r;

q2 := bpv0;
q3 := bpv1;



if not is_invalid q2:
  apex1 := q2;

else:
    if not is_invalid q3:
       apex1 := q3;
fi;
fi;


path cap;
path base;

cap  := get_cap c;
base := get_base c;

for i = 0 upto 31:
    q0 := get_point (i) cap;
    q4 := get_point (i) base;
    q1 := q0 + (p * 10);
    s0 := q0 -- q1;
    bpv := s0 intersection_points r;

    q2 := bpv0;
    q3 := bpv1;

    if not is_invalid q2:
       proj0 += q2;
       draw q4 -- apex1 -- q2;
    fi;

    if not is_invalid q3:
       proj0 += q3;
       draw q4 -- apex1 -- q3;
   fi;

endfor;

proj0 += ..;
proj0 += cycle;

draw proj0;


draw c;
%draw r;

%label("point light source:  angle $25^\circ$, elevation $32^\circ$", (5, 0, 0));

save_picture := current_picture;
endfig with_focus f no_sort; 

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

verbatim_metapost "end";
end;