%%%% elpsd_17.ldf
%%%% Created  by Laurence D. Finston (LDF) Tue Dec 13 21:47:16 CET 2005
%%   Modified by Laurence D. Finston (LDF) Fri Dec 16 14:27:59 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 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. 
%%%% 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 

%%%% Laurence.Finston@gmx.de 
 


%% *** (3) The intersection of a `plane' and an `ellipsoid'.
%%         This seems to work now.
%%         LDF 2005.12.15.

verbatim_metapost "verbatimtex \magnification=\magstep5 etex";

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

focus f;
set f with_position (-12, 15, -30) with_direction (-12, 15, 100) with_distance 20; 

picture save_picture;

beginfig(1); 
ellipsoid E;

Ew := 20;
Eh := 16;
Ed := 8;

rw := Ew + 10;
rd := Ed + 15;

set E with_center origin with_axis_x Ew with_axis_y Eh with_axis_z Ed
       with_divisions_x 8 with_divisions_y 8 with_divisions_z 2
       with_point_count 64;


rectangle r[];

%r0 := unit_rectangle scaled (rw, 0, rd) rotated (15, 15, 20) shifted (0, 0, 4);  %% These work.
%r0 := unit_rectangle scaled (rw, 0, rd) rotated (15, 15, 0);
%r0 := unit_rectangle scaled (rw, 0, rd) rotated (30, 15, 0);
%r0 := unit_rectangle scaled (rw, 0, rd) rotated (45, 0, 0);
                                                          
%r0 := unit_rectangle scaled (rw, 0, rd) rotated (45, 11, 0);  

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (80, 0, 0) shifted (0, 0, 1);  %% This works.

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (0, 90, 0) shifted (0, 0, 1);  %% This works.

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (0, 0, 90) shifted (0, 0, 1);  %% This works.

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (0, 10, 80) shifted (0, 0, 1);  %% This works.

r0 := unit_rectangle scaled (rw, 0, rd) rotated (60, 25, 10) shifted (0, 0, 1);  %% This works.

%r0 := unit_rectangle scaled (rw, 0, rd) rotated (15, 15, 20) shifted (0, 0, 4);  %% This works.

%r0 := unit_rectangle scaled (rw, 0, rd) rotated (90, 0) shifted (0, 0, 1);  %% This works.

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (90, 0) shifted (0, 0, 2);  %% This works.

% r0 := unit_rectangle scaled (rw, 0, rd) rotated (90, 0) shifted (0, 0, 1);  %% This works.

%% **** (4) 

transform t;
t := identity rotated (5, 5) shifted (2, 3);
%t := identity;

E *= t;
r0 *= t;

cuboid c;
c := out_cuboid E;

plane q;
q := (plane) r0;

ellipse e;
e := E intersection q;

message "is_elliptical e:";  %% It fails the test, but all of its `points' are
                             %% on the `ellipsoid'.
show is_elliptical e;

filldraw e with_color red;

draw r0 with_color blue;
draw E;

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;
%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;
%label("Parallel Projection, X-Y Plane", label_pt);
endfig with_projection parallel_x_y;

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

verbatim_metapost "end";
end;