%%%% elpsd_06.ldf
%%%% Created by Laurence D. Finston (LDF) Wed Dec  7 20:16:45 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 location of a `point p' with respect to an `ellipsoid e'.
%%         `location' returns 0 if `p' lies on the surface of `e',
%%         1 if `p' lies within `p', and -1 if it lies outside of `e'.
%%
%%         LDF 2005.12.07.

verbatim_metapost "verbatimtex \magnification=\magstep5 \font\large=cmr12 etex";

pickup pencircle scaled (1mm, 1mm);

picture save_picture;

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

beginfig(1);

ellipsoid E;
set E with_center origin with_axis_x 24 with_axis_y 16 with_axis_z 10
      with_divisions_x 8 with_divisions_y 8 with_divisions_z 2
      with_point_count 64;

%rotate E (15, 15);
%shift E (1, 2, 3);

draw E;

point p[];

p0 := (1, 2, 1);  %% Inside.
p1 := (4, 9, 0);  %% Outside.

ellipse e;
e := get_ellipse 3 E;

p2 := get_point 60 e; %% On the surface.

message "p0 location E:";
show p0 location E;

message "p1 location E:";
show p1 location E;

message "p2 location E:";
show p2 location E;

pickup pencircle scaled (1.5mm, 1.5mm);

pickup red;

drawdot p0;
drawdot p1;
drawdot p2;

label.ulft("$p_0$", p0); 
label.top("$p_1$", p1); 
label.urt("$p_2$", p2); 

endfig with_focus f no_sort;

verbatim_metapost "end";
end;