%%%% hyprb_03.ldf
%%%% Created by Laurence D. Finston (LDF) Mon Nov 28 16:06:23 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. 
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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 

%%%% lfinsto1@gwdg.de 
%%%% s246794@stud.uni-goettingen.de 


%% *** (3) Classifying `points' with respect to a `hyperbola' using 
%%         the `location' operator.
%%
%%         LDF 2005.11.28.

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

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

beginfig(1); 
hyperbola h[];
set h0 with_max_extent 10;
set h1 with_max_extent 7;

point p[];
numeric L[];

%% **** (4) On hyperbola segment:

p0 := get_point 32 h1;
L0 := p0 location h1;
message "L0:";
show L0;

%% **** (4) On hyperbola, but not segment:

p1 := get_point 5 h0;
L1 := p1 location h1;
message "L1:";
show L1;


%% **** (4) Between center and one of the foci:

p2 := (.5, 0, 3);
L2 := p2 location h1;
message "L2:";
show L2;

%% **** (4) Within the region enclosed by the branches of 
%% one of the halves of the hyperbola segment.

p3 := p0 rotated (180, 0, 180) shifted -1;

L3 := p3 location h1;
message "L3:";
show L3;

%% **** (4) Within the region enclosed by the branches of 
%% one of the halves of the hyperbola, but not the segment.

p4 := p1 rotated (180, 0, 180) shifted -1;

L4 := p4 location h1;
message "L4:";
show L4;

%% **** (4) `point' is coplanar with the hyperbola, but does not lie on the curve,
%%          within one of the regions enclosed by the branches, or between the branches.
%% 

p5 := p1 rotated 180 shifted -1;

L5 := p5 location h1;
message "L5:";
show L5;

%% **** (4) `point' is not coplanar with the hyperbola.

p6 := p0 shifted (-1, 1, -5);

L6 := p6 location h1;
message "L6:";
show L6;

%% **** (4) Drawing commands.

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

draw h0 dashed with_dots;
draw h1 with_color blue;

%% **** (4) Labels.

pickup pencircle scaled (2mm, 2mm);

for i = 0 upto 6:
   drawdot p[i] with_color red;
endfor;

string s;

s := "$p_0$, $l = " & decimal L[0] & "$";
label.rt(s, p0 shifted .25);

s := "$p_1$, $l = " & decimal L[1] & "$";
label.lft(s, p1 shifted -.25);

s := "\setbox0=\hbox{$l = " & decimal L[2] & "$}\vbox{\hbox to \wd0{\hfil$p_2$,\hfil}\box0}";
label.top(s, p2 shifted (0, 0, .25));

s := "$p_3$, $l = " & decimal L[3] & "$";
label.lft(s, p3 shifted -.25);

s := "$p_4$, $l = " & decimal L[4] & "$";
label.lft(s, p4 shifted -.25);

s := "$p_5$, $l = " & decimal L[5] & "$";
label.lft(s, p5 shifted -.25);

s := "\setbox0=\hbox{$p_6$ ($y \\neq 0$),}\vbox{\copy0\hbox to \wd0{\hfil $l = " 
   & decimal L[6] & "$\hfil}}";
label.bot(s, p6 shifted (0, 0, -.25));


%% **** (4) 

endfig with_projection parallel_x_z;

verbatim_metapost "end";

end;