%%%% prbla_10.ldf
%%%% Created by Laurence D. Finston (LDF) Mon Nov 21 17:58:07 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 
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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 


%% Run these commands:

%% 3dldf prbla_10.ldf
%% mpost prbla_10
%% tex prbla_10.txt
%% dvips -o prbla_10.ps prbla_10.dvi 
%% gv prbla_10.ps &

%% *** (3) The location of a `point' with respect to a `parabola'.
%%         LDF 2005.11.21.

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

picture axis_picture;

%% **** (4) axis_picture.

beginfig(0);

pickup pencircle scaled (1mm, 1mm);

axis_x_lft   := 5;
axis_x_rt    := 15;
axis_y_bot   := 10;
axis_y_top   := 10;
axis_z_front := 7;
axis_z_back  := 10;

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

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

drawarrow origin -- (0, 0, -axis_z_front);
drawarrow origin -- (0, 0, axis_z_back);
label.lft("z", (-.25, 0, axis_z_back)); 

axis_picture := current_picture;
clear current_picture;
endfig; 

focus f;
set f with_position (-5, 10, -20) with_direction (-5, 10, 100) with_distance 15; 

pickup pencircle scaled (1mm, 1mm);

beginfig(1);
parabola parab[];
set parab0 with_parameter 3 with_extent 7;

set parab1 with_parameter 3 with_extent 12;

transform t;
t := identity rotated (60, 15)  shifted (1, 0, -2);

parab0 *= parab1 *= t;

draw parab1 with_color red dashed with_dots;

draw parab0 with_color blue;

point p[];

%% **** (4) 

%% ***** (5) 0:  On parabola segment.

p0 := get_point 4 parab0;

numeric pos[];

pos0 := p0 location parab0;  

message "pos0:";
show pos0;

%% ***** (5) 1:   On parabola, but not segment.

p1 := get_point 2 parab1;

numeric pos[];

pos1 := p1 location parab0;  

message "pos1:";
show pos1;

%% ***** (5) 2:  Within the region enclosed by the branches of  
%%               the parabola and the line connecting the end points 
%%               of the segment.

p10 := get_point (size parab0 - 2) parab0;

p2 := mediate(p0, p10);

pos2 := p2 location parab0;  

message "pos2:";
show pos2;

%% ***** (5) 3:  Between the branches of the parabola, but
%%               outside the region enclosed by them and the 
%%               line connecting the end points of the segment.

p11 := get_point (size parab1 - 2) parab1;

p3 := mediate(p1, p11);

draw p1 -- p11 dashed withdots with_color red;

pos3 := p3 location parab0;  

message "pos3:";
show pos3;

%% ***** (5) -1: Coplanar with the parabola, but
%%               does not lie on the curve or between the branches.

p4 := mediate(p0, p10, 1.25);

draw p0 -- p4 dashed withdots with_color dark_gray;

pos4 := p4 location parab0;  

message "pos4:";
show pos4;

%% ***** (5) -2: Not coplanar with the parabola.

p5 := (13, 9, -2);

pos5 := p5 location parab0;  

message "pos5:";
show pos5;

%% ***** (5) 

%% **** (4) 

output axis_picture with_focus f;
output current_picture with_focus f;

clear current_picture;

%% **** (4) 

verbatim_metapost "pickup pencircle scaled 1mm;";

%pickup pencircle scaled (1mm, 1mm);

dotlabel.ulft("\vbox{\hbox{$p_0$,}\hbox{$l = 0$}}", p0);

drawdot p1;
label.rt("$p_1$, $l = 1$", p1 shifted (.25, 0)); 

dotlabel.lrt("$p_2$, $l = 2$", p2); 

drawdot p3;
label.urt("$p_3$, $l = 3$", p3 shifted (.25, 0));

dotlabel.lrt("$p_4$, $l = -1$", p4);

label.top("$p_5$", p5 shifted (0, .25));
dotlabel.bot("$l = -2$", p5);

%dotlabel.llft("$p_{10}$", p10); 

%dotlabel.bot("$p_{11}$", p11); 

%% **** (4) 

endfig with_focus f no_sort;  %with_projection parallel_x_z;

verbatim_metapost "end";

end;