%%%% tngnts_1.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Feb  6 20:26:09 CET 2007

%% * (0) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 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 
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%%%% 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) Tangents to a circle.
%%         Find the tangents to a circle from a given point,
%%         coplanar to the circle.
%%         LDF 2007.02.06.

%% verbatim_metapost "verbatimtex \magnification=\magstep3 etex";

%% **** (4) 

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

picture save_picture;

pickup pencircle scaled (.6mm, .6mm);

%% **** (4) 

pen_width := .75mm; 

w := 60cm;
h := 80cm;


frame_w := w - .5pen_width;
frame_h := h - .5pen_width;

path frame;
frame := origin -- (frame_w, 0) -- (frame_w, frame_h) 
                -- (0, frame_h) -- cycle;

shift frame (-.5frame_w, -.5frame_h);

circle c;
point C;
point P;
point S[];
point T[];
point Q[];
bool_point_vector bpv;
point D[];

r := 5;

D0 := (-1.5r, 0, 0);
D1 := (1.5r, 0, 0);

c := unit_circle scaled (r, 0, r) rotated (90, 0);

C := get_center c;

%% **** (4) 

beginfig(0); 

draw c;

label.rt("$r$", (0, .5r));

P := C;

d := r + i;

shift P (0, d, 0);

draw D0 -- D1 dashed evenly;

dotlabel.top("$P = T$", P);
dotlabel.bot("$C$", C);

draw P -- C;

draw (-5, r, 0) -- (5, r, 0);

draw frame;
endfig with_projection parallel_x_y with_factor .25;

%% **** (4) 

for i = 1 step 1 until 30:
beginfig(i); 

draw c;

P := C;

d := r + i;

shift P (0, d, 0);

draw D0 -- D1 dashed evenly;

dotlabel.top("$P$", P);
dotlabel.bot("$C$", C);

draw P -- C;

label.rt("$d$", (0, .5d));

beta := arcsind (r / d );

% % message "beta:";
% % show beta;

S0 := C;

point normal;
normal := P shifted (0, 0, -1);

rotate_around S0 (P, normal) beta;

S1 := C;

rotate_around S1 (P, normal) -beta;

Q0 := 5 * unit_vector(S0 - P) shifted S0;

Q1 := 5 * unit_vector(S1 - P) shifted S1;

draw P -- Q0;
draw P -- Q1;

a := sqrt((d * d) - (r * r));

T0 := (a * unit_vector(Q0 - P)) shifted P;
T1 := (a * unit_vector (Q1 - P)) shifted P;

drawdot T0 withpen pencircle scaled (1mm, 1mm);
label.lft("$T_0$", T0 shifted (-.25, 0));
draw C -- T0;

label.llft("$r$", mediate(C, T0));
label.lrt("$r$", mediate(C, T1));


drawdot T1 withpen pencircle scaled (1mm, 1mm);
label.rt("$T_1$", T1 shifted (.25, 0));
draw C -- T1;

label.lft("$a$", mediate(T0, P));
label.rt("$a$", mediate(T1, P));


draw frame;
endfig with_projection parallel_x_y with_factor .25;
endfor;

%% **** (4) 

beginfig(31); 

draw c;
dotlabel.bot("$C$", C);

P := C;

d := r + 31;

draw D0 -- D1 dashed evenly;

drawarrow (-r, 0, 0) -- (-r, d, 0);
drawarrow (r, 0, 0) -- (r, d, 0);

label.lft("$d = \infty$", (-r, .5d, 0));
label.rt("$d = \infty$", (r, .5d, 0));

draw (-r, 0, 0) -- (r, 0, 0);

label.bot("$r$", (-.5r, 0, 0));
label.bot("$r$", (.5r, 0, 0));

draw frame;
endfig with_projection parallel_x_y with_factor .25;

%% **** (4) 

verbatim_metapost "end";
end;