%%%% arc_1.ldf
%%%% Created by Laurence D. Finston (LDF) Thu Mar  1 11:55:01 CET 2007

%% * (1) 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 
%%%% 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 
 


%% Run the following commands:
%% 3dldf arc_1.ldf
%% mpost arc_1.mp
%% tex arc_1.txt
%% dvips -o arc_1.ps arc_1.dvi

%% * (1) Beginning of 3DLDF code.

%% **** (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 := 12cm;
h := 16cm;


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);

rad := 5;
circle circ;
point M;
point p[];

%% **** (4) 

beginfig(1); 

circ := unit_circle scaled (rad, 0, rad) rotated 90;

M := get_center circ;

dotlabel.bot("$M$", M);

draw circ;

p0 := (rad, 0)  rotated (0, 0, 45);
p1 := (-rad, 0) rotated (0, 0, -39);

dotlabel.rt("$p_0$", p0);
dotlabel.top("$p_1$", p1);

draw p0 -- p1;

p2 := mediate(p0, p1);
dotlabel.llft("$p_2$", p2);

bool_point_vector bpv;

bpv := circ intersection_points (M -- p2);

p3 := bpv[0];

dotlabel.top("$p_3$", p3);

p4 := mediate(p0, p3);

dotlabel("\space", p4);
label.lft("$p_4$", p4 shifted (-.1, -.1));

bpv := circ intersection_points (M -- p4);

p5 := bpv[1];

dotlabel.top("$p_5$", p5);

draw p3 -- p0;

draw M -- p5;
draw M -- p3;

a := magnitude (p3 - p2);
b := magnitude (p0 - p2);
c := magnitude (p0 - p3);

point A;
point B;
point C;
point D;

A := mediate (p3, p2);
B := mediate (p0, p2);
C := mediate (p0, p3);
D := mediate (p0, p3, .75);

label.lft("$a$", A); 
label.lrt("$b$", B); 
label.urt("$c$", C shifted (3mm, -1mm)); 
label.urt("$d$", D shifted (0mm, -.5mm)); 

alpha := arcsind (a / c);
beta  := arcsind (b / c);

% message "alpha:";
% show alpha;

% message "beta:";
% show beta;

label.lrt("$\beta$", p3 shifted (0, -1mm));

label.lft("$\alpha$", p0 shifted (-4mm, 1mm));

p6 := M shifted (.1, .5);

p7 := p6 shifted (.5, 0);

drawarrow p7 -- p6;
label.rt("$\gamma = \alpha$", p7);

point R;
R := mediate(M, p3);
label.lft("$r$", R);

d := .5c;

r := d / sind alpha;

message "r:";
show r;

p8 := p0 rotated (0, 0, 67.5);
label.top("$q$", p8);

message "alpha:";
show alpha;

ang := (p0 - M) angle (p1 - M);
show ang;


draw frame;
endfig with_projection parallel_x_y;

verbatim_metapost "end;";

end;

%% ** (2) End of 3DLDF code.

%% * Local variables for Emacs.

%% Local Variables:
%% mode:Metafont
%% eval:(outline-minor-mode t)
%% eval:(read-abbrev-file abbrev-file-name)
%% outline-regexp:"%% [*\f]+"
%% End: