%%%% cycld_1.ldf
%%%% Created by Laurence D. Finston (LDF) Mon Aug 18 17:31:48 CEST 2008

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2008, 2009, 2010, 2011, 2012, 2013 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 sending 
%%%% 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 Free Software Foundation, Inc. 
%%%% 51 Franklin St, Fifth Floor 
%%%% Boston, MA  02110-1301  
%%%% USA

%%%% Laurence.Finston@gmx.de
 


%% Last updated:  August 14, 2008

%% Run like this:

%% 3dldf cycld_1.ldf 
%% mpost cycld_1.mp 
%% tex cycld_1.txt 
%% dvips -o cycld_1.ps cycld_1.dvi

%% All on one line:
if false:
3dldf cycld_1.ldf; mpost cycld_1.mp; tex cycld_1.txt; \
dvips -o cycld_1.ps cycld_1.dvi
fi;

%% View using Ghostview like this:
%% gv cycld_1.ps &

%% Generate animated GIF like this:
%% conveps --start=0 --end=121 --output-format=jpeg --border=0 cycld_1
%% convert -delay 15 cycld_1_*.jpg cycld_1.gif
%%
%% Other formats can be used;  it doesn't have to be JPEG.

%% The animated GIF can be viewed using the `animate' program from ImageMagick:
%% animate cycld_1.gif 

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

%% ** (2) Cycloid Pattern 1

pickup pencircle scaled (.675mm, .675mm, .675mm);

circle c[];
point p[];
path q[];
transform t[];

m := 7;
n := 7;

q2 := (-m, 0, -n) -- (m, 0, -n) -- (m, 0, n) -- (-m, 0, n) -- cycle;

numeric d[];
d0 := 5;
d1 := d0 / 5;

numeric r[];

r0 := .5d0;
r1 := .5d1;

set c0 with_diameter d0 with_point_count 32;
set c1 with_diameter d1;

pi := 3.141592653589793;

alpha := 3 * 2pi / 360;

dist := r0 * alpha;

if false: 
   message "2pi:"; 
   show 2pi;
   message "dist:"; 
   show dist;
fi; 

beta := dist / r1;  %% angle of rotation of c1 about its center.

if false: 
   message "beta in radians:"; 
   show beta;

   message "alpha in radians:"; 
   show alpha;
fi;

alpha *= 180;
alpha /= pi;

beta *= 180;
beta /= pi;

if false: 
   message "alpha in deg:"; 
   show alpha;

   message "beta in deg.:"; 
   show beta;
fi; 

p0 := get_point 8 c0;


shift c1 by p0;
shift c1 by (0, 0, .5d1);

p1 := get_center c1;
p2 := p1 shifted (0, 1);


q0 := origin -- p1;

q1 += p0;

beginfig(1);
draw p0 -- p1;
draw q2;
draw c0;
draw c1;
draw q0;

if false: 
   dotlabel.bot("o", origin);
   dotlabel.lrt("$p_0$", p0);
   dotlabel.rt("$p_1$", p1);
fi; 

endfig with_projection parallel_x_z no_sort;  

t0 := identity rotated (0, alpha);

for i = 2 upto 121:
   beginfig(i);
      draw q2;
      p0 *= p1 *= p2 *= c1 *= q0 *= t0;
      t1 := identity rotated_around (p1, p2) beta;

      p0 *= c1 *= t1;

      q1 += ..;
      q1 += p0;

      draw p0 -- p1;
      draw c0;
      draw c1;
      draw q0;

      draw q1 with_color blue;


      if false: 
         dotlabel.bot("o", origin);
         dotlabel.lrt("$p_0$", p0);
         dotlabel.rt("$p_1$", p1);
      fi; 

   endfig with_projection parallel_x_z no_sort;  
endfor;

shift p0 (0, 0, -.5);
q1 += cycle;  %% Correction.  LDF 2009.01.09.

for i = 122 upto 240:
   beginfig(i);
      draw q2;
      draw q1 with_color blue;
      p0 *= p1 *= p2 *= c1 *= q0 *= t0;
      t1 := identity rotated_around (p1, p2) 15;

      p0 *= c1 *= t1;

      q3 += ..;
      q3 += p0;

      draw p0 -- p1;
      draw c0;
      draw c1;
      draw q0;
      draw q3 with_color red;

      if false: 
         dotlabel.bot("o", origin);
         dotlabel.lrt("$p_0$", p0);
         dotlabel.rt("$p_1$", p1);
      fi; 

   endfig with_projection parallel_x_z no_sort;  
endfor;

shift p0 (0, 0, 1.5);
q3 += cycle;

for i = 241 upto 361:
   beginfig(i);
      draw q2;
      draw q1 with_color blue;
      draw q3 with_color red;
      p0 *= p1 *= p2 *= c1 *= q0 *= t0;
      t1 := identity rotated_around (p1, p2) 15;

      p0 *= c1 *= t1;

      q4 += ..;
      q4 += p0;

      if i == 361:
         q4 += cycle;
      fi;

      draw p0 -- p1;
      draw c0;
      draw c1;
      draw q0;
      draw q4 with_color green;

      if false: 
         dotlabel.bot("o", origin);
         dotlabel.lrt("$p_0$", p0);
         dotlabel.rt("$p_1$", p1);
      fi; 

   endfig with_projection parallel_x_z no_sort;  
endfor;

shift p0 (0, 0, -2.0);
q4 += cycle;

for i = 362 upto 482:
   beginfig(i);
      draw q2;
      draw q1 with_color blue;
      draw q3 with_color red;
      draw q4 with_color green;
      p0 *= p1 *= p2 *= c1 *= q0 *= t0;
      t1 := identity rotated_around (p1, p2) 15;

      p0 *= c1 *= t1;

      q5 += ..;
      q5 += p0;

      if i == 361:
         q5 += cycle;
      fi;

      draw p0 -- p1;
      draw c0;
      draw c1;
      draw q0;
      draw q5 with_color orange;

      if false: 
         dotlabel.bot("o", origin);
         dotlabel.lrt("$p_0$", p0);
         dotlabel.rt("$p_1$", p1);
      fi; 

   endfig with_projection parallel_x_z no_sort;  
endfor;


p0 := get_point 7 c0;

p1 := unit_vector p0;
p1 *= r1;
p1 += p0;
p2 := p1 shifted (0, 1);

set c1 with_diameter d1;

shift c1 by p1;

q0 := origin -- p1;

beginfig(483);
draw q2;
draw q1 with_color blue;
draw q3 with_color red;
draw q4 with_color green;
draw q5 with_color orange;

draw p0 -- p1;
draw q2;
draw c0;
draw c1;
draw q0;

if false: 
   dotlabel.bot("o", origin);
   dotlabel.lrt("$p_0$", p0);
   dotlabel.rt("$p_1$", p1);
fi; 

endfig with_projection parallel_x_z no_sort;  

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

verbatim_metapost "end;";

end;

%% ** (2) 

%% * (1) Emacs-Lisp code for use in indirect buffers when using the          
%%   	 GNU Emacs editor.  The local variable list is not evaluated when an 
%%   	 indirect buffer is visited, so it's necessary to evaluate the       
%%   	 following s-expression in order to use the facilities normally      
%%   	 accessed via the local variables list.                              
%%   	 \initials{LDF 2004.02.12}.                                          

%% (progn (metafont-mode) (outline-minor-mode t) (setq fill-column 80) (ignore '(  
%% )) (setq outline-regexp "%% [*\f]+"))

%% * (1) Local variables for Emacs.

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