%%%% trchd_1.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Jan 13 18:00:51 CET 2009

%%%% $Id: trchd_1.ldf,v 1.4 2009/01/13 18:13:04 lfinsto1 Exp $

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2009 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 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

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

%% Last updated:  January 13, 2009

%% Run like this:

%% 3dldf trchd_1.ldf 
%% mpost trchd_1.mp 
%% tex trchd_1.txt 
%% dvips -o trchd_1.ps trchd_1.dvi
%% ps2pdf trchd_1.ps

%% All on one line:
if false:
3dldf trchd_1.ldf && mpost trchd_1.mp && tex trchd_1.txt && \
dvips -o trchd_1.ps trchd_1.dvi \
&& ps2pdf trchd_1.ps
fi;

%% View the PostScript file using Ghostview like this:
%% gv trchd_1.ps &
%% or with GNU Ghostview like this:
%% ggv trchd_1.ps &

%% View the PDF file with Acrobat Reader like this:
%% acroread trchd_1.pdf &

%% Convert the final EPS image to JPEG like this:
%% conveps --start=1211 --end=1211 --output-format=jpeg --border=0 trchd_1

%% Convert EPS files to JPEG like this:
%% conveps --start=1 --end=1211 --output-format=jpeg --border=0 trchd_1

%% Generate animated GIF like this:
%% convert -delay 15 trchd_1_*.jpg trchd_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 trchd_1.gif 

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


%% ** (2)  Trochoid Pattern 1

m := 10;
n := 10;

w := 6.4cm;
h := 4.8cm;

w *= 4;
h *= 4;

w /= 1.1375;
h /= 1.1375;

pen_width := .5mm; 

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

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

shift frame (-.5frame_w, 0, -.5frame_h);

%% *** (3)

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

pen dot_pen;

dot_pen := pencircle scaled (1mm, 1mm, 1mm);

string s;

boolean inner;
boolean outer;
boolean perimeter;

perimeter := false;  % true
inner     := true; % false
outer     := false; % true

pickup pencircle scaled (.5mm, .5mm, .5mm);

r0 := unit_rectangle scaled (12, 0, 12) shifted origin;

%% *** (3) The circle.

radius := 2.5;

set c0 with_diameter 2*radius with_point_count 32;

%% *** (3) Get points

for i := 0 upto 3:
   p[i] := get_point (i) r0;
endfor;

p5 := get_center c0;

for i := 6 upto 9:
   p[i] := get_point ((i - 6) * 8) c0;
endfor;

p10 := (p5 - p8) shifted by p0;

t0 := identity shifted by (p10 - p9);

c0 *= p5 *= p6 *= p7 *= p8 *= p9 *= t0;

p15 := mediate(p5, p9, .75);

for j = 6 upto 9:
   q[iter_ctr][j] += ..;
   q[iter_ctr][j] += p[j];
endfor;

q[iter_ctr]15 += ..;
q[iter_ctr]15 += p15;

numeric ang[];

PI := 3.141592653589793;

p11 := p5 shifted (0, 1);

p12 := (p0 - p8) shifted by p3;
p13 := (p5 - p8) shifted by p12;
p14 := p13 - p5;

%message "p14:"; 
%show p14;

distance := zpart p14;
message "distance:"; 
show distance;

circumference := 2 * PI * radius;
message "circumference:"; 
show circumference;

ang0 := (360 * distance) / circumference;

message "ang0:"; 
show ang0;

step_value := 256;  %% The number of iterations for each side

total_iterations := 4 * 256;  %% Total iterations per cycle

figure_divisor := 16;  %% Set to 256 for 32 images

numeric curr_value;
numeric curr_figure;

iter_ctr := 0;

color_vector cv;

boolean do_colors;

do_colors := true; % false

if do_colors:
   cv += blue;
   cv += red;
   cv += green;
   cv += cyan;
   cv += magenta;
   cv += yellow;
   cv += violet;
   cv += orange;
else:
   cv += black;
   cv += black;
   cv += black;
   cv += black;
   cv += black;
   cv += black;
   cv += black;
   cv += black;
fi;

%% *** (3) Figure 0

beginfig(0); 

   %draw frame;

%% **** (4)  The rectangle

   draw r0;

%    dotlabel.llft("$p_0$", p0);   
%    dotlabel.lrt("$p_1$", p1);   
%    dotlabel.urt("$p_2$", p2);   
%    dotlabel.ulft("$p_3$", p3);   

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

   drawdot p5 with_pen dot_pen;

   %label("$p_5$", p5);

   draw c0;

   if perimeter:
      draw p5 -- p9;
      drawdot p9 with_pen dot_pen with_color cv[n];
%      dotlabel.rt("$p_{9}$", p9);   
   fi;

   if inner:
      draw p5 -- p15;
      drawdot p15 with_pen dot_pen with_color cv[n];
%      dotlabel.rt("$p_{15}$", p15);   
   fi;

   %if outer:
   %   draw p5 -- p;
   %fi;

   % dotlabel.top("$p_7$", p7);   
   % dotlabel.lft("$p_8$", p8);   
   % dotlabel.llft("$p_9$", p9);   


endfig with_projection parallel_x_z; 

%% *** (3)  Roll the circle.

curr_value := 1;
curr_figure := 1;

%% *** (3) Outer loop.  One iteration per complete cycle around the square.

for iter_ctr := 0 upto 7:

%% **** (4) Inner loop.  One iteration for each step in paths.
%%          The number of iterations is `total_iterations'.

   for i = ((iter_ctr * 4 * step_value) + 1) 
           upto ((iter_ctr * 4 * step_value) + (4 * step_value)):

      t1 := (identity rotated_around (p5, p11) ang0/step_value);

      if i <= ((iter_ctr * 4 * step_value) + step_value):            %% left side
         shift t1 (0, 0, distance/step_value);
      elseif i <= ((iter_ctr * 4 * step_value) + (2 * step_value)):  %% top
         shift t1 (distance/step_value, 0, 0);
      elseif i <= ((iter_ctr * 4 * step_value) + (3 * step_value)):  %% right side
         shift t1 (0, 0, -distance/step_value);
      elseif i <= ((iter_ctr * 4 * step_value) + (4 * step_value)):  %% bottom
         shift t1 (-distance/step_value, 0, 0);
      fi;

      c0 *= p5 *= p6 *= p7 *= p8 *= p9 *= p11 *= p15 *= t1;

%    message "ang0/step_value:"; 
%    show ang0/step_value;

%% ***** (5) Add point to the paths.

     for j = 6 upto 9:
        q[iter_ctr][j] += ..;
        q[iter_ctr][j] += p[j];
%        draw q[iter_ctr][j];
     endfor;

     q[iter_ctr]15 += ..;
     q[iter_ctr]15 += p15;

     q[iter_ctr]15 += ..;
     q[iter_ctr]15 += p15;

%% ***** (5)  Test whether to output a figure

     k := curr_value / figure_divisor;

     if k == floor k:

        s := "Figure " & decimal curr_figure;

        message s;

%% ***** (5) Output a figure

         beginfig(curr_figure); 

            %draw frame;
            draw r0;

            draw c0;

            drawdot p5 with_pen dot_pen;

            %label("$p_5$", p5);

%             dotlabel.rt("$p_6$", p6);   
%             dotlabel.top("$p_7$", p7);   
%             dotlabel.lft("$p_8$", p8);   
%             dotlabel.llft("$p_9$", p9);   
%             dotlabel.lft("$p_{12}$", p12);
%             dotlabel.lft("$p_{13}$", p13);

             if perimeter:
                %dotlabel.rt("$p_{9}$", p9);   
                draw p5 -- p9;

                for n = 0 upto iter_ctr:
                   draw q[n]9 with_color cv[n];
                   drawdot p9 with_pen dot_pen with_color cv[n];
                endfor;
             fi;

            if inner:
               %dotlabel.rt("$p_{15}$", p15);   
               draw p5 -- p15;
               for n = 0 upto iter_ctr:
                  draw q[n]15 with_color cv[n];
                  drawdot p15 with_pen dot_pen with_color cv[n];
               endfor;
            fi;

%             if outer:
%             fi
            
         endfig with_projection parallel_x_z; 

         curr_figure += 1;

%% ***** (5)

      fi;  %% Output a figure

%% ***** (5)

      curr_value += 1;

   endfor;  %% End of inner loop

%% **** (4)

endfor;  %% End of outer loop

%% *** (3)

% message "next curr_figure:"; 
% show curr_figure;

% message "next curr_value:"; 
% show curr_value;


%% *** (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: