%%%% strspr01.ldf
%%%% Created by Laurence D. Finston (LDF) Fri Jan 28 14:11:11 CET 2011


%% * (1) Copyright and License.

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

%% Run the following commands:
%% 3dldf strspr01.ldf
%% mpost strspr01.mp
%% tex strspr01.txt
%% dvips -o strspr01.ps strspr01.dvi

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

verbatim_metapost "prologues := 3;";

% verbatim_metapost "verbatimtex \font\large=cmr12 scaled \magstep2 etex;";
% verbatim_metapost "verbatimtex \font\Large=cmr17 scaled \magstep2 etex;";

%% * (1) Star spiral

%% Created:       January 28, 2011
%% Last updated:  January 28, 2011

%% ** (2) Macros

%% *** (3) crosshair

def crosshair {point aa,
               numeric offset} =

    draw aa -- (aa shifted (offset, 0)) with_pen pencircle scaled (.25mm, .25mm, .25mm);
    draw aa -- (aa shifted (-offset, 0)) with_pen pencircle scaled (.25mm, .25mm, .25mm);
    draw aa -- (aa shifted (0, 0, offset)) with_pen pencircle scaled (.25mm, .25mm, .25mm);
    draw aa -- (aa shifted (0, 0, -offset)) with_pen pencircle scaled (.25mm, .25mm, .25mm);

enddef;


%% *** (3) spiral_pattern

%pentagon_scale_factor := 0.1875cm;

%pentagon_help_line_length := .375cm;



def spiral_pattern {bool do_labels, bool do_stars, bool do_help_lines, bool do_reverse,
                    numeric pentagon_scale_factor, 
                    numeric shift_value,
                    numeric pentagon_help_line_length,
                    numeric ang, numeric_vector NV} = 

%% **** (4) pentagon and its stellations

reg_polygon pentagon;

point m[];
point p[];
point r[];

path q[];

circle c[];

string s;

pentagon := unit_pentagon scaled (pentagon_scale_factor, 0, pentagon_scale_factor) rotated (0, 180);

for i = 0 upto 4:
   m[i] := get_point (i) pentagon;
endfor;

if false: % true:
if do_labels:
   label(0, m0) with_text_color green;
   label(1, m1) with_text_color green;
   label(2, m2) with_text_color green;
   label(3, m3) with_text_color green;
   label(4, m4) with_text_color green;
fi;
fi;

m5 := (m0 -- m1) intersection_point (m2 -- m3);

m6 := (m2 -- m1) intersection_point (m0 -- m4);

m7 := (m1 -- m2) intersection_point (m4 -- m3);

m8 := (m2 -- m3) intersection_point (m0 -- m4);

m9 := (m3 -- m4) intersection_point (m1 -- m0);

if false: % true:
if do_labels:
   label(5, m5) with_text_color red;
   label(6, m6) with_text_color red;
   label(7, m7) with_text_color red;
   label(8, m8) with_text_color red;
   label(9, m9) with_text_color red;
fi;
fi;

q2 := m0 -- m6 -- m1 -- m5 -- m2 -- m7 -- m3 -- m8 --m4 -- m9 -- m0 -- cycle;

m10 := (pentagon_help_line_length * unit_vector(m6 - m0)) shifted by m6;
m11 := (pentagon_help_line_length * unit_vector(m6 - m1)) shifted by m6;

%label(11, m11) with_text_color blue;

%draw pentagon;
%draw q2;





%% **** (4)

set c0 with_diameter 19.5 with_point_count 64;

if do_reverse:
   filldraw c0 with_color black;
else:
   draw c0;
fi;


%draw pentagon with_color dark_grey;
%draw q2;

%% **** (4)

p0 := (.25cm, 0);

%r0 := p0;

q0 += p0;
q0 += ..;

%q1 += r0;
%q1 += ..;


i := 1;

forever:
   p[i] := p0 shifted (i * shift_value, 0) rotated (0, i * ang);

%   r[i] := r0 shifted (i * shift_value, 0) rotated (0, i * ang_b);

   exit_if magnitude (p[i]) > 9.75;
  
   q0 += p[i];
%   q1 += r[i];
  
   i += 1;

endfor;

if do_labels:

   if false:
      for i = 0 step 5 until 20:
         s := "$p_{" & decimal i & "}$";
         dotlabel.top(s, p[i]);
      endfor;

      for i = 23 step 3 until 50:
         s := "$p_{" & decimal i & "}$";
         dotlabel.top(s, p[i]);
      endfor;

      for i = 52 step 2 until 182:

         s := "$p_{" & decimal i & "}$";
         dotlabel.top(s, p[i]);

      endfor;
   fi;

   for i = 0 step 5 until 99:
      s := "$p_{" & decimal i & "}$";

      if is_odd i:
         dotlabel.lft(s, p[i]);
      else:
         dotlabel.rt(s, p[i]);
      fi;
   endfor;

   i := 100;

   forever:
      exit_if magnitude(p[i]) > 9.75;

      s := "$p_{" & decimal i & "}$";
 
      if is_odd i:
         dotlabel.lft(s, p[i]);
      else:
         dotlabel.rt(s, p[i]);
      fi;

      i += 1;
   endfor;

fi;

if do_help_lines:
   draw q0 with_color dark_grey dashed evenly;
fi;

if do_stars:

for i = 0 upto (size NV - 1):

   k := NV[i];

   if do_help_lines:
      draw pentagon shifted by p[k] with_color dark_grey;
 
      for j = 0 upto 4:
         draw ((m6 -- m10) rotated (0, j * 72)) shifted by p[k] dashed evenly with_color dark_grey;
         draw ((m6 -- m11) rotated (0, j * 72)) shifted by p[k] dashed evenly with_color dark_grey;
      endfor;
   fi;

   if do_reverse:
      fill q2 shifted by p[k] with_color white;
   else:
      draw q2 shifted by p[k];
   fi;

    
endfor;

fi;


%draw q1 with_color red;


enddef;

%% !! START HERE:  LDF 2011.01.28.
%% Try to get the stars that are on successive turns of the spiral to 
%% not to lie on straight lines.

%% ** (2) Declarations

path frame;

numeric frame_wd;
numeric frame_ht;

point h[];

transform frame_transform;

%% ** (2) Frame path

frame_wd := 20cm;
frame_ht := 24cm;

frame := origin -- (frame_wd, 0) -- (frame_wd, 0, frame_ht) -- (0, 0, frame_ht) -- cycle;

frame_transform := identity shifted (-.5frame_wd, 0, -.5frame_ht);

frame *= frame_transform;

%% ** (2) Points for the crosshairs

h0 := mediate(get_point 0 frame, get_point 1 frame) shifted (0, 0, 1cm);
h1 := mediate(get_point 2 frame, get_point 3 frame) shifted (0, 0, -1cm);
h2 := mediate(get_point 0 frame, get_point 1 frame, 1/16) shifted (0, 0, 1cm);
h3 := mediate(get_point 2 frame, get_point 3 frame, 1/16) shifted (0, 0, -1cm);
h4 := mediate(get_point 0 frame, get_point 1 frame, 15/16) shifted (0, 0, 1cm);
h5 := mediate(get_point 2 frame, get_point 3 frame, 15/16) shifted (0, 0, -1cm);

%% ** (2) Preparation for the figures

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

%% ** (2) Figure 1

beginfig(1); 

%% *** (3) Frame and crosshairs

draw frame;

for i = 0 upto 5:
   crosshair {h[i], .5};
endfor;

%% *** (3) Put the numbers of the points where the stars should go onto `nv'.

%% First, one must call `spiral_pattern' with `do_labels == true'
%% and `do_stars == false' in order to see which points are the ones where the stars 
%% should go.
%%
%% LDF 2011.01.28.

numeric_vector nv;

nv +=  0;
nv += 15;
nv += 22;
nv += 28;
nv += 33;
nv += 37;
nv += 41;
nv += 44;

for i = 47 step 3 until 74:
   nv += i;
endfor;

for i = 76 step 2 until 178:
   nv += i;
endfor;

spiral_pattern {false, true, true, false, 0.1875cm, .05cm, .375cm, 
                10, nv};

%% Original values:
%spiral_pattern {true, false, true, false, 0.1875cm, .05cm, .375cm, 
%                10, nv};

%% For testing.  Use in another figure.
%spiral_pattern {true, false, true, false, 0.1875cm, .025cm, .375cm, 
%                5, nv};



%% *** (3)

endfig with_projection parallel_x_z no_sort; 

%% ** (2) Figure 2

beginfig(2); 

%% *** (3)


draw frame;

for i = 0 upto 5:
   crosshair {h[i], .5};
endfor;

spiral_pattern {false, true, false, false, 0.1875cm, .05cm, .375cm, 
                10, nv};

endfig with_projection parallel_x_z no_sort; 


%% ** (2) Figure 3

beginfig(3); 

%% *** (3)

draw frame;

for i = 0 upto 5:
   crosshair {h[i], .5};
endfor;

spiral_pattern {false, true, false, true, 0.1875cm, .05cm, .375cm, 
                10, nv};

endfig with_projection parallel_x_z no_sort; 




%% ** (2)

verbatim_metapost "end";

%% ** (2) End

end;

%% * (1) End of 3DLDF code

%% * (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)
%% abbrev-mode:t
%% eval:(read-abbrev-file "~/.abbrev_defs")
%% outline-regexp:"%% [*\f]+"
%% End: