%%%% dodec_03.ldf
%%%% Created by Laurence D. Finston (LDF) Thu Nov  8 21:21:51 CET 2007

%% $Id: dodec_03.ldf,v 1.3 2007/11/08 21:15:01 lfinsto1 Exp $

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2007, 2008 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:  November 8, 2007

%% Run like this:

%% 3dldf dodec_03.ldf 
%% mpost dodec_03.mp 
%% tex dodec_03.txt 
%% dvips -o dodec_03.ps dodec_03.dvi

%% All on one line:
if false:
3dldf dodec_03.ldf; mpost dodec_03.mp; tex dodec_03.txt; \
dvips -o dodec_03.ps dodec_03.dvi
fi;

%% View using Ghostview like this:
%% gv dodec_03.ps &

% * (1) Beginning of 3DLDF code.

%% ** (2) draw_dodecahedron_net

input "dodec_03.lmc";

%% ** (2) Plan for dodecahedron with sundial faces.
%%        So far, I've only one face.
%%        LDF 2007.11.08.

%% *** (3) Global declarations and initializations

focus f;
set f with_position (7, 8, -20) 
      with_direction (7, 8, 10) with_distance 20; 

pen hour_line_pen;
pen path_pen;

hour_line_pen := pencircle scaled (.0333, .0333);
path_pen := pencircle scaled (.0333, .0333);

polyhedron d[];

point p[][];  %% Points on pentagons of d0
point n[];    %% normals
point c[];    %% centers
point q[];    %% Scratch points

point g[];    %% Points on gnomen

point_vector pv;  %% Scratch point vector

reg_polygon_vector rpv; %% The faces of the dodecahedron net

reg_polygon r[];

circle k[];

point K[];  %% Points on k1

point E[];  %% Points on equatorial dial

plane epsilon[];
plane rho[];

path h[][];  %% The hour lines on the pentagonal faces of the dodecahedron

point H[][]; %% One point on each of the `h[][]' paths.

path m[];    %% The hour lines on the net

string s;

transform t[];

%% Greenwich, England:  Latitude 51 deg. 28' 38'' N 
%% (+ 51 (/ 28.0 60) (/ 38.0 3600))  51.4772

%% *** (3) Figure 1 has been moved to the bottom, in order to be able to
%%         move the hour lines for face 10 (r10) to the net.

%% *** (3) Figure 2

beginfig(2);
d0 := unit_dodecahedron scaled 2;
%draw d0;

for i = 0 upto 11:
   r[i] := get_reg_polygon (i) d0;
   c[i] := get_center r[i];
   if false: 
      s := decimal i;
      label(s, c[i]);
   fi; 
endfor;

rho10 := get_plane r10;

draw r10;

p[1][3] := get_point 3 r1;


set k0 with_diameter 10 with_point_count 32;

shift k0 (0, ypart p[1][3]);

if false:  
   for i = 0 upto 4:
      s := "$2_" & decimal i & "$";
      label.top(s, get_point (i) r2);
   endfor;

   for i = 0 upto 4:
      s := "$9_" & decimal i & "$";
      label.lft(s, get_point (i) r9);
   endfor;

   for i = 0 upto 4:
      s := "$10_" & decimal i & "$";
      label.rt(s, get_point (i) r10);
   endfor;
fi; 



%label(2, c2) with_text_color red;
%label.bot(1, c1) with_text_color blue;

%label.lft(0, r1);

% filldraw r1 with_draw_color blue;
% filldraw r2;
% filldraw r0;
% filldraw r6;

%% **** (4) Compass rose

point north, south, east, west;

point c_k;

c_k := get_center k0;

y_val := ypart c_k;
diam := get_diameter k0;

direction_val := .6 * diam;

north := ( 0,  y_val,  direction_val);
south := ( 0,  y_val, -direction_val);
east :=  (direction_val,  y_val,   0);
west :=  (-direction_val, y_val,   0);

label.lft("W", west);
label.rt("E", east);
label.bot("S", south);

g0 := south shifted (0, 0, 1);
q0 := south shifted(-1, 0, 0);

curr_latitude := 51.4772;  %% Greenwich, England

rotate_around g0 (q0, south) curr_latitude;

%dotlabel.lft("$q_{0}$", q0);

%% This doesn't work, because the same `vector<real>' is
%% used to store the `numeric' values for the coordinates
%% as is used for the subscripts of the variable `g0'.
%% This will require some effort to fix.
%% LDF 2007.11.04.

%%g1 := (xpart g0, ypart south, zpart g0);  

%% This is a workaround.  
%% LDF 2007.11.04.

a := xpart g0;
b := ypart south;
g := zpart g0;

g1 := (a, b, g);
 
draw south -- g0 -- g1 -- cycle;

%message "g1:"; 
%show g1;

dotlabel.lft("$g_{0}$", g0);
dotlabel.rt("$g_{1}$", g1);


%% **** (4) Gnomon on r10

n10 := (get_normal r10) shifted c10 scaled 3;

for i = 0 upto 4:
   p[10][i] := get_point (i) r10;
endfor;

q0 := mediate(p[10][0], p[10][4]);

dotlabel.top("$q_{0}$", q0);

q1 := p[10][2] shifted (0, 0, 25);

dotlabel.rt("$q_{1}$", q1);

q3 := mediate(c10, q0, .75);

dotlabel.rt("$q_{3}=g_2$", q3);


g2 := g0;
g3 := south;

t0 := identity shifted by (q3 - g0);  %% `by' is necessary, because without it,
                                      %% a `point_variable' would need to be used
                                      %% instead of a `point_primary'.  I can't change
                                      %% the parser rule without `by', because this causes
                                      %% over 200 shift/reduce conflicts.
                                      %% LDF 2007.11.08.
g2 *= g3 *= t0;

g4 := mediate(g2, g3, 1.5);

g5 := get_perpendicular_base g4, r10;


%% **** (4) Equatorial dial

t0 := align (g4 -- g2) with_axis y_axis;

invert t0;

set k1 with_diameter 1 with_point_count 32;

k1 *= t0;

draw k1 with_color blue with_pen path_pen;

size_k1 := size k1;

for i = 0 upto size_k1 - 1:
   K[i] := get_point (i) k1;
endfor;

if false: 
   message "K0:";  %% K0 and K[size_k1 / 2] lie over the z-axis, i.e., their
                   %% x-component is 0.
   show K0;

   message "K[size_k1 / 2]:";  
   show K[size_k1 / 2];
fi; 

%% g4 is the center of k1

for i = 0 step 15 until 180:
   E[i] := K[3 * size_k1 / 4] rotated_around (g2, g4) i;
endfor;

%% **** (4) The hour lines on r10

epsilon[0] := get_plane (g2 -- g4 -- E[0]);
h[10][0] := epsilon[0] intersection rho10;
clear pv;
pv := h[10][0] intersection_points r10;

draw pv0 -- pv1 with_color red;

if xpart pv0 > xpart pv1:
   H[10][0]   := pv0;
   H[10][180] := pv1;
else:
   H[10][0]   := pv1;
   H[10][180] := pv0;
fi;

for i = 15 step 15 until 165:
   epsilon[i] := get_plane (g2 -- g4 -- E[i]);
   h[10][i] := epsilon[i] intersection rho10;
   clear pv;
   pv := h[10][i] intersection_points r10;
   if zpart pv0 < zpart pv1:
      H[10][i] := pv0;
   else:
      H[10][i] := pv1;
   fi;
   draw g2 -- H[10][i] with_color red;
endfor;

dotlabel.rt("\uppercase\expandafter{\romannumeral 18}  $(0^\circ)$",  H[10][0]);
dotlabel.rt("\uppercase\expandafter{\romannumeral 16} $(30^\circ)$",  H[10][30]);
dotlabel.lrt("\uppercase\expandafter{\romannumeral 14} $(60^\circ)$", H[10][60]);
dotlabel.bot("\uppercase\expandafter{\romannumeral 12} $(90^\circ)$", H[10][90]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 10} $(120^\circ)$", H[10][120]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 8} $(150^\circ)$", H[10][150]);

dotlabel.lft("\uppercase\expandafter{\romannumeral 6} $(180^\circ)$", H[10][180]);



%% **** (4) Drawing commands

draw north -- south;
draw west -- east;

if false: 
   draw k0 with_color blue;

   filldraw r1;
   filldraw r2;
   filldraw r6;
   filldraw r9;
   filldraw r10;
   filldraw r11;
fi; 

% filldraw r10;
% filldraw r11;

%n1 := ((get_normal r1) * -1) shifted c1;
%label.urt("$n_1$", n1) with_text_color blue;
%drawarrow c1 -- n1 with_color blue;

%drawarrow c10 -- n10;

draw p[10][2] -- q0 dashed evenly;

draw p[10][2] -- q1 dashed evenly;

%message "(q0 - p[10][2]) angle (q1 - p[10][2]):"; 
%show (q0 - p[10][2]) angle (q1 - p[10][2]);


label.lft("$g_{4}$", g4);
label.rt("$g_{5}$", g5);

draw g2 -- g4 -- g5 -- cycle with_pen path_pen;


g6 := mediate(g2, g4);

%% **** (4) Labels

if false: 
   label( 1, c1);
   label( 2, c2);
   label( 6, c6);
   label( 9, c9);
   label(11, c11);
fi; 

%dotlabel.lrt("$c_{10}$", c10);

dotlabel.top(0, p[10][0]);
dotlabel.urt(1, p[10][1]);
dotlabel.top(2, p[10][2]);
dotlabel.lft(3, p[10][3]);
dotlabel.top(4, p[10][4]);

%label.bot("$n_{10}$", n10);



%% **** (4) End of figure 2

endfig with_focus f no_sort;  

%% *** (3) Figure 3

beginfig(3);
draw d0;
%draw r6 with_color red;
%draw r7 with_color blue;
%draw r8 with_color cyan;
draw r10 with_color green;

%draw k0 with_color blue;

draw north -- south;
draw west -- east;

%label.lrt("$r_{6}$", c6) with_text_color red;
%label.lrt("$r_{7}$", c7) with_text_color blue;
%label.lrt("$r_{8}$", c8) with_text_color cyan;
label.lrt("$r_{10}$", c10) with_text_color green;

label.lft("W", west);
label.rt("E", east);
label.bot("S", south);
label.top("N", north);


endfig with_projection parallel_x_z;

%% *** (3) Figure 4

beginfig(4); 

draw d0;
%draw r10 with_color red;

%drawarrow c10 -- n10;

draw north -- south;

q2 := mediate(p[10][2], q1, .333);
label.rt("$q_{2}$", q2);

draw p[10][2] -- q2 dashed evenly;

draw g2 -- g4 -- g5 -- cycle with_pen path_pen;

draw k1 with_color blue with_pen path_pen;

label.lft("$g_{2}$", g2);
label.lft("$g_{4}$", g4);
label.rt("$g_{5}$", g5);

%dotlabel.rt("$g_{6}$", g6);


%label.lrt("$c_{10}$", c10) with_text_color red;
%label.top("$n_{10}$", n10);

label.bot("S", south);
label.bot("N", north);

rotate current_picture (0, -90);
%scale current_picture (.5, .5, .5);

%% **** (4) End of figure 4

endfig with_projection parallel_x_y with_factor 1 no_sort;

%% *** (3) Figure 5

beginfig(5);

draw g2 -- g4 with_color green;
draw r10;

%dotlabel.top(0, k1);

%% **** (4) Labels on r10

dotlabel.bot(0, p[10][0]);
dotlabel.lrt(1, p[10][1]);
dotlabel.lrt(2, p[10][2]);
dotlabel.llft(3, p[10][3]);
dotlabel.bot(4, p[10][4]);

%% **** (4) 

dotlabel.lrt("$g_{4}$", g4);

if false: 
   message "g2"; 
   show g2;
   message "g4"; 
   show g4;
   message "g2 - g4:"; 
   show g2 - g4;
fi; 

%% **** (4) 

if false: 
   message "g4 is_in_plane rho10:";  %% g4 does not lie in rho10.  It just looks like
                                     %% it in the diagram.
                                     %% LDF 2007.11.08.
   show g4 is_in_plane rho10;
fi; 

%% **** (4) The hour lines on r10

draw H[10][0] -- H[10][180] with_color red;

dotlabel.rt("\uppercase\expandafter{\romannumeral 18} $(0^\circ)$", H[10][0]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 6} $(180^\circ)$", H[10][180]);

for i = 15 step 15 until 165:
   draw g2 -- H[10][i] with_color red;
endfor;

draw k1 with_color blue;

%% **** (4) Labels for the hour points on r10

dotlabel.rt("\uppercase\expandafter{\romannumeral 18}  $(0^\circ)$",  H[10][0]);
dotlabel.rt("\uppercase\expandafter{\romannumeral 17}  $(15^\circ)$",  H[10][15]);
dotlabel.lrt("\uppercase\expandafter{\romannumeral 16} $(30^\circ)$",  H[10][30]);
dotlabel.rt("\uppercase\expandafter{\romannumeral 15} $(45^\circ)$",  H[10][45]);
dotlabel.urt("\uppercase\expandafter{\romannumeral 14} $(60^\circ)$", H[10][60]);
dotlabel.top("\uppercase\expandafter{\romannumeral 13} $(75^\circ)$", H[10][75]);

dotlabel.top("\vbox{}", H[10][90]);
q5 := mediate(g5, H[10][90], 1.333);

label("\uppercase\expandafter{\romannumeral 12} $(90^\circ)$", q5);

draw q5 -- H[10][90] dashed evenly;

dotlabel.top("\uppercase\expandafter{\romannumeral 11} $(105^\circ)$", H[10][105]);
dotlabel.ulft("\uppercase\expandafter{\romannumeral 10} $(120^\circ)$", H[10][120]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 9} $(135^\circ)$", H[10][135]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 8} $(150^\circ)$", H[10][150]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 7} $(165^\circ)$", H[10][165]);
dotlabel.lft("\uppercase\expandafter{\romannumeral 6} $(180^\circ)$", H[10][180]);

%% ***** (5) Transform current_picture

t0 := align (g4 -- g2) with_axis y_axis;

rotate t0 (0, 90);

current_picture *= t0;

%draw g4 -- g4 shifted (1, 0);
%dotlabel.top("$+x$", g4 shifted (1, 0));

%% **** (4) End of figure 5
 
endfig with_projection parallel_x_z with_factor 5 no_sort;


%% *** (3) Figure 1

beginfig(1); 

draw_dodecahedron_net {4, true, 6, .375mm, .75mm, identity};

rpv := get_net dodecahedron with_diameter 4;

rotate rpv10 (180, 180);  %% This is the rotation performed in draw_dodecahedron_net.

q6 := get_center rpv10;
q7 := q6 shifted (0, 1);

t2 := align (c10 -- n10) with_axis y_axis;
rotate t2 (0, 90);
shift t2 by q6;

m0 := (H[10][0] -- H[10][180]) transformed t2;

draw m0 with_pen hour_line_pen;

for i = 15 step 15 until 165:
   draw (g2 -- H[10][i]) transformed t2 with_pen hour_line_pen;
endfor;

label(10, q6 shifted (1, 0, .75));


dotlabel.ulft(0, get_point 0 rpv[10]);
dotlabel.rt(1, get_point 1 rpv[10]);
dotlabel.bot(2, get_point 2 rpv[10]);
dotlabel.lft(3, get_point 3 rpv[10]);
dotlabel.urt(4, get_point 4 rpv[10]);

endfig with_projection parallel_x_z no_sort; 

%% *** (3) Figure 6

beginfig(6); 

q22 := g2;
q24 := g4;
q25 := g5;

t3 := identity rotated (0, -90);

q22 *= q24 *= q25 *= t3;

q26 := mediate(q22, q25) shifted .333;

s := "\setbox0=\hbox{2.\space}\vbox{\hbox{2.  Gnomon for latitude of Greenwich, England}"
     & "\hbox{\hskip\wd0($51^\circ$ $28'$ $38''$ N)}}";

label.rt(s, q26);

if false: 
   message "q22:"; 
   show q22;

   message "q24:"; 
   show q24;

   message "q25:"; 
   show q25;
fi;

label.top("$g_{2}$", q22);
label.lft("$g_{4}$", q24);
label.rt("$g_{5}$", q25);

draw q22 -- q24 -- q25 -- cycle;

endfig with_projection parallel_x_y; 

%% *** (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: