%%%% sphrmd02.ldf
%%%% Created by Laurence D. Finston (LDF) Mon May 31 19:22:33 CEST 2010

%%%% $Id: sphrmd02.ldf,v 1.13 2012/08/06 12:32:25 lfinsto1 Exp $

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2010, 2011, 2012 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 6, 2012
%%                August 5, 2012
%%                June 4, 2010

%% Run like this:

%% 3dldf sphrmd02.ldf 
%% mpost sphrmd02.mp 
%% tex sphrmd02.txt 
%% dvips -o sphrmd02.ps sphrmd02.dvi
%% ps2pdf sphrmd02.ps

%% All on one line:
if false:
3dldf sphrmd02.ldf && mpost sphrmd02.mp && tex sphrmd02.txt && \
dvips -o sphrmd02.ps sphrmd02.dvi \
&& ps2pdf sphrmd02.ps
fi;

%% View the PostScript file using Ghostview like this:
%% gv sphrmd02.ps &
%% or with GNU Ghostview like this:
%% ggv sphrmd02.ps &

%% View the PDF file with Acrobat Reader like this:
%% acroread sphrmd02.pdf &

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

%% ** (2) Plans for a paper (not cardboard!) model of a sphere (Sphere Development 2)

%% LOG
%% LDF 2010.06.02.
%% Replaced dots with crosshairs.
%% ENDLOG 


input "sphrmd00.lmc";

verbatim_metapost "verbatimtex \font\large=cmr17 etex;";

%% *** (3) Declarations and initializations


PI := 3.141592653589793;

focus f[];

set f0 with_position (0, 10, -30) 
       with_direction (0, 10, 10) with_distance 20; 

circle c[];       

point p[];

point u[][];

path q[];

transform t[];

pen thin_pen;
pen line_pen;
pen dot_pen;

thin_pen := pencircle scaled (.25mm, .25mm, .25mm);

line_pen := pencircle scaled (.333mm, .333mm, .333mm);

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

pickup line_pen;

color_vector cv;

cv += blue;
cv += red;
cv += green;
cv += cyan;
cv += magenta;
cv += yellow;
cv += violet;
cv += orange;
cv += black;

picture v[];

bool_point_vector bpv;

string s;

numeric m[];  %% Angles

numeric r[];  %% Radii

numeric d[][];  %% Lengths of the horizontals.

string s;


%% *** (3) Figure 0

beginfig(0); 
  
k := 5;

m[0] := 45;  %% Angle for main curves

m[1] := 35; %% Angle for inner curve for stitches

m[2] := 60; %% Angle for outer curve for stitches

%% m[3] := 70; %% Angle for even further out curve for offset beyond the stitches

m[4] := 25;  %% Angle for further inner curves for separate tabs

m[5] :=  5;  %% Angle for tabs
m[6] := 10;  
m[7] := 15;  

r0 := 5;

set c0 with_diameter 2*r0 with_point_count 64;

d[0][0] := 2 * PI * r0 * m[0] / 360;

d[1][0] := 2 * PI * r0 * m[1] / 360;

d[2][0] := 2 * PI * r0 * m[2] / 360;

%% d[3][0] := 2 * PI * r0 * m[3] / 360;

d[4][0] := 2 * PI * r0 * m[4] / 360;

d[5][0] := 2 * PI * r0 * m[5] / 360;

d[6][0] := 2 * PI * r0 * m[6] / 360;

d[7][0] := 2 * PI * r0 * m[7] / 360;

% for i = 0 upto 2:
%    s := "d[" & decimal i & "][0]:";
%    message s;
%    show d[i][0];
% endfor;

p0 := get_center c0;

%dotlabel.rt("$p_0$", p0);

rotate c0 (90, 0);

draw c0;

p1 := p0 shifted (0, -r0);
%dotlabel.lrt("$p_1$", p1);

%draw p0 -- p1;  %% Not really necessary.

j := 2;

n := 17;

for i := k step k until (180 - k):

%    message "i:"; 
%    show i;

   p[j] := p1 rotated (0, 0, i);

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

   draw p0 -- p[j];  %% Not really necessary.

   j += 1;

   p[j] := (0, ypart p[j - 1]);

   r[i] := magnitude (p[j] - p[j - 1]);

   %s := "r[" & decimal i & "]:";
   %message s;
   %show r[i];

   %s := "Points " & decimal (j - 1) & " and " & decimal j;
   %message s;  

   %s := "$p_{" & decimal j & "}$";

   %dotlabel.ulft(s, p[j]);

   draw p[j - 1] -- p[j];  %% Not really necessary.

   j += 1;

   d[0][i] := (2 * PI * r[i] *  m[0]) / 360;
   d[1][i] := (2 * PI * r[i] *  m[1]) / 360;
   d[2][i] := (2 * PI * r[i] *  m[2]) / 360;
%  d[3][i] := (2 * PI * r[i] *  m[3]) / 360;
   d[4][i] := (2 * PI * r[i] *  m[4]) / 360;
   d[5][i] := (2 * PI * r[i] *  m[5]) / 360;
   d[6][i] := (2 * PI * r[i] *  m[6]) / 360;
   d[7][i] := (2 * PI * r[i] *  m[7]) / 360;


%   s := "d[0][" & decimal i & "]:";
%
%   message s;
%   show d[0][i];


endfor;

dotlabel.bot("$p_{1}$", p1);
dotlabel.lft("$p_{13}$", p13);

%message "magnitude(p13 - p1):";
%show magnitude(p13 - p1);

% message "p0:"; 
% show p0;

% message "p13:"; 
% show p13;

% show p0;
% show p8;
% show p9;

set c1 with_diameter (2 * r30);  %% Added LDF 2012.08.05.  Used in fig. 3, below.
rotate c1 (90, 0);
%shift c1 by p13;
%draw c1;  

endfig with_projection parallel_x_y no_sort;


%% *** (3) Figure 1

e := PI * r0;
f := e * k / 180;

numeric ZERO;
ZERO := 0;

numeric h_offset;
numeric ht;


beginfig(1); 

p2 := (0, e);

draw origin -- p2 with_pen thin_pen;

j := 1;

q0  += origin;
q1  += origin;
q2  += origin;
q3  += origin;
q4  += origin;
q5  += origin;
q6  += origin;
q7  += origin;
q8  += origin;
q9  += origin;
q10 += origin;
q11 += origin;
q12 += origin;
q13 += origin;
q14 += origin;

q0  += ..;
q1  += ..;
q2  += ..;
q3  += ..;
q4  += ..;
q5  += ..;
q6  += ..;
q7  += ..;
q8  += ..;
q9  += ..;
q10 += ..;
q11 += ..;
q12 += ..;
q13 += ..;
q14 += ..;

m := 1;

%message "k:"; 
%show k;

path temp_path;
numeric tab_dir_val;

tab_dir_val := 1;

for i := k step k until (180 - k):

   if (i == 35) or (i == 155):
      % message "iteration (j):";
      % show j;
      % message "i:"; 
      % show i;
      % message "magnitude (p3 - p4):"; 
      % show magnitude (p3 - p4);
      %drawdot p3 with_color red with_pen pencircle scaled (1.5mm, 1.5mm, 1.5mm);
      %drawdot p4 with_color red with_pen pencircle scaled (1.5mm, 1.5mm, 1.5mm);

      temp_path := p3 -- p4;

      tab (temp_path, ZERO, h_offset, ht) {0, 1, .875, .75, .2, 5, tab_dir_val};
      tab_dir_val *= -1; %% Switch direction for second tab.  LDF 2012.08.05.

   fi;
  

   p3 := (-d[0][i]/2, j * f);  %% Points on main curves
   p4 := (d[0][i]/2, j * f);

   p5 := (-d[1][i]/2, j * f);  %% Points on inner curves
   p6 := (d[1][i]/2, j * f);

   p7 := (-d[2][i]/2, j * f);  %% Points on outer curves
   p8 := (d[2][i]/2, j * f);


   p9 := (d[3][i]/2, j * f);  %% Point on even further out curve

   p10 := (-d[4][i]/2, j * f);  %% Points on further inner curves
   p11 := (d[4][i]/2, j * f);   

   p12 := (-d[5][i]/2, j * f);  %% Points on tabs
   p13 := (d[5][i]/2, j * f);  

   p14 := (-d[6][i]/2, j * f);  
   p15 := (d[6][i]/2, j * f);  

   p16 := (-d[7][i]/2, j * f);  
   p17 := (d[7][i]/2, j * f);  


   if (i == 45) or (i == 90) or (i == 135):  %% Horizontals
      draw p3 -- p4 dashed evenly;
   else: 
      draw p3 -- p4 with_color gray;  
   fi;



   q0 += p3;                   %% Main curves
   q1 += p4;

   q2 += p5;                   %% Inner curves
   q3 += p6;

   if magnitude n == 15:          %% Added.  LDF 2010.06.04.
      old_crosshair{(mediate(p4, p5, .25)), .1cm};
      old_crosshair{(mediate(p5, p4, .25)), .1cm};
   fi;
 
   if magnitude n < 15:
      old_crosshair{p5, .1cm};
      old_crosshair{p6, .1cm};  
   fi;

   %drawdot p6 with_pen dot_pen;

   q4 += p7;                   %% Outer curves

   q5 += p8;                   %% Even futher out curve

   q6 += p9;                   

   p32 := p5 shifted (-.333cm, 0);
   p34 := p32 shifted (-.333cm, 0);

   p33 := p6 shifted (.333cm, 0);
   p35 := p33 shifted (.333cm, 0);

   tick{p32, -.25cm};
   tick{p33, .25cm};

   if n >= 0:
      s := decimal n;
   else:
      s := decimal -n;
   fi;

   if is_even n:
      label.lft(s, p34);
   fi;

   if is_even n:
      label.rt(s, p35);
   fi;

   q9  += p12;  %% Tabs
   q10 += p13;

   q11 += p14;
   q12 += p15;

   q13 += p16;
   q14 += p17;


   
   if magnitude n < 15:
      old_crosshair{p6, .1cm};
   fi;


   %drawdot p8 with_pen dot_pen;
   
   n -= 1;

   j += 1;

   m += 1;

endfor;

q0 += p2;
q1 += p2;

q2  += p2;
q3  += p2;
q4  += p2;
q5  += p2;
q6  += p2;
q7  += p2;
q8  += p2;
q9  += p2;
q10 += p2;

draw q0;  %% Outer curve, left.
draw q1;  %% Outer curve, right.

draw q2 dashed evenly withpen thin_pen;  %% Inner curves for stitches
draw q3 dashed evenly withpen thin_pen;

%draw q4;
%draw q5 dashed evenly withpen thin_pen;

draw q7 dashed evenly;
draw q8 dashed evenly;

draw q6;  %% Middle vertical line

%dotlabel.rt("$p_0$", p0);
%dotlabel.lrt("$p_1$", p1);
%dotlabel.lrt("$p_2$", p2);

v0 := currentpicture;
v1 := v0;

p30 := (0, .5e);
p31 := p30;

a := 6.5;

t0 := identity shifted (a, 0);

clear current_picture;

t2 := identity shifted (.5a, 0);

q15 := q6;

for i = 9 upto 15:
   q[i] *= t2;
endfor;

%%draw q9;   %% Curves for tabs
%%draw q10;
draw subpath (4, 33) of q11 dashed evenly;
draw subpath (4, 33) of q12 dashed evenly;
draw subpath (4, 33) of q13;
draw subpath (4, 33) of q14;

draw q15;  %% Middle line of tab

n := -14;

for i = 4 upto 32:

   if n < 0:
      s := decimal -n;
   else:
      s := decimal n;
   fi;

   if (i == 9) or (i == 18) or (i == 27):
      draw get_point(i) q13 -- get_point (i) q14 dashed evenly;
   else:
      draw get_point(i) q13 -- get_point (i) q14 with_color gray;
   fi;

   p36 := (get_point (i) q11);
   p37 := p36 shifted (-.5cm, 0);

   p38 := (get_point (i) q12);
   p39 := p38 shifted (.5cm, 0);

   if is_even n:
      label.lft(s, p37);
      label.rt(s, p39);
   fi;

   tick{p37, .25cm};
   tick{p39, -.25cm};

   if (i > 4) and (i < 32):
      %drawdot get_point (i) q11 with_pen dot_pen;
      %drawdot get_point (i) q12 with_pen dot_pen;
      old_crosshair{get_point (i) q11, .1cm}; 
      old_crosshair{get_point (i) q12, .1cm}; 
   fi;

   n += 1;

endfor;

p40 := get_point(4) q13;
p41 := get_point (4) q14;

draw p40 -- p41;

p44 := mediate(p40, p41, 5);
p45 := mediate(p41, p40, 5);

draw p44 -- p41 dashed evenly with_color gray;
draw p45 -- p40 dashed evenly with_color gray;

p42 := get_point(32) q13;
p43 := get_point(32) q14;

draw p42 -- p43;

p46 := mediate(p43, p42, 5);
p47 := mediate(p42, p43, 5);

draw p46 -- p42 dashed evenly with_color gray;
draw p47 -- p43 dashed evenly with_color gray;


v2 := current_picture;
v4 := v2;

clear current_picture;

for i = 1 upto 4:  %% 4
   s := "{\large " & decimal i & "}";
   label.urt(s, p31);
   currentpicture += v1;
   v1 *= t0;
   p31 *= t0;
endfor;

%% Second row

v1 := v0;
v2 := v4;

p31 := p30;

t1 := identity shifted (0, -19);

v2 *= v1 *= t1;
p31 *= t1;

for i = 5 upto 8:
   s := "{\large " & decimal i & "}";
   label.urt(s, p31);
   currentpicture += v1;
   v1 *= t0;
   p31 *= t0;
endfor;

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

endfig with_projection parallel_x_y no_sort;

%% *** (3)

beginfig(2); 

v2 := v4;

t3 := identity shifted (3cm, 0);

for i = 0 upto 8:
   current_picture += v2;
   v2 *= t3;
endfor;

t4 := identity shifted (0, -14cm);  %% -17.5cm

v2 := v4;
v2 *= t4;


for i = 0 upto 8:
   current_picture += v2;
   v2 *= t3;
endfor;

endfig with_projection parallel_x_y no_sort;

%% *** (3) Figure 3, Octagonal caps

beginfig(3); 

%draw c1;

%message "circumference c1:"; 
%show circumference c1;

numeric side_length;

side_length := (circumference c1) / 8;

% message "side_length:"; 
% show side_length;

%message "r30:"; 
%show r30;

reg_polygon rp[];
rp0 := unit_octagon scaled (r30, 0, r30) rotated (90, 0);

%draw rp0;

point p[];

for i = 0 upto 7:
   p[i] := get_point (i) rp0;
endfor;

numeric rp_zero_side_length;

rp_zero_side_length := magnitude (p0 - p1);

%message "rp_zero_side_length:"; 
%show rp_zero_side_length;

numeric temp_val;

temp_val := side_length / rp_zero_side_length;

%message "temp_val:"; 
%show temp_val;

rp1 := rp0 scaled (temp_val, temp_val);

%message "rp1:"; 
%show rp1;

c2 := in_circle rp1;

%message "c2:"; 
%show c2;

%draw c2;


draw rp1;  %% rp1 is scaled so that the length of one side is equal to 
           %% 1/8 of the circumference of c1.
           %% LDF 2012.08.05.


old_crosshair{origin, .1cm};

for i = 0 upto 7:
   p[i + 8] := get_point (i) rp1;
endfor;

point temp_pt;

temp_pt := mediate(p[8], p[15]);
old_crosshair{mediate(origin, temp_pt, .675), .1cm};

for i = 8 upto 14:
   temp_pt := mediate(p[i], p[i + 1]);
   old_crosshair{mediate(origin, temp_pt, .675), .1cm};
endfor;


numeric rp_one_side_length;

rp_one_side_length := magnitude (p8 - p9);  %% 1.9635 Current value.  LDF 2012.08.06.

%message "rp_one_side_length:"; 
%show rp_one_side_length;

%show rp1;

%message "p8:";      %% Radius of rp1:  2.56543cm
%show magnitude p8;

%message "get_center rp1:"; 
%show get_center rp1;

% label.top("$p_8$", p0);
% label.top("$p_9$", p1);
% label.top("$p_{10}$", p10);
% label.top("$p_{11}$", p11);
% label.top("$p_{12}$", p12);
% label.top("$p_{13}$", p13);
% label.top("$p_{14}$", p14);
% label.top("$p_{15}$", p15);


reg_polygon poly;
poly := rp1;

tab (poly, ZERO, h_offset, ht) {0, 1, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {1, 2, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {2, 3, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {3, 4, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {4, 5, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {5, 6, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {6, 7, .875, .75, .2, 5, 1};
tab (poly, ZERO, h_offset, ht) {7, 0, .875, .75, .2, 5, 1};

picture octagon_picture;
octagon_picture := current_picture;

shift octagon_picture (6cm, 0);

current_picture += octagon_picture;

picture tab_picture;

temp_path := p8 -- p15;

temp_val := magnitude (p8 - p15);

for i = 0 upto 3:
   temp_path := (p8 -- p15) shifted (6cm, 0);
   shift temp_path (i * temp_val, 0);
   for j = 0 upto 7:
      tab (temp_path, tab_picture, h_offset, ht) {0, 1, .875, .75, .2, 5, 1};
      tab (temp_path, tab_picture, h_offset, ht) {0, 1, .875, .75, .2, 5, -1};
      shift temp_path (0, -3.5ht);
   endfor;
endfor;

shift tab_picture (5cm, 0);
current_picture += tab_picture;


endfig with_projection parallel_x_y no_sort;

% r[30]:
% >> 2.5
% Points 12 and 13

%% *** (3) Figure 999 (scratch picture) Crosshairs

picture crosshair_picture;

beginfig(999);
   old_crosshair{origin, .1cm};

   temp_pt := mediate(p[8], p[15]);
   old_crosshair{mediate(origin, temp_pt, .675), .1cm};

   for i = 8 upto 14:
      temp_pt := mediate(p[i], p[i + 1]);
      old_crosshair{mediate(origin, temp_pt, .675), .1cm};
   endfor;

   crosshair_picture := current_picture;

endfig;  



%% *** (3) Figure 4 (1004, 2004, 3004, 4004)
%% *** (3) Octagonal pyramid.
%% LDF 2012.08.06.

picture u, v, w, text_picture, dbl_tab_picture;

numeric diameter_two;

clear u;
clear v;
clear w;
clear text_picture;
clear dbl_tab_picture;



% 2.56543

pyramid (u, v, w, text_picture, dbl_tab_picture, diameter_two, ZERO, ZERO) 
        {8, (2 * 2.56543), 0.669873, 0, 0, 5, 0, true, false};

beginfig(4);
   current_picture := u;
endfig with_focus f0 no_sort;

beginfig(1004);
   current_picture += v;
   current_picture += crosshair_picture;
endfig with_projection parallel_x_y no_sort;

beginfig(2004);
   current_picture += w;
   current_picture += crosshair_picture;
endfig with_projection parallel_x_y no_sort;

beginfig(3004);
   current_picture += text_picture;
endfig with_projection parallel_x_y no_sort;

beginfig(4004);
   current_picture += dbl_tab_picture;
endfig with_projection parallel_x_y 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.                              
%%       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: