%%%% sphrmd01.ldf
%%%% Created by Laurence D. Finston (LDF) Thu Jan 22 17:09:19 CET 2009

%%%% $Id: sphrmd01.ldf,v 1.8 2010/12/17 14:47:41 lfinsto1 Exp $

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2009, 2010, 2011 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:  June 4, 2010

%% Run like this:

%% 3dldf sphrmd01.ldf 
%% mpost sphrmd01.mp 
%% tex sphrmd01.txt 
%% dvips -o sphrmd01.ps sphrmd01.dvi
%% ps2pdf sphrmd01.ps

%% All on one line:
if false:
3dldf sphrmd01.ldf && mpost sphrmd01.mp && tex sphrmd01.txt && \
dvips -o sphrmd01.ps sphrmd01.dvi \
&& ps2pdf sphrmd01.ps
fi;

%% View the PostScript file using Ghostview like this:
%% gv sphrmd01.ps &
%% or with GNU Ghostview like this:
%% ggv sphrmd01.ps &

%% View the PDF file with Acrobat Reader like this:
%% acroread sphrmd01.pdf &

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

%% ** (2) Plans for a paper (not cardboard!) model of a sphere (Sphere Development 1)

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

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

%% *** (3) Macros

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

enddef;

%% Use negative length for tick mark on the left of aa, positive for one on the right.
%% LDF 2010.06.02.

def tick {point aa,
          numeric offset} =

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

enddef;

%% *** (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[];
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;

numeric r[];  %% Radii

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

string s;

%% *** (3) Figure 0

beginfig(0); 
  
k := 5;

m[0] := 45;  %% Main curves

m[1] := 30; %% Inner curve for stitches

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

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

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;


%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;

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

%    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;

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


endfor;

endfig with_projection parallel_x_y no_sort;

%% *** (3) Figure 1

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

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;

q0 += ..;
q1 += ..;
q2 += ..;
q3 += ..;
q4 += ..;
q5 += ..;
q6 += ..;

n := 17;

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

%    message "i:"; 
%    show i;

   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

   draw p3 -- p9 with_color gray;  %% Horizontals

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

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

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


   %drawdot p5 with_pen dot_pen;

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

   tick{p32, -.25cm};


   p33 := p8 shifted (.333cm, 0);
   p35 := p33 shifted (.333cm, 0);

   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;

   q4 += p7;                   %% Outer curves
   q5 += p8;

   q6 += p9;                   %% Even futher out curve

   
   if magnitude n < 15:
      crosshair{p8, .1cm};
   fi;


   %drawdot p8 with_pen dot_pen;
   
   n -= 1;

   j += 1;

endfor;

q0 += p2;
q1 += p2;

q2 += p2;
q3 += p2;
q4 += p2;
q5 += p2;
q6 += p2;


draw q0;
draw q1 dashed evenly;

draw q2 dashed evenly withpen thin_pen;
%draw q3;

%draw q4;
draw q5 dashed evenly withpen thin_pen;

draw q6;

v0 := currentpicture;
v1 := v0;

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

a := 6.5;
t0 := identity shifted (a, 0);

for i = 1 upto 4:
   s := "{\large " & decimal i & "}";
   label.rt(s, p31);
   label("{\large R}", p31 shifted (.75cm, 1.5cm));
   label("{\large L}", p31 shifted (-.75cm, 1.5cm));
   currentpicture += v1;
   v1 *= t0;
   p31 *= t0;
endfor;

%% Second row

v1 := v0;
p31 := p30;

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

v1 *= t1;
p31 *= t1;

for i = 5 upto 8:
   s := "{\large " & decimal i & "}";
   label.rt(s, p31);
   label("{\large R}", p31 shifted (.75cm, 1.5cm));
   label("{\large L}", p31 shifted (-.75cm, 1.5cm));
   currentpicture += v1;
   v1 *= t0;
   p31 *= t0;
endfor;

endfig with_projection parallel_x_y no_sort;



%% *** (3)

%% *** (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: