%%%% fctcn01.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Oct 27 17:14:40 CET 2009

%%%% $Id: fctcn01.ldf,v 1.5 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:  October 20, 2009

%% Run like this:

%% 3dldf fctcn01.ldf 
%% mpost fctcn01.mp 
%% tex fctcn01.txt 
%% dvips -o fctcn01.ps fctcn01.dvi
%% ps2pdf fctcn01.ps

%% All on one line:
if false:
3dldf fctcn01.ldf && mpost fctcn01.mp && tex fctcn01.txt && \
dvips -o fctcn01.ps fctcn01.dvi \
&& ps2pdf fctcn01.ps
fi;

%% View the PostScript file using Ghostview like this:
%% gv fctcn01.ps &
%% or with GNU Ghostview like this:
%% ggv fctcn01.ps &

%% View the PDF file with Acrobat Reader like this:
%% acroread fctcn01.pdf &

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

%% ** (2) Plans for a paper model of a facetted cone (Facetted Cone 1)

%% *** (3) Declarations and initializations

picture v[];

focus f[];
set f0 with_position (0, 30, -100) 
       with_direction (0, 30, 10) with_distance 50; 

circle c[];

point p[];

path q[];

bool b;
bool_point_vector bpv;

h := 10;  % 30

point n[]; %% Normals
              
pen dot_pen;

dot_pen := pencircle scaled (.75mm, .75mm, .75mm);

transform t[];

string s;


%% *** (3) Figure 0
       
beginfig(0);
  
%% **** (4)

outer_diam := 10;  %% 20
inner_diam :=  8;  %% 15;

c0 := unit_circle scaled (outer_diam, 0, outer_diam);
c1 := unit_circle scaled (inner_diam, 0, inner_diam);

draw c0;  
draw c1;  

%% **** (4)

j := 2;

for i := 0 step 4 until 28:
   p[j] := get_point (i) c0;
   drawdot p[j] with_pen pencircle scaled (1.5mm, 1.5mm, 1.5mm);
   j += 1;
endfor;

%dotlabel.lft(7, p7);
%dotlabel.lft(8, p8);

p0 := get_center c0;
p1 := p0 shifted (0, h);

%dotlabel.bot(0, p0);   
%dotlabel.top(1, p1);   

p10 := mediate(p7, p8);

%dotlabel.top(10, p10);   



bpv := (p0 -- p10) intersection_points c0;

%show bpv;

p11 := bpv[0];

%dotlabel.lft(11, p11);

bpv := (p0 -- p10) intersection_points c1;

p12 := bpv[0];

%dotlabel.rt(12, p12);

draw p0 -- p1 -- p7 -- p12 -- p1 -- p8 -- p12;

%% **** (4) Paths.

q0 :=  p12 -- p7 -- p1 -- cycle;

triangle w[];

set w0 with_points (p12, p7, p1);

p13 := get_center w0;

n0 := (get_normal w0) shifted p13;

%dotlabel.rt(13, p13);

%message "n0:"; 
%show n0;

label.top("$n_0$", n0);
drawarrow p13 -- n0;

v0 := current_picture;


%% **** (4) End of figure 0
  
endfig with_focus f0;

%% *** (3) Figure 1 --- Base circles

beginfig(1);

draw c0;
draw c1 dashed evenly;

c3 := unit_circle scaled (.25, 0, .25);

draw c3 with_color red;

drawdot origin with_pen dot_pen;

j := 2;

for i = 0 step 4 until 28:
   a := 40 + j;
   p[a] := p[j] rotated (0, 22.5);
   draw origin -- p[40 + j] dashed evenly;
   draw origin -- p[j] dashed evenly;
   s := "$p_{" & decimal j & "}$";
   %dotlabel.top(s, p[j]);
   s := "$p_{" & decimal a & "}$";
   %dotlabel.top(s, p[a]);
   j += 1;
%  message "a:"; 
%  show a;
%  message "j:"; 
%  show j;
endfor; 

unfilldraw c3;

draw (-.25, 0) -- (.25, 0);
draw (0, 0, -.25) -- (0, 0, .25);


p60 := get_point 0 c1;
%dotlabel.top("$p_{60}$", p60);

for i = 1 upto 15:
   a := 60 + i;
   p[a] := p60 rotated (0, i * 22.5);
   s := "$p_{" & decimal a & "}$";
   %dotlabel.top(s, p[a]);
endfor;


%% **** (4)

q3 :=    p2 -- p61 -- p3 -- p63 -- p4 -- p65 -- p5 -- p67 -- p6 -- p69
      -- p7 -- p71 -- p8 -- p73 -- p9 -- p75 -- p2;

draw q3;

%% **** (4) Tabs 

%% ***** (5) First tab

p80 := mediate(p5, p65, .2);
p81 := mediate(p65, p5, .2);

%dotlabel.top("$p_{80}$", p80);
%dotlabel.top("$p_{81}$", p81);

p82 := p80 shifted (0, 1);

p83 := (unit_vector(p81 - p80) scaled .5 shifted p80) rotated_around (p80, p82) -60;

%dotlabel.top("$p_{83}$", p83);

p84 := p81 shifted (0, 1);

p85 := (unit_vector(p80 - p81) scaled .5 shifted p81) rotated_around (p81, p84) 60;

%dotlabel.top("$p_{85}$", p85);

q4 := p80 -- p83 -- p85 -- p81;

draw q4;

p86 := mediate(p80, p83);
p87 := mediate(p81, p85);

%dotlabel.lft("$p_{86}$", p86);
%dotlabel.rt("$p_{87}$", p87);

draw p86 -- p87 dashed evenly;

for i = 1 upto 4:
   drawdot mediate(p86, p87, i/5) with_pen dot_pen;
endfor;


%% ***** (5)

t2 := identity rotated_around (origin, p5) 180;

q5 := q4;
p88 := p86;
p89 := p87;

q5 *= p88 *= p89 *= t2;

draw q5;
for i = 1 upto 4:
   drawdot mediate(p88, p89, i/5) with_pen dot_pen;
endfor;


t3 := identity rotated (0, 45);

for i := 1 upto 7:
   q4 *= q5 *= p86 *= p87 *= p88 *= p89 *= t3;
   draw q4;
   draw q5;
   draw p86 -- p87 dashed evenly;
   draw p88 -- p89 dashed evenly;
   for j = 1 upto 4:
      drawdot mediate(p86, p87, j/5) with_pen dot_pen;
      drawdot mediate(p88, p89, j/5) with_pen dot_pen;
   endfor;
endfor;

%% **** (4) End of figure 1

endfig with_projection parallel_x_z with_factor .5 no_sort;

%% *** (3)

%% *** (3) Figure 2

beginfig(2); 

p14 := p13;
n1 := n0;  
  
t0 := align (p13 -- n0) with_axis y_axis;

rotate t0 (180, 0);

w1 :=  w0;

w1 *= p14 *= n1 *= t0;

%draw w1 dashed evenly;

%dotlabel.lft($p_{14}$, p14);
%dotlabel.rt("$n_1$", n1);

%message "n1:"; 
%show n1;

%message "p14:"; 
%show p14;

for i = 0 upto 2:
   p[15 + i] := get_point (i) w1;
   a := 15 + i;
   s := "$p_{" & decimal a & "}$";
endfor;


%dotlabel.rt("$p_{15}$", p15);
%dotlabel.lft("$p_{16}$", p16);

%label.rt("$p_{17}$", p17);


% message "magnitude (p1 - p7):"; 
% show magnitude (p1 - p7);

% message "magnitude (p1 - p12):"; 
% show magnitude (p1 - p12);

% message "magnitude (p7 - p12):"; 
% show magnitude (p7 - p12);

% message "magnitude (p17 - p15):"; 
% show magnitude (p17 - p15);

% message "magnitude (p17 - p16):"; 
% show magnitude (p17 - p16);

% message "magnitude (p15 - p16):"; 
% show magnitude (p15 - p16);

% magnitude (p1 - p7):
% >> 36.0555
% magnitude (p17 - p16):
% >> 36.0555

% magnitude (p17 - p15):
% >> 33.541
% magnitude (p1 - p12):
% >> 33.541

% magnitude (p7 - p12):
% >> 8.40668
% magnitude (p15 - p16):
% >> 8.40668

%% **** (4) Second triangle

p20 := p16;

t1 := identity rotated_around (p15, p17) 180;

%show t1;

w1 *= p20 *= t1;

%draw w1 dashed evenly;

%dotlabel.top("$p_{20}$", p20);

%% **** (4) Third triangle

p21 := p15;
t1 := identity rotated_around (p20, p17) 180;

w1 *= p21 *= t1;

%draw w1 dashed evenly;
%dotlabel.top("$p_{21}$", p21);

%% **** (4) The remaining 13 triangles


for i = 22 upto 34:
   s := "$p_{" & decimal i & "}$";
   p[i] := p[i-2];
   t1 := identity rotated_around (p[i-1], p17) 180;
   w1 *= p[i] *= t1;
 %  draw w1 dashed evenly;
   %dotlabel.top(s, p[i]);
endfor;

%% **** (4) Clear out the the lines surrounding p17

c2 := unit_circle scaled (.375, 0, .375) shifted p17;
draw c2 dashed evenly;

a := 35;

for_suffixes i := 16, 15:

   bpv := (p[i] -- p17) intersection_points c2;

   b := bpv0;
    
   if b:
      p[a] := bpv0;
   else:
      p[a] := bpv1;
   fi;

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

   %drawdot p[a] with_pen dot_pen;

   a += 1;

endfor;

draw p36 -- p15 dashed evenly;

for i := 20 upto 34:

   bpv := (p[i] -- p17) intersection_points c2;

   b := bpv0;
    
   if b:
      p[a] := bpv0;
   else:
      p[a] := bpv1;
   fi;

   %s := "$p_{" & decimal a & "}$";
   %dotlabel.top(s, p35);
 
   %drawdot p[a] with_pen dot_pen;

   draw p[a] -- p[i] dashed evenly;

%    message "i:"; 
%    show i;
%    message "a:"; 
%    show a;

   a += 1;

endfor;



draw p17 -- p38;
draw p17 -- p40;
draw p17 -- p43;
draw p17 -- p48;


q1 += --;

q1 += p17;
q1 += p16;
q1 += p15;

for i := 20 upto 34:
   q1 += p[i];
endfor;

q1 += p17;

draw q1;

%% **** (4) Tabs on short sides

%% ***** (5) First tab on short side

p90 := mediate(p15, p16, .2);
p91 := mediate(p16, p15, .2);

%dotlabel.top("$p_{90}$", p90);
%dotlabel.top("$p_{91}$", p91);

p92 := p90 shifted (0, 1);
p93 := (unit_vector(p91 - p90) scaled .5 shifted p90) rotated_around (p90, p92) 60;

%dotlabel.lrt("$p_{93}$", p93);

p94 := p91 shifted (0, 1);

p95 := (unit_vector(p90 - p91) scaled .5 shifted p91) rotated_around (p91, p94) -60;

%dotlabel.llft("$p_{95}$", p95);

q6 := p90 -- p93 -- p95 -- p91;

draw q6;

p96 := mediate(p90, p93);
p97 := mediate(p91, p95);

%dotlabel.rt("$p_{96}$", p96);
%dotlabel.lft("$p_{97}$", p97);

draw p96 -- p97 dashed evenly;

for i = 1 upto 4:
   drawdot mediate(p96, p97, i/5) with_pen dot_pen;
endfor;

%% ***** (5) Second tab on short side

t4 := identity rotated_around (p15, p17) 180;

p90 *= p91 *= p93 *= p95 *= p96 *= p97 *= q6 *= t4;

draw q6;
draw p96 -- p97 dashed evenly;

for i = 1 upto 4:
   drawdot mediate(p96, p97, i/5) with_pen dot_pen;
endfor;

%% ***** (5)  Remaining tabs on short sides

for j := 20 upto 33:
   t4 := identity rotated_around (p[j], p17) 180;

   p90 *= p91 *= p93 *= p95 *= p96 *= p97 *= q6 *= t4;

   draw q6;
   draw p96 -- p97 dashed evenly;

   for i = 1 upto 4:
      drawdot mediate(p96, p97, i/5) with_pen dot_pen;
   endfor;
endfor;

%% **** (4) Tabs on long sides

%% ***** (5) Inner tab on p16 -- p17

p100 := unit_vector (p17 - p16) shifted p16;
p101 := (unit_vector (p16 - p17) scaled 2.5) shifted p17;

% dotlabel.lft("$p_{100}$", p100);
% dotlabel.lft("$p_{101}$", p101);

p102 := p101 shifted (0, 1);

p103 := ((unit_vector (p16 - p17) scaled .5) shifted p101) rotated_around (p101, p102) 60;
%dotlabel.rt("$p_{103}$", p103);

p104 := p100 shifted  (0, 1);

p105 := ((unit_vector (p17 - p16) scaled .5) shifted p100) rotated_around (p100, p104) -60;
%dotlabel.rt("$p_{105}$", p105);

draw p100 -- p105 -- p103 -- p101;

p106 := mediate(p100, p105);
%dotlabel.bot("$p_{106}$", p106);

p107 := mediate(p101, p103);
%dotlabel.urt("$p_{107}$", p107);

draw p106 -- p107 dashed evenly;

for i := 1 upto 15:
   drawdot mediate(p106, p107, i/16) with_pen dot_pen;
endfor;

%% ***** (5) Outer tab on p34 -- p17

a := (p34 - p17) angle (p16 - p17);


p108 := p17 shifted (0, 1);

t5 := identity rotated_around (p17, p108) -a;

p100 *= p101 *= p103 *= p105 *= p106 *= p107 *= t5;

draw p100 -- p105 -- p103 -- p101;
draw p106 -- p107 dashed evenly;


for i := 1 upto 15:
   drawdot mediate(p106, p107, i/16) with_pen dot_pen;
endfor;

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

rotate current_picture (0, -90);

endfig with_projection parallel_x_z with_factor .5 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.                              
%%       \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: