%%%% braik_01.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Jun 26 18:54:02 CEST 2007

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 2007, 2008, 2009, 2010, 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 the maintainer of 
%%%% GNU 3DLDF to send 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 The Free Software Foundation, Inc.
%%%% 51 Franklin St, Fifth Floor 
%%%% Boston, MA  02110-1301 
%%%% USA 

%%%% Laurence.Finston@gmx.de 
 



%% Run like this:
%% 3dldf braik_01.ldf
%% mpost braik_01.mp
%% tex braik_01.txt
%% dvips -o braik_01.ps braik_01.dvi 
%% ps2pdf braik_01.ps %% Create PDF file.

%% *** (3) The Braikenridge-Maclaurin Construction.
%%         Constructing an ellipse from 5 points.  
%%         LDF 2007.06.26.


verbatim_metapost "verbatimtex  \magnification=\magstep2 \font\small=cmr8 etex ";



%% **** (4) Frame

pen_width := .5mm; 

pickup pencircle scaled (pen_width, pen_width, pen_width);

w := 16cm;
h := 16cm;

frame_w := w - .5pen_width;
frame_h := h - .5pen_width;

path frame;
frame := origin -- (frame_w, 0) -- (frame_w, 0, frame_h) 
                -- (0, 0, frame_h) -- cycle;

shift frame (-.5frame_w, 0, -.5frame_h);


%% **** (4) Declarations

numeric i;
numeric j;

point A, B, C, D, E;  %% The given points.

point F;              %% determined below.

point p[];
point_vector pv;


point X;
point Y;
point Z;

path q[];

p0 := (5, 0);

bool_point bp;

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

pen path_pen;
path_pen := pencircle scaled (.7mm, .7mm);

macro_vector mv;

ellipse e;

%% **** (4) Set ellipse and initial points.

e := unit_ellipse scaled (4, 0, 3);

A := get_point (15) e;
B := get_point (11) e;
C := get_point (8)  e;
D := get_point (6)  e;
E := get_point (4)  e;

point axis[]; 

%% **** (4) Macro definitions.

%% ***** (5) Inner macro.

%% If the `boolean bbool' argument is `true', there are two images 
%% where `F' is at the same position as `B', `C', `D', and `E'.
%% LDF 2007.06.26.

def mv {numeric sstart, 
       	numeric ccount,
       	boolean bbool,
       	point aa, point bb, point cc, point dd, point ee} +=

numeric eend;

if bbool:
   eend := ccount;
else:
   eend := ccount - 1;
fi;

%% ****** (6)

for i = 0 upto eend:
beginfig(sstart + i);

pickup path_pen;

draw e;

pickup dot_pen;

dotlabel.rt("$A$", A) with_dot_color red;
dotlabel.bot("$B$", B) with_dot_color red;
dotlabel.lft("$C$", C) with_dot_color red;
dotlabel.top("$D$", D) with_dot_color red;
dotlabel.top("$E$", E) with_dot_color red;

%% ****** (6)

pickup path_pen;
draw aa -- cc dashed evenly;
draw bb -- dd dashed evenly;

bp := (aa -- cc) intersection_point (bb -- dd);

X := bp;

pickup dot_pen;

dotlabel.urt("$X$", X) with_dot_color red;

%% ****** (6)

pickup path_pen;

draw aa -- ee dashed evenly;
draw bb -- ee dashed evenly;

Z := mediate(aa, ee, (i / ccount));

pickup dot_pen;
dotlabel.bot("$Z$", Z) with_dot_color red;

bp := (X -- Z) intersection_point (bb -- ee);

Y := bp;

pickup dot_pen;

dotlabel.urt("$Y$", Y) with_dot_color red;

p1 := mediate(Z, X, 1.5);

dotlabel.bot("$p_1$", p1) with_dot_color red;

p2 := mediate(X, Z, 1.5);

dotlabel.bot("$p_2$", p2) with_dot_color red;

draw p1 -- p2 with_color green with_pen path_pen;


%% ****** (6)

bp := (cc -- Y) intersection_point (dd -- Z);

F := bp;

pickup dot_pen;
dotlabel.llft("$F$", F) with_dot_color red;

pickup path_pen;

draw cc -- F with_color blue;
draw dd -- F with_color blue;

%% ****** (6)

pickup path_pen;
draw frame;

pickup path_pen;
draw frame;

label("{\small Copyright {\copyright} 2007, 2008, 2009, 2010, 2011, 2012, 2013 The Free Software Foundation}", 
      (0, 0, -.5frame_h) shifted (0, 0, -.5cm));  

endfig with_projection parallel_x_z no_sort; 
endfor;

%% ****** (6)

enddef;

%% ***** (5) Outer macro.  It calls the `mv0' (the "inner" macro).

def mv {numeric Sstart, 
        numeric Ccount, 
        boolean Bbool,
        point AA, point BB, point CC, point DD, point EE} +=

%% ****** (6)  First set of images.

  mv0 {Sstart, Ccount, Bbool, AA, BB, CC, DD, EE};  %% 0 -- 20 or 0 -- 19

%% ****** (6)  Second set of images.

  Sstart += Ccount;

  if Bbool:
     Sstart += 1;
     %% message "Incrementing `Sstart'.";
  % else:
  % message "Not incrementing `Sstart'.";
  fi;


  %message "`Sstart' before second set:";
  %show Sstart;

  mv0 {Sstart, Ccount, Bbool, EE, AA, BB, CC, DD}; %% 21 -- 41 or 20 -- 39

%% ****** (6) Third set of images.

  Sstart += Ccount;

  if Bbool:
     Sstart += 1;
     %% message "Incrementing `Sstart'.";
  % else:
  % message "Not incrementing `Sstart'.";
  fi;

  %message "`Sstart' before third set:";
  %show Sstart;

  mv0 {Sstart, Ccount, Bbool, D, E, A, B, C}; %% 42 -- 62 or 40 -- 59

%% ****** (6) Fourth set of images.

  Sstart += Ccount;

  if Bbool:
     Sstart += 1;
     %% message "Incrementing `Sstart'.";
  % else:
  % message "Not incrementing `Sstart'.";
  fi;

  %message "`Sstart' before fourth set:";
  %show Sstart;

  mv0 {Sstart, Ccount, Bbool, C, D, E, A, B}; %% 63 -- 83 or 60 -- 79

%% ****** (6) Fifth set of images.

  Sstart += Ccount;

  if Bbool:
     Sstart += 1;
     %% message "Incrementing `Sstart'.";
  % else:
  % message "Not incrementing `Sstart'.";
  fi;

  %message "`Sstart' before fifth set:";
  %show Sstart;

  mv0 {Sstart, Ccount, Bbool, B, C, D, E, A}; %% 84 -- 104 or 80 -- 99

  Sstart += Ccount;

  %message "`Sstart' after fifth set:";
  %show Sstart;

%% ****** (6) End of `mv1' definition.

enddef;

%% **** (4) Call outer macro.

%% If the third argument is `true', there are two images where `F' 
%% is at the same position as `B', `C', `D', and `E'.
%% LDF 2007.06.26.

mv1 {0, 30, true, A, B, C, D, E};
%mv1 {0, 20, false, A, B, C, D, E};

%% **** (4) End.

verbatim_metapost "end";
end;