%%%% braik_03.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Aug  7 20:06:12 CEST 2007

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 2007, 2008, 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 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 
%%%% Kreuzbergring 41 
%%%% D-37075 Goettingen 
%%%% Germany 

%%%% Laurence.Finston@gmx.de 
 


%% *** (3) Braikenridge-Maclaurin Construction.
%% Constructing a conic section from 5 points.  

%% Run like this:
%% 3dldf braik_03
%% mpost braik_03
%% tex braik_03.txt
%% dvips -o braik_03.ps braik_03.dvi  %% Create PostScript file
%% ps2pdf braik_03.ps                 %% Create PDF file

%% 3dldf braik_03; mpost braik_03; tex braik_03.txt; dvips -o braik_03.ps braik_03.dvi 

%% *** (3) Pascal's Theorem and Braikenridge-Maclaurin Construction.
%% Constructing a conic section from 5 or 6 points.  

verbatim_metapost "verbatimtex  \magnification=\magstep2 etex";

%% **** (4) Frame

pen_width := .5mm; 

pickup pencircle scaled (pen_width, pen_width, pen_width);

w := 18cm;
h := 18cm;

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

boolean b;

numeric i;
numeric j;

point A, B, C, D, E; %% The given points
point F;             %% The point found using `get_point'
point X, Y, Z;       %% The intersection points

point save_A, save_B, save_C, save_D, save_E;

bool_point bp;

pen dot_pen;
dot_pen := pencircle scaled (1.5mm, 1.5mm);

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


string s;

ellipse e[];

point p[];

path q[];

conic_section_lattice c;

point label_pt;

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

e0 := unit_ellipse scaled (5, 0, 3) rotated (15, 15, 15) shifted (0, 0, .5) ;

p0 := get_point (6)  e0;
p1 := get_point (11)  e0;
p2 := get_point (18) e0;
p3 := get_point (2) e0;
p4 := get_point (25)  e0;
p5 := get_point (19) e0;

%% **** (4) 

point_vector pv;

pv += p0;
pv += p2;  
pv += p3;  
pv += p1;  
pv += p5;  
pv += p4;  

%% **** (4) Set conic section lattice.

c := get_conic_section_lattice pv;

%shift_lattice c, 1;

%% **** (4) Set label point

label_pt := (0, 0, .5frame_h -1.5);

%% **** (4) Commands for labels

verbatim_metapost "verbatimtex \font\largebf=cmbx12 etex;";

%% **** (4) Figures


%% ***** (5) Figures 0 to 9

for i = 0 upto 9:

beginfig(i);

draw e0 with_pen path_pen;

A := get_point c with_increment 0;
B := get_point c with_increment 1;
C := get_point c with_increment 2;
D := get_point c with_increment 3;
E := get_point c with_increment 4;

if (i) == 0:
   F := A;
else:
      F := get_point c with_increment i / 10 with_no_shift;
fi;

pickup dot_pen;

dotlabel.llft("$A$", A) with_text_color red;
dotlabel.ulft("$B$", B) with_text_color red;
dotlabel.top("$C$", C) with_text_color red;
dotlabel.urt("$D$",  D) with_text_color red;
dotlabel.bot("$E$", E) with_text_color red;

label.llft("$A'$", A shifted (0, 0, -.5));
label.ulft("$B'$", B shifted (0, 0, .5));
label.top("$C'$",  C shifted (0, 0, .5));
label.urt("$D'$",  D shifted (.5, 0, .5));
label.bot("$E'$",  E shifted (0, 0, -.5));


dotlabel.bot("$F$", F) with_text_color red;


pickup path_pen;

draw A -- C;
draw B -- D;
draw B -- E;
draw E -- A;

draw C -- F;
draw F -- D;

bp := (A -- C) intersection_point (B -- D);

X := bp;


bp := (C -- F) intersection_point (B -- E);

Y := bp;

bp := (F -- D) intersection_point (E -- A);

if (i) == 0:
     Z := A;
else:
   Z := bp;
fi;

draw X -- Z with_color green;

pickup dot_pen;

dotlabel.ulft("$X$", X) with_dot_color blue;

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

dotlabel.lrt("$Z$", Z) with_dot_color blue;

if false: 
if (i) == 0:
    s :=     "\vtop{\centerline{{\largebf The Braikenridge-Maclaurin Construction 3}}"
          &  "\vskip.5\baselineskip"
       	 &  "\centerline{Copyright {\copyright} 2007, 2008, 2009, 2010, 2011 The Free Software Foundation}"
       	 &  "\centerline{Author:  Laurence D. Finston}}"; 
    label(s, label_pt);
fi;
fi;

draw frame with_pen pensquare scaled (1.5mm, 1.5mm);

endfig with_projection parallel_x_z no_sort; 
endfor;

%% ***** (5) Figures 10 to 19

save_A := A;
save_B := B;
save_C := C;
save_D := D;
save_E := E;

shift_lattice c, 1;

for i = 0 upto 9:

beginfig(10 + i);

draw e0 with_pen path_pen;

dotlabel.llft("$A$", save_A) with_text_color red;
dotlabel.ulft("$B$", save_B) with_text_color red;
dotlabel.top("$C$", save_C) with_text_color red;
dotlabel.urt("$D$",  save_D) with_text_color red;
dotlabel.bot("$E$", save_E) with_text_color red;


A := get_point c with_increment 0;
B := get_point c with_increment 1;
C := get_point c with_increment 2;
D := get_point c with_increment 3;
E := get_point c with_increment 4;

label.llft("$B'$", B shifted (0, 0, -.5));
label.ulft("$C'$", C shifted (0, 0, .5));
label.top("$D'$",  D shifted (0, 0, .5));
label.urt("$E'$",  E shifted (.5, 0, .5));
label.bot("$A'$",  A shifted (0, 0, -.5));


if (i) == 0:
   F := A;
else:
   F := get_point c with_increment i / 10;
fi;

dotlabel.bot("$F$", F) with_text_color red;

pickup path_pen;

draw A -- C;
draw B -- D;
draw B -- E;
draw E -- A;

draw C -- F;
draw F -- D;

bp := (A -- C) intersection_point (B -- D);

X := bp;

bp := (C -- F) intersection_point (B -- E);


Y := bp;

bp := (F -- D) intersection_point (E -- A);

if (i) == 0:
   Z := F;
else:
   Z := bp;
fi;

draw X -- Z with_color green;

pickup dot_pen;

dotlabel.ulft("$X$", X) with_dot_color blue;

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

dotlabel.lrt("$Z$", Z) with_dot_color blue;


draw frame with_pen pensquare scaled (1.5mm, 1.5mm);

endfig with_projection parallel_x_z no_sort; 
endfor;

%% ***** (5) Figures 20 to 29

shift_lattice c, 1;

for i = 0 upto 9:

beginfig(20 + i);

draw e0 with_pen path_pen;

dotlabel.llft("$A$", save_A) with_text_color red;
dotlabel.ulft("$B$", save_B) with_text_color red;
dotlabel.top("$C$",  save_C) with_text_color red;
dotlabel.urt("$D$",  save_D) with_text_color red;
dotlabel.bot("$E$",  save_E) with_text_color red;

A := get_point c with_increment 0;
B := get_point c with_increment 1;
C := get_point c with_increment 2;
D := get_point c with_increment 3;
E := get_point c with_increment 4;


label.llft("$C'$", C shifted (0, 0, -.5));
label.ulft("$D'$", D shifted (0, 0, .5));
label.top("$E'$",  E shifted (0, 0, .5));
label.urt("$A'$",  A shifted (.5, 0, .5));
label.bot("$B'$",  B shifted (0, 0, -.5));



if (i) == 0:
   F := A;
else:
   F := get_point c with_increment i / 10;
fi;

dotlabel.bot("$F$", F) with_text_color red;

pickup path_pen;

draw A -- C;
draw B -- D;
draw B -- E;
draw E -- A;

draw C -- F;
draw F -- D;

bp := (A -- C) intersection_point (B -- D);

X := bp;

bp := (C -- F) intersection_point (B -- E);


Y := bp;

bp := (F -- D) intersection_point (E -- A);

if (i) == 0:
   Z := F;
else:
   Z := bp;
fi;

draw X -- Z with_color green;

pickup dot_pen;

dotlabel.ulft("$X$", X) with_dot_color blue;

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

dotlabel.lrt("$Z$", Z) with_dot_color blue;


draw frame with_pen pensquare scaled (1.5mm, 1.5mm);

endfig with_projection parallel_x_z no_sort; 
endfor;

%% ***** (5) Figures 30 to 39

shift_lattice c, 1;

for i = 0 upto 9:

beginfig(30 + i);

draw e0 with_pen path_pen;

dotlabel.llft("$A$", save_A) with_text_color red;
dotlabel.ulft("$B$", save_B) with_text_color red;
dotlabel.top("$C$",  save_C) with_text_color red;
dotlabel.urt("$D$",  save_D) with_text_color red;
dotlabel.bot("$E$",  save_E) with_text_color red;

A := get_point c with_increment 0;
B := get_point c with_increment 1;
C := get_point c with_increment 2;
D := get_point c with_increment 3;
E := get_point c with_increment 4;


label.llft("$D'$", D shifted (0, 0, -.5));
label.ulft("$E'$", E shifted (0, 0, .5));
label.top("$A'$",  A shifted (0, 0, .5));
label.urt("$B'$",  B shifted (.5, 0, .5));
label.bot("$C'$",  C shifted (0, 0, -.5));

if (i) == 0:
   F := A;
else:
   F := get_point c with_increment i / 10;
fi;

dotlabel.bot("$F$", F) with_text_color red;

pickup path_pen;

draw A -- C;
draw B -- D;
draw B -- E;
draw E -- A;

draw C -- F;
draw F -- D;

bp := (A -- C) intersection_point (B -- D);

X := bp;

bp := (C -- F) intersection_point (B -- E);


Y := bp;

bp := (F -- D) intersection_point (E -- A);

if (i) == 0:
   Z := F;
else:
   Z := bp;
fi;

draw X -- Z with_color green;

pickup dot_pen;

dotlabel.ulft("$X$", X) with_dot_color blue;

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

dotlabel.lrt("$Z$", Z) with_dot_color blue;


draw frame with_pen pensquare scaled (1.5mm, 1.5mm);

endfig with_projection parallel_x_z no_sort; 
endfor;


%% ***** (5) Figures 40 to 49

shift_lattice c, 1;

for i = 0 upto 9:

beginfig(40 + i);

draw e0 with_pen path_pen;

dotlabel.llft("$A$", save_A) with_text_color red;
dotlabel.ulft("$B$", save_B) with_text_color red;
dotlabel.top("$C$",  save_C) with_text_color red;
dotlabel.urt("$D$",  save_D) with_text_color red;
dotlabel.bot("$E$",  save_E) with_text_color red;

A := get_point c with_increment 0;
B := get_point c with_increment 1;
C := get_point c with_increment 2;
D := get_point c with_increment 3;
E := get_point c with_increment 4;


label.llft("$E'$", E shifted (0, 0, -.5));
label.ulft("$A'$", A shifted (0, 0, .5));
label.top("$B'$",  B shifted (0, 0, .5));
label.urt("$C'$",  C shifted (.5, 0, .5));
label.bot("$D'$",  D shifted (0, 0, -.5));

if (i) == 0:
   F := A;
else:
   F := get_point c with_increment i / 10;
fi;

dotlabel.bot("$F$", F) with_text_color red;

pickup path_pen;

draw A -- C;
draw B -- D;
draw B -- E;
draw E -- A;

draw C -- F;
draw F -- D;

bp := (A -- C) intersection_point (B -- D);

X := bp;

bp := (C -- F) intersection_point (B -- E);


Y := bp;

bp := (F -- D) intersection_point (E -- A);

if (i) == 0:
   Z := F;
else:
   Z := bp;
fi;

draw X -- Z with_color green;

pickup dot_pen;

dotlabel.ulft("$X$", X) with_dot_color blue;

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

dotlabel.lrt("$Z$", Z) with_dot_color blue;


draw frame with_pen pensquare scaled (1.5mm, 1.5mm);

endfig with_projection parallel_x_z no_sort; 
endfor;

%% **** (4) End.

verbatim_metapost "end";
end;