unit Unit0;
{
This software has been designed and it is
CopyLefted by Han de Bruijn:

                          (===)
                         @-O^O-@
                          #/_\#
                           ###
}
INTERFACE

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtCtrls, Grafisch;

type
  TForm1 = class(TForm)
    Image1: TImage;
    procedure Toetsdruk(Sender: TObject; var Key: Char);
    procedure Scheppen(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

IMPLEMENTATION

{$R *.dfm}

procedure tekenen;
const
  N : integer = 1239;
  M : integer = 360;
  d : integer = 2;
var
  invoer : TextFile;
  k,i,j : integer;
  x,y : array of double;
  mu_x,mu_y : double;
  s_xx,s_yy,s_xy : double;
  det,a_x,a_y,b_x,b_y : double;
  t,p,q : double;
begin
  SetLength(x,N);
  SetLength(y,N);
  Assign(invoer,'data.txt');
  Reset(invoer);
  k := 0;
  while not EoF(invoer) do
  begin
    Readln(invoer,x[k],y[k]);
    k := k + 1;
  end;
  Close(invoer);
  Form1.Image1.Canvas.Pen.Color := clBlack;
  for k := 0 to N-1 do
  begin
    i := x2i(x[k]); j := y2j(y[k]);
    Form1.Image1.Canvas.Ellipse(i-d,j-d,i+d,j+d);
  end;
  mu_x := 0; mu_y := 0;
  for k := 0 to N-1 do
  begin
    mu_x := mu_x + x[k];
    mu_y := mu_y + y[k];
  end;
  mu_x := mu_x/N; mu_y := mu_y/N;
  Form1.Image1.Canvas.Pen.Color := clRed;
  Form1.Image1.Canvas.Pen.Width := 2;
  i := x2i(mu_x); j := y2j(mu_y);
  Form1.Image1.Canvas.Ellipse(i-d,j-d,i+d,j+d);
  s_xx := 0; s_yy := 0; s_xy := 0;
  for k := 0 to N-1 do
  begin
    s_xx := s_xx + sqr(x[k]-mu_x);
    s_yy := s_yy + sqr(y[k]-mu_y);
    s_xy := s_xy + (x[k]-mu_x)*(y[k]-mu_y);
  end;
  s_xx := 2*s_xx/N; s_yy := 2*s_yy/N; s_xy := 2*s_xy/N;
  a_x := sqrt(s_xx); a_y := 0;
  det := s_xx*s_yy-sqr(s_xy);
  b_x := s_xy/sqrt(s_xx); b_y := sqrt(det/s_xx);
  p := mu_x + a_x; q := mu_y + b_x;
  Form1.Image1.Canvas.MoveTo(x2i(p),y2j(q));
  for k := 0 to M do
  begin
    t := k*Pi/180;
    p := mu_x + a_x*cos(t) + a_y*sin(t);
    q := mu_y + b_x*cos(t) + b_y*sin(t);
    Form1.Image1.Canvas.LineTo(x2i(p),y2j(q));
  end;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  On KeyPress
}
begin
  Exit;
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  At moment of creation
}
begin
  xmin := -3; xmax := 76;
  ymin := -3; ymax := 76;
  TV(Form1.Image1);
  ClearDevice;
  tekenen;
  Form1.Image1.Picture.SaveToFile('ellips.bmp');
end;

END.