unit Unit4;
{
This software has been designed and it is
CopyLefted by Han de Bruijn:

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

http://www.alternatievewiskunde.nl/kammen/proper.htm

One-dimensional analogy of DTFE
-------------------------------
}
INTERFACE

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtCtrls, Math, 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(N : integer);
{
  Calculate and Draw
}
var
  k : integer;
  x,y,max,x1,x2,d : double;
  rij : array of double;
begin
{ Sample density }
  Setlength(rij,N);
  d := 1/tan((1/2-1/(N+1))*Pi);
  Form1.Image1.Canvas.Brush.Color := clBlack;
  for k := 0 to N-1 do
  begin
    rij[k] := d*tan(((k+1)/(N+1)-1/2)*Pi);
    Writeln(rij[k]); x := rij[k];
    with Form1.Image1.Canvas do
    Ellipse(x2i(x)-3,y2j(0)-3,x2i(x)+3,y2j(0)+3);
  end;
  Form1.Image1.Canvas.MoveTo(x2i(xmin),y2j(0));
  Form1.Image1.Canvas.LineTo(x2i(xmax),y2j(0));

{ Exact }
  Form1.Image1.Canvas.Pen.Color := clBlack;
  Form1.Image1.Canvas.MoveTo(x2i(xmin-3),y2j(0));
  for k := 0 to Wijd-1 do
  begin
    x := i2x(k); y := 1/(1+sqr(x/d));
    Form1.Image1.Canvas.LineTo(k,y2j(y));
  end;

{ Voronoi 1-D }
  max := 0;
  Form1.Image1.Canvas.Pen.Color := clGreen;
  for k := 0 to N-3 do
  begin
    y := 2/(rij[k+2]-rij[k]);
    if y > max then max := y;
  end;
  for k := 0 to N-3 do
  begin
    x1 := (rij[k]+rij[k+1])/2;
    x2 := (rij[k+1]+rij[k+2])/2;
    y := 2/(rij[k+2]-rij[k])/max;
  { Histogram }
    with Form1.Image1.Canvas do
    begin
      MoveTo(x2i(x1),y2j(0));
      LineTo(x2i(x1),y2j(y));
      LineTo(x2i(x2),y2j(y));
      LineTo(x2i(x2),y2j(0));
    end;
  end;

{ Delaunay 1-D }
  Form1.Image1.Canvas.Pen.Color := clRed;
  x := rij[0]; y := 0;
  Form1.Image1.Canvas.MoveTo(x2i(x),y2j(y));
  for k := 0 to N-3 do
  begin
    x := rij[k+1];
    y := 2/(rij[k+2]-rij[k])/max;
   Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
  end;
  x := rij[N-1]; y := 0;
  Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
{ Delaunay alternative }
  Form1.Image1.Canvas.Pen.Color := clMaroon;
  k := 0;
  x := rij[k+1];
  y := 2/(rij[k+2]-rij[k])/max;
  Form1.Image1.Canvas.MoveTo(x2i(x),y2j(y));
  x := rij[k];
  y := 2/(rij[k+1]-rij[k])/max;
  Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
  k := N-3;
  x := rij[k+1];
  y := 2/(rij[k+2]-rij[k])/max;
  Form1.Image1.Canvas.MoveTo(x2i(x),y2j(y));
  k := N;
  x := rij[k-1];
  y := 2/(rij[k-1]-rij[k-2])/max;
  Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
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 := -1.01; xmax := +1.01;
  ymin := -0.1; ymax := 1.1;
  TV(Form1.Image1);
  ClearDevice;
  Tekenen(16);
  Form1.Image1.Picture.SaveToFile('eendim.bmp');
end;

END.