unit Unit3;

interface

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

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

var
  Form1: TForm1;

implementation

{$R *.dfm}

var
  keer : integer;

procedure Konstant;
const
  N : integer = 50;
var
  k : integer;
  x : double;
begin
  Form1.Image1.Canvas.Pen.Width := 2;
  for k := 0 to N do
  begin
    x := k/N;
    Form1.Image1.Canvas.MoveTo(x2i(x),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0.1));
  end;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(0.5));
  Form1.Image1.Canvas.LineTo(x2i(1),y2j(0.5));
  Form1.Image1.Picture.SaveToFile('constant.bmp');
end;

procedure Lineair;
const
  N : integer = 50;
var
  k : integer;
  x,D : double;
begin
  Form1.Image1.Canvas.Pen.Width := 2;
  D := 1/(sqrt(1/4+2*N)-1/2);
  for k := 0 to N do
  begin
    x := (sqrt(1/4+2*k)-1/2)*D;
    Form1.Image1.Canvas.MoveTo(x2i(x),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0.1));
  end;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(1/2*D));
  Form1.Image1.Canvas.LineTo(x2i(1),y2j(1+1/2*D));
  Form1.Image1.Picture.SaveToFile('lineair.bmp');
end;

procedure Cauchy;
const
  N : integer = 30;
var
  k : integer;
  x,y,D : double;
begin
  Form1.Image1.Canvas.Pen.Width := 2;
  D := 1/tan((1/2-1/N)*Pi);
  for k := 0 to (N div 2) do
  begin
    x := tan((k/N-1/N)*Pi)*D;
    Form1.Image1.Canvas.MoveTo(x2i(x),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0.1));
  end;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(1));
  for k := 1 to Wijd do
  begin
    x := i2x(k); y := 1/(1+sqr(x/d));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
  end;
  Form1.Image1.Picture.SaveToFile('cauchy.bmp');
end;

procedure Gitaar;
const
  N : integer = 20;
var
  k : integer;
  x,D : double;
begin
  Form1.Image1.Canvas.Pen.Width := 2;
  for k := 0 to N do
  begin
    x := exp(-ln(2)*k/12);
    Form1.Image1.Canvas.MoveTo(x2i(x),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0.1));
  end;
  D := exp(-ln(2)*N/12);
  Form1.Image1.Canvas.MoveTo(x2i(D),y2j(1));
  for k := 0 to Wijd do
  begin
    x := i2x(k); if x < D then Continue;
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(D/x));
  end;
  Form1.Image1.Picture.SaveToFile('gitaar.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
begin
  TV(Form1.Image1);
  ClearDevice;
  xmin := 0; xmax := 1;
  ymin := 0; ymax := 1;
  Konstant;
  keer := 0;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
begin
  keer := keer + 1;
  if keer > 3 then keer := 0;
  ClearDevice;
  case keer of
  0 : Konstant;
  1 : Lineair;
  2 : Cauchy;
  3 : Gitaar;
  end;
end;

end.