unit Unit4;

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 Histogram(maal : integer);
const
  N : integer = 100;
  L : double = 1/4;
var
  k : integer;
  x,v,D,A,y,M : double;
begin
  D := 1/N; A := L/(2*pi)/maal;
  x := 0; M := 0;
  for k := 1 to N do
  begin
    v := x;
    x := k*D + A*sin(2*pi/L*k*D);
    y := 1/(x-v);
    if y > M then M := y;
  end;
  x := 0;
  Form1.Image1.Canvas.Pen.Width := 1;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(0));
  for k := 1 to N do
  begin
    v := x;
    x := k*D + A*sin(2*pi/L*k*D);
    y := 1/(x-v)/M;
    Form1.Image1.Canvas.LineTo(x2i(v),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(v),y2j(y));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(y));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0));
  end;
  if maal = 2 then
  Form1.Image1.Picture.SaveToFile('golf1.bmp');
  if maal = 8 then
  Form1.Image1.Picture.SaveToFile('golf2.bmp');
end;

procedure Driehoeken(maal : integer);
const
  N : integer = 100;
  L : double = 1/4;
var
  k : integer;
  D,A,y,M : double;
  x : array of double;
begin
  D := 1/N; A := L/(2*pi)/maal;
  SetLength(x,N+1);
  for k := 0 to N do
  begin
    x[k] := k*D + A*sin(2*pi/L*k*D);
  end;
  M := 0;
  for k := 1 to N-1 do
  begin
    y := 2/(x[k+1]-x[k-1]);
    if y > M then M := y; 
  end;
  Form1.Image1.Canvas.Pen.Width := 2;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(0));
  for k := 1 to N-1 do
  begin
    y := 2/(x[k+1]-x[k-1])/M;
    Form1.Image1.Canvas.LineTo(x2i(x[k]),y2j(y));
  end;
  Form1.Image1.Canvas.LineTo(x2i(x[N]),y2j(0));
  for k := 1 to N do
  begin
    Form1.Image1.Canvas.MoveTo(x2i(x[k]),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x[k]),y2j(0.1));
  end;
  if maal = 2 then
  Form1.Image1.Picture.SaveToFile('golf3.bmp');
  if maal = 8 then
  Form1.Image1.Picture.SaveToFile('golf4.bmp');
end;

procedure Gaussians(N : integer);
const
  L : double = 1/4;
  eps : double = 1/256;
  maal : integer = 2;
var
  k,i : integer;
  D,A,M,v : double;
  mu,sigma,factor,norm : double;
  x,y : array of double;
begin
  D := 1/N; A := L/(2*pi)/2;
  factor := sqrt(2*ln(2/eps))/(2*Pi)*maal;
  Writeln(factor);
  SetLength(x,N+1);
  for k := 0 to N do
  begin
    x[k] := k*D + A*sin(2*pi/L*k*D);
  end;
  M := 0;
  SetLength(y,Wijd);
  for i := 0 to Wijd-1 do
    y[i] := 0;
  for k := 1 to N do
  begin
    mu := (x[k]+x[k-1])/2;
    sigma := (x[k]-x[k-1])*factor;
    norm := 1/sqrt(sigma*2*Pi);
    for i := 0 to Wijd-1 do
    begin
      v := i2x(i);
      y[i] := y[i] + exp(-sqr((v-mu)/sigma)/2)*norm;
    end;
  end;
  for i := 0 to Wijd-1 do
    if y[i] > M then M := y[i]; 
  Form1.Image1.Canvas.Pen.Width := 2;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(y[0]/M));
  for i := 1 to Wijd-1 do
  begin
    v := i2x(i);
    Form1.Image1.Canvas.LineTo(x2i(v),y2j(y[i]/M));
  end;
  for k := 1 to N do
  begin
    Form1.Image1.Canvas.MoveTo(x2i(x[k]),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x[k]),y2j(0.2));
  end;
  Form1.Image1.Picture.SaveToFile('golf6.bmp');
end;

procedure Omgekeerd(N : integer);
const
  L : double = 1/4;
var
  k : integer;
  D,A,x,y,f : double;

  function P(x : double) : double;
  begin
    P := (1-A*2*Pi/L*cos(2*Pi/L*x))/D;
  end;

  function Q(x : double) : double;
  begin
    Q := A*sqr(2*Pi/L)*cos(2*Pi/L*x)/D;
  end;

begin
  D := 1/N; A := L/(2*Pi)/2;
  Form1.Image1.Canvas.Pen.Width := 2;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(0));
  x := 0;
  for k := 1 to N do
  begin
    x := x + 1/(sqrt(sqr(P(x)/2)+Q(x)/2)+P(x)/2);
    Form1.Image1.Canvas.MoveTo(x2i(x),y2j(0));
    Form1.Image1.Canvas.LineTo(x2i(x),y2j(0.2));
  end;
  y := P(0)*D; f := (1+A*2*Pi/L);
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(y/f));
  for k := 1 to Wijd do
  begin
    x := i2x(k); y := P(x)*D;
    Form1.Image1.Canvas.LineTo(k,y2j(y/f));
  end;
  Form1.Image1.Picture.SaveToFile('golf5.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
begin
  TV(Form1.Image1);
  ClearDevice;
  xmin := 0; xmax := 1;
  ymin := 0; ymax := 1;
  Histogram(2);
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
begin
  keer := keer + 1;
  if keer > 5 then keer := 0;
  ClearDevice;
  case keer of
  0 : Histogram(2);
  1 : Histogram(8);
  2 : Driehoeken(2);
  3 : Driehoeken(8);
  4 : Omgekeerd(50);
  5 : Gaussians(25);
  end;
end;

end.