unit Unit6;
{
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 test(n : integer);
{
  Test with known functions
}
var
  x,y,v : double;
  i,k : integer;
begin
  with Form1.Image1.Canvas do
  begin
  { Orthogonal Hyperbola }
    Pen.Width := 2;
    Pen.Color := clBlack;
    x := 1/ymax; y := ymax;
    MoveTo(x2i(x),y2j(y));
    i := x2i(x);
    for k := i to Wijd-1 do
      LineTo(k,y2j(1/i2x(k)));

  { Coordinate system, y=x }
    Pen.Color := clYellow;
    MoveTo(x2i(xmin),y2j(0));
    LineTo(x2i(xmax),y2j(0));
    MoveTo(x2i(0),y2j(ymin));
    LineTo(x2i(0),y2j(ymax));
    MoveTo(x2i(xmin),y2j(ymin));
    LineTo(x2i(xmax),y2j(ymax));

  { Numerical integration }
    Pen.Color := clRed;
    x := 1;
    MoveTo(x2i(x),y2j(0));
    LineTo(x2i(x),y2j(1/x));
    i := Round((xmax-1)*n);
    for k := 1 to i do
    begin
      MoveTo(x2i(x),y2j(0));
      LineTo(x2i(x),y2j(1/x));
      v := x;
      x := x + x/n;
      LineTo(x2i(x),y2j(1/v));
      LineTo(x2i(x),y2j(0));
    end;

  { Logarithm numerically }
    x := 1; y := 0;
    MoveTo(x2i(x),y2j(y));
    for k := 1 to i do
    begin
      x := x + x/n;
      y := y + 1/n;
      LineTo(x2i(x),y2j(y));
    end;
  { Logarithm analytically }
    x := 1; y := 0;
    MoveTo(x2i(x),y2j(y));
    Pen.Width := 1;
    for k := x2i(1) to Wijd-1 do
    begin
      x := i2x(k); y := ln(x);
      LineTo(x2i(x),y2j(y));
    end;

  { Its inverse numerically }
    Pen.Color := clGreen;
    Pen.Width := 2;
    y := 1;
    for k := 1 to i do
    begin
      y := y + y/n;
      MoveTo(x2i(-0.1),y2j(y));
      LineTo(x2i(0.1),y2j(y));
    end;
    x := 0;
    for k := 1 to 25 do
    begin
      x := x + 1/n;
      MoveTo(x2i(x),y2j(0));
      LineTo(x2i(x),y2j(-0.1));
    end;
    y := 1; x := 0;
    MoveTo(x2i(x),y2j(y));
    for k := 1 to i do
    begin
      y := y + y/n;
      x := x + 1/n;
      LineTo(x2i(x),y2j(y));
    end;
  { Its inverse analytically }
    Pen.Width := 1;
    MoveTo(x2i(0),y2j(1));
    for k := x2i(0) to Wijd-1 do
    begin
      x := i2x(k); y := exp(x);
      LineTo(x2i(x),y2j(y));
    end;
  { Refinement trapezium rule
    Pen.Width := 1;
    Pen.Color := clBlack;
    y := 1; x := 0;
    MoveTo(x2i(x),y2j(y));
    for k := 1 to i do
    begin
      y := y*(1/n+sqrt(1+sqr(1/n)));
      x := x + 1/n;
      LineTo(x2i(x),y2j(y));
    end; }
  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 := -0.1; xmax := 9;
  ymin := -0.1; ymax := 9;
  TV(Form1.Image1);
  ClearDevice;
  test(10);
  Form1.Image1.Picture.SaveToFile('prijs.bmp');
end;

END.