unit Unit2;
{
  This software has been designed and 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 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 Tekst(nr : integer);
{
  Display Enumerations
}
var
  Ox,Oy : integer;
begin
  with Form1.Image1.Canvas do
  begin
    Ox := PenPos.x; Oy := PenPos.y;
    TextOut(Ox,Oy,IntToStr(nr));
    MoveTo(Ox,Oy);
  end;
end;

procedure Tekenen;
{
  Pictures
}
const
  eps : double = 0.02;
var
  x,y,D : array[1..4] of double;
  xi,eta,p,q,G : double;
  k,i,j,m,n : integer;
  scherm : array of array of double;
  nr : string[2];
begin
{ Random Quadrilateral }
  for k := 1 to 4 do
  begin
    x[k] := Random-1/2; y[k] := Random-1/2;
  end;
{ Jacobian Determinant }
  D[1] := (x[2]-x[1])*(y[3]-y[1])-(x[3]-x[1])*(y[2]-y[1]);
  D[2] := (x[2]-x[1])*(y[4]-y[2])-(x[4]-x[2])*(y[2]-y[1]);
  D[3] := (x[4]-x[3])*(y[3]-y[1])-(x[3]-x[1])*(y[4]-y[3]);
  D[4] := (x[4]-x[3])*(y[4]-y[2])-(x[4]-x[2])*(y[4]-y[3]);
  SetLength(scherm,Wijd,Hoog);
  for i := 0 to Wijd-1 do
  begin
    for j := 0 to Hoog-1 do
    begin
      scherm[i,j] := 0;
    end;
  end;
{ -1/2 < xi,eta < +1/2 }
  for j := 0 to Hoog do
  begin
    eta := j/Hoog-1/2;
    for i := 0 to Wijd do
    begin
      xi := i/Wijd-1/2;
      p := (1/2-xi)*(1/2-eta)*x[1]
         + (1/2+xi)*(1/2-eta)*x[2]
         + (1/2-xi)*(1/2+eta)*x[3]
         + (1/2+xi)*(1/2+eta)*x[4];
      q := (1/2-xi)*(1/2-eta)*y[1]
         + (1/2+xi)*(1/2-eta)*y[2]
         + (1/2-xi)*(1/2+eta)*y[3]
         + (1/2+xi)*(1/2+eta)*y[4];
    { G := (1/2-xi)*(1/2-eta)*D[1]
         + (1/2+xi)*(1/2-eta)*D[2]
         + (1/2-xi)*(1/2+eta)*D[3]
         + (1/2+xi)*(1/2+eta)*D[4]; }
      G := (D[1]+D[2]+D[3]+D[4])/4
         + (D[2]-D[1]+D[4]-D[3])/2*xi
         + (D[3]-D[1]+D[4]-D[2])/2*eta;
      m := x2i(p); n := y2j(q);
    { 1:1 mapping + or - }
      if (G < 0) and (scherm[m,n] = 0) then scherm[m,n] := 1;
      if (G > 0) and (scherm[m,n] = 0) then scherm[m,n] := 2;
    { double valued mapping }
      if (G < 0) and (scherm[m,n] = 2) then scherm[m,n] := 3;
      if (G > 0) and (scherm[m,n] = 1) then scherm[m,n] := 4;
    { approximately zero }
      if abs(G) < eps then scherm[m,n] := 5;
    end;
  end;
  for j := 0 to Hoog-1 do
  begin
    for i := 0 to Wijd-1 do
    begin
      if scherm[i,j] = 1 then Form1.Image1.Canvas.Pixels[i,j] := clRed;
      if scherm[i,j] = 2 then Form1.Image1.Canvas.Pixels[i,j] := clGreen;
      if scherm[i,j] = 3 then Form1.Image1.Canvas.Pixels[i,j] := clGray;
      if scherm[i,j] = 4 then Form1.Image1.Canvas.Pixels[i,j] := clGray;
      if scherm[i,j] = 5 then Form1.Image1.Canvas.Pixels[i,j] := clBlue;
    end;
  end;
  Form1.Image1.Canvas.Pen.Color := clBlack;
  Form1.Image1.Canvas.Moveto(x2i(x[1]),y2j(y[1])); Tekst(1);
  Form1.Image1.Canvas.Lineto(x2i(x[2]),y2j(y[2])); Tekst(2);
  Form1.Image1.Canvas.Lineto(x2i(x[4]),y2j(y[4])); Tekst(4);
  Form1.Image1.Canvas.Lineto(x2i(x[3]),y2j(y[3])); Tekst(3);
  Form1.Image1.Canvas.Lineto(x2i(x[1]),y2j(y[1]));
  nr[1] := char((keer div 10)+byte('0'));
  nr[2] := char((keer mod 10)+byte('0'));
  Form1.Image1.Picture.SaveToFile('film\2P'+nr+'.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  On Create
}
begin
  TV(Form1.Image1);
  ClearDevice;
  xmin := -0.6; xmax := +0.6;
  ymin := -0.6; ymax := +0.6;
  Form1.Image1.Canvas.Font.Size := 15;
  Form1.Image1.Canvas.Pen.Width := 2;
  keer := 0;
  Tekenen;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  On KeyPress
}
begin
  ClearDevice;
  keer := keer + 1;
  Tekenen;
end;

end.