unit Unit7;
{
  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
  x,y : array[1..4] of double;
  hoek : double;
  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 mapping(xi,eta : double; var p,q : double);
{
  Bilinear interpolation at quadrilateral
  i.e. transformation (xi,eta) -> (x,y) .
}
begin
  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];
end;

procedure Raster;
{
  Yellow Grid
}
begin
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clYellow;
    MoveTo(x2i(-1/2),y2j(0));
    LineTo(x2i(+1/2),y2j(0));
    MoveTo(x2i(0),y2j(-1/2));
    LineTo(x2i(0),y2j(+1/2));
    MoveTo(x2i(-1/2),y2j(-1/2));
    LineTo(x2i(+1/2),y2j(-1/2));
    LineTo(x2i(+1/2),y2j(+1/2));
    LineTo(x2i(-1/2),y2j(+1/2));
    LineTo(x2i(-1/2),y2j(-1/2));
  end;
end;

procedure Ouderschap;
{
  Parent Square
}
var
  i,j : integer;
begin
  Raster; { Grid }
  with Form1.Image1.Canvas do
  begin
    Brush.Color := clWhite;
    Pen.Color := clBlack;
    MoveTo(x2i(-1/2),y2j(-1/2)); Tekst(1);
    LineTo(x2i(+1/2),y2j(-1/2)); Tekst(2);
    LineTo(x2i(+1/2),y2j(+1/2)); Tekst(4);
    LineTo(x2i(-1/2),y2j(+1/2)); Tekst(3);
    LineTo(x2i(-1/2),y2j(-1/2));
    Pen.Color := clRed;
    MoveTo(x2i(-1/2),y2j(-1/2));
    LineTo(x2i(+1/2),y2j(+1/2));
    MoveTo(x2i(-1/2),y2j(+1/2));
    LineTo(x2i(+1/2),y2j(-1/2));
    Brush.Color := clRed;
    i := x2i(0); j := y2j(0);
    Ellipse(i-5,j-5,i+5,j+5);
  end;
  Form1.Image1.Picture.SaveToFile('film\7Pma.bmp');
end;

procedure Tekenen;
{
  Special Quadrilateral
}
var
  xi,eta,p,q : double;
  i,j,m,n : integer;
  nr : string[2];
begin
  Raster; { Yellow grid }
  x[1] := -1/2; y[1] := 0;
  x[2] := +1/2; y[2] := -1/2;
  x[3] := +1/2; y[3] := +1/2;
  x[4] := hoek; y[4] := 0;
{ -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;
      mapping(xi,eta,p,q);
      m := x2i(p); n := y2j(q);
      Form1.Image1.Canvas.Pixels[m,n] := clGray;
    end;
  end;
{ Curved boundary gray area }
  with Form1.Image1.Canvas do
    Moveto(x2i(x[1]),y2j(y[1]));
  xi := (x[4]-x[1])/(x[2]+x[3]-x[1]-x[4])/2;
  if xi > 1/2 then xi := 1/2;
  eta := xi;
  mapping(xi,eta,p,q);
  i := x2i(p); j := y2j(q);
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clBlue; { green dot }
    Brush.Color := clBlue;
    Ellipse(i-5,j-5,i+5,j+5);
{ Mapping diagonals of square }
    Pen.Color := clRed; { red }
    LineTo(x2i(p),y2j(q));
  end;
  with Form1.Image1.Canvas do
    Moveto(x2i(x[3]),y2j(y[3]));
  for i := 0 to Wijd do
  begin
    xi := i/Wijd-1/2; eta := -xi;
    mapping(xi,eta,p,q);
    Form1.Image1.Canvas.LineTo(x2i(p),y2j(q));
  end;
{ Diagonals intersection point }
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clRed;
    Brush.Color := clRed;
    p := (x[1]+x[2]+x[3]+x[4])/4;
    i := x2i(p); j := y2j(0);
    Ellipse(i-5,j-5,i+5,j+5);
  end;
{ Alternative x-coordinate of vertex(4): mark Green }
  Writeln('xi[4] = ',1/2,',',(1-6*hoek)/(4*hoek-6));
  xi := (1-6*hoek)/(4*hoek-6); eta := xi;
  mapping(xi,eta,p,q);
  i := x2i(p); j := y2j(q);
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clGreen;
    Brush.Color := clGreen;
    Ellipse(i-5,j-5,i+5,j+5);
{ Quadrilateral last but not least }
    Pen.Color := clBlack;
    Brush.Color := clWhite;
    Moveto(x2i(x[1]),y2j(y[1])); Tekst(1);
    Lineto(x2i(x[2]),y2j(y[2])); Tekst(2);
    Lineto(x2i(x[4]),y2j(y[4])); Tekst(4);
    Lineto(x2i(x[3]),y2j(y[3])); Tekst(3);
    Lineto(x2i(x[1]),y2j(y[1]));
  end;
  nr[1] := char((keer div 10)+byte('0'));
  nr[2] := char((keer mod 10)+byte('0'));
  Form1.Image1.Picture.SaveToFile('film\7P'+nr+'.bmp');
end;

procedure Grafiek;
{
  Graph of the function x(xi)
  for y = 0 and/or xi = eta 
}
var
  i,j : integer;
  xi,eta,p,q,max : double;
  nr : string[2];
begin
  Raster; { Grid }
  with Form1.Image1.Canvas do
  begin
    MoveTo(x2i(-1/2),y2j(1/2));
    i := PenPos.x; j := PenPos.y;
    TextOut(i+10,j+10,'x');
    MoveTo(x2i(+1/2),y2j(-1/2));
    i := PenPos.x; j := PenPos.y;
    TextOut(i-30,j-30,'xi');
  end;
  mapping(0,0,p,q);
{ At Midpoint }
  with Form1.Image1.Canvas do
  begin
    Pen.Color := clRed;
    MoveTo(x2i(0),y2j(-1/2));
    LineTo(x2i(0),y2j(p));
  end;
  Form1.Image1.Canvas.MoveTo(x2i(-1/2),y2j(-1/2));
{ The function x(xi) }
  for i := 0 to Wijd do
  begin
    xi := i/Wijd-1/2; eta := xi;
    mapping(xi,eta,p,q);
    Form1.Image1.Canvas.Pen.Color := clBlack;
    Form1.Image1.Canvas.LineTo(x2i(xi),y2j(p));
  end;
{ Mark x-coordinate of vertex(4) }
  Form1.Image1.Canvas.Pen.Color := clGreen;
  Form1.Image1.Canvas.LineTo(x2i(-1/2),y2j(p));
{ Mark alternative x-coordinate of vertex(4) }
  xi := (1-6*hoek)/(4*hoek-6); eta := xi;
  mapping(xi,eta,p,q);
  Form1.Image1.Canvas.MoveTo(x2i(xi),y2j(-1/2));
  Form1.Image1.Canvas.LineTo(x2i(xi),y2j(p));
{ Mark curved boundary of gray area  }
  xi := -(x[4]-x[1])/(x[1]+x[4]-x[2]-x[3])/2;
  Form1.Image1.Canvas.MoveTo(x2i(xi),y2j(-1/2));
  max := -sqr(x[4]-x[1])/(x[1]+x[4]-x[2]-x[3])/4
       + (x[1]+x[2]+x[3]+x[4])/4;
  Form1.Image1.Canvas.Pen.Color := clBlue;
  Form1.Image1.Canvas.LineTo(x2i(xi),y2j(max));
  Writeln(xi,max);
  nr[1] := char((keer div 10)+byte('0'));
  nr[2] := char((keer mod 10)+byte('0'));
  Form1.Image1.Picture.SaveToFile('film\7P'+nr+'.bmp');
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  On Create
}
begin
  keer := 0; hoek := 0;
  TV(Form1.Image1);
  xmin := -0.7; xmax := +0.7;
  ymin := -0.7; ymax := +0.7;
  Form1.Image1.Canvas.Pen.Width := 2;
  Form1.Image1.Canvas.Font.Size := 15;
  ClearDevice;
  Ouderschap;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  On KeyPress
}
begin
  hoek := (keer div 2)*1/8;
  ClearDevice;
  case keer mod 2 of
  0: Tekenen;
  1: Grafiek;
  end;
  keer := keer + 1;
end;

end.