Rotate Bitmap by one Point

uses ExtCtrls, StdCtrls, Math

private
    { Private declarations }
    function Vektor(FromP, Top: TPoint): TPoint;
    function xComp(Vektor: TPoint; Angle: Extended): Integer;
    function yComp(Vektor: TPoint; Angle: Extended): Integer;
    function RotImage(srcbit: TBitmap; Angle: Extended; FPoint: TPoint;
             Background: TColor): TBitmap;
             
//

function TForm1.Vektor(FromP, Top: TPoint): TPoint;
begin
  Result.x := Top.x - FromP.x;
  Result.y := Top.y - FromP.y;
end;

// new x-component of the vector
function TForm1.xComp(Vektor: TPoint; Angle: Extended): Integer;
begin
  Result := Round(Vektor.x * cos(Angle) - (Vektor.y) * sin(Angle));
end;

// new y-component of the vector
function TForm1.yComp(Vektor: TPoint; Angle: Extended): Integer;
begin
  Result := Round((Vektor.x) * (sin(Angle)) + (vektor.y) * cos(Angle));
end;


function TForm1.RotImage(srcbit: TBitmap; Angle: Extended; FPoint: TPoint;
  Background: TColor): TBitmap;
var
  highest, lowest, mostleft, mostright: TPoint;
  topoverh, leftoverh: integer;
  x, y, newx, newy: integer;
begin
  Result := TBitmap.Create;

  // Calculate angle down on one rotation, if necessary
  while Angle >= (2 * pi) do
  begin
    angle := Angle - (2 * pi);
  end;

  // specify new size
  if (angle <= (pi / 2)) then
  begin
    highest := Point(0,0);
    Lowest := Point(Srcbit.Width, Srcbit.Height);
    mostleft := Point(0,Srcbit.Height);
    mostright := Point(Srcbit.Width, 0);
  end 
  else if (angle <= pi) then
  begin
    highest := Point(0,Srcbit.Height);
    Lowest := Point(Srcbit.Width, 0);
    mostleft := Point(Srcbit.Width, Srcbit.Height);
    mostright := Point(0,0);
  end
  else if (Angle <= (pi * 3 / 2)) then
  begin
    highest := Point(Srcbit.Width, Srcbit.Height);
    Lowest := Point(0,0);
    mostleft := Point(Srcbit.Width, 0);
    mostright := Point(0,Srcbit.Height);
  end 
  else
  begin
    highest := Point(Srcbit.Width, 0);
    Lowest := Point(0,Srcbit.Height);
    mostleft := Point(0,0);
    mostright := Point(Srcbit.Width, Srcbit.Height);
  end;

  topoverh := yComp(Vektor(FPoint, highest), Angle);
  leftoverh := xComp(Vektor(FPoint, mostleft), Angle);
  Result.Height := Abs(yComp(Vektor(FPoint, lowest), Angle)) + Abs(topOverh);
  Result.Width  := Abs(xComp(Vektor(FPoint, mostright), Angle)) + Abs(leftoverh);

  // change of FPoint in the new picture in relation on srcbit
  Topoverh := TopOverh + FPoint.y;
  Leftoverh := LeftOverh + FPoint.x;

  // at first fill with background color
  Result.Canvas.Brush.Color := Background;
  Result.Canvas.pen.Color   := background;
  Result.Canvas.Fillrect(Rect(0,0,Result.Width, Result.Height));

  // Start of actual rotation
  for y := 0 to srcbit.Height - 1 do
  begin
    for x := 0 to srcbit.Width - 1 do
    begin
      newX := xComp(Vektor(FPoint, Point(x, y)), Angle);
      newY := yComp(Vektor(FPoint, Point(x, y)), Angle);
      newX := FPoint.x + newx - leftoverh;
      newy := FPoint.y + newy - topoverh;
      // Move beacause of new size
      Result.Canvas.Pixels[newx, newy] := srcbit.Canvas.Pixels[x, y];
      // also fil lthe pixel beside to prevent empty pixels
      if ((angle < (pi / 2)) or
        ((angle > pi) and
        (angle < (pi * 3 / 2)))) then
      begin
        Result.Canvas.Pixels[newx, newy + 1] := srcbit.Canvas.Pixels[x, y];
      end 
      else
      begin
        Result.Canvas.Pixels[newx + 1,newy] := srcbit.Canvas.Pixels[x, y];
      end;
    end;
  end;
end;

Beispiel :

procedure TForm1.Button1Click(Sender: TObject);
var
  mybitmap, newbit: TBitMap;
begin
  begin
    mybitmap := TBitmap.Create;
    mybitmap.Assign(Image1.Picture.Bitmap);
    newbit := RotImage(mybitmap, DegToRad(45),
      Point(mybitmap.Width div 2, mybitmap.Height div 2), clBlack);
    Image1.Canvas.Draw(0,0, newBit);
  end;
end;