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const
  PixelMax = 32768;

type
  pPixelArray = ^TPixelArray;
  TPixelArray = array [0..PixelMax-1] of TRGBTriple;

procedure RotateBitmap_ads(SourceBitmap: TBitmap;
out DestBitmap: TBitmap; Center: TPoint; Angle: Double);
var
  cosRadians : Double;
  inX : Integer;
  inXOriginal : Integer;
  inXPrime : Integer;
  inXPrimeRotated : Integer;
  inY : Integer;
  inYOriginal : Integer;
  inYPrime : Integer;
  inYPrimeRotated : Integer;
  OriginalRow : pPixelArray;
  Radians : Double;
  RotatedRow : pPixelArray;
  sinRadians : Double;
begin
  DestBitmap.Width := SourceBitmap.Width;
  DestBitmap.Height := SourceBitmap.Height;
  DestBitmap.PixelFormat := pf24bit;
  Radians := -(Angle) * PI / 180;
  sinRadians := Sin(Radians);
  cosRadians := Cos(Radians);
  for inX := DestBitmap.Height-1 downto 0 do
  begin
    RotatedRow := DestBitmap.Scanline[inX];
    inXPrime := 2*(inX - Center.y) + 1;
    for inY := DestBitmap.Width-1 downto 0 do
    begin
      inYPrime := 2*(inY - Center.x) + 1;
      inYPrimeRotated := Round(inYPrime * CosRadians - inXPrime * sinRadians);
      inXPrimeRotated := Round(inYPrime * sinRadians + inXPrime * cosRadians);
      inYOriginal := (inYPrimeRotated - 1) div 2 + Center.x;
      inXOriginal := (inXPrimeRotated - 1) div 2 + Center.y;
      if (inYOriginal >= 0) and (inYOriginal <= SourceBitmap.Width-1) and
      (inXOriginal >= 0) and (inXOriginal <= SourceBitmap.Height-1) then
      begin
        OriginalRow := SourceBitmap.Scanline[inXOriginal];
        RotatedRow[inY] := OriginalRow[inYOriginal]
      end
      else
      begin
        RotatedRow[inY].rgbtBlue := 255;
        RotatedRow[inY].rgbtGreen := 0;
        RotatedRow[inY].rgbtRed := 0
      end;
    end;
  end;
end;

{Usage:}
procedure TForm1.Button1Click(Sender: TObject);
var
  Center : TPoint;
  Bitmap : TBitmap;
begin
  Bitmap := TBitmap.Create;
  try
    Center.y := (Image.Height div 2)+20;
    Center.x := (Image.Width div 2)+0;
    RotateBitmap_ads(
    Image.Picture.Bitmap,
    Bitmap,
    Center,
    Angle);
    Angle := Angle + 15;
    Image2.Picture.Bitmap.Assign(Bitmap);
  finally
    Bitmap.Free;
  end;
end;