// Vektor von FromP nach ToP
// Vector from FromP to ToP

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

// neue x Komponente des Verktors
// 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;

// neue Y-Komponente des Vektors
// 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;
{
srcbit: TBitmap; // Bitmap dass gedreht werden soll ; Bitmap to be rotated
Angle: extended; // Winkel in Bogenma?, angle
FPoint: TPoint; // Punkt um den gedreht wird ; Point to be rotated around
Background: TColor): TBitmap; // Hintergrundfarbe des neuen Bitmaps ;
// Backgroundcolor of the new bitmap
}
var
highest, lowest, mostleft, mostright: TPoint;
topoverh, leftoverh: integer;
x, y, newx, newy: integer;
begin
Result := TBitmap.Create;

// Drehwinkel runterrechnen auf eine Umdrehung, wenn notig
// Calculate angle down on one rotation, if necessary
while Angle >= (2 * pi) do
begin
angle := Angle - (2 * pi);
end;

// neue Ausma?e festlegen
// specify new size
if (angle <= (pi / 2)) then
begin
highest := Point(0,0); //OL
Lowest := Point(Srcbit.Width, Srcbit.Height); //UR
mostleft := Point(0,Srcbit.Height); //UL
mostright := Point(Srcbit.Width, 0); //OR
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);

// Verschiebung des FPoint im neuen Bild gegenuber srcbit
// change of FPoint in the new picture in relation on srcbit
Topoverh := TopOverh + FPoint.y;
Leftoverh := LeftOverh + FPoint.x;

// erstmal mit Hintergrundfarbe fullen
// 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 des eigentlichen Rotierens
// Start of actual rotation
for y := 0 to srcbit.Height - 1 do
begin // Zeilen ; Rows
for x := 0 to srcbit.Width - 1 do
begin // Spalten ; Columns
newX := xComp(Vektor(FPoint, Point(x, y)), Angle);
newY := yComp(Vektor(FPoint, Point(x, y)), Angle);
newX := FPoint.x + newx - leftoverh;
// Verschieben wegen der neuen Ausma?e
newy := FPoint.y + newy - topoverh;
// Move beacause of new size
Result.Canvas.Pixels[newx, newy] := srcbit.Canvas.Pixels[x, y];
// auch das Pixel daneben fullen um Leerpixel bei Drehungen zu verhindern
// 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;

procedure TForm1.Button1Click(Sender: TObject);
var
mybitmap, newbit: TBitMap;
begin
if OpenDialog1.Execute then
begin
mybitmap := TBitmap.Create;
mybitmap.LoadFromFile(OpenDialog1.FileName);
newbit := RotImage(mybitmap, DegToRad(45),
Point(mybitmap.Width div 2, mybitmap.Height div 2), clBlack);
Image1.Canvas.Draw(0,0, newBit);
end;
end;

end;