DistanceToBox

function DistanceToBox(pt: TPoint; bx: TBox): Extended;
var
  p: TPoint;
begin
  if not ((pt.X >= bx.X1) and (pt.X <= bx.X2) and (pt.Y >= bx.Y1) and (pt.Y <= bx.Y2)) then
  begin
    p := Point(Max((bx.X1 - pt.X), (pt.X - bx.X2)), Max((bx.Y1 - pt.Y), (pt.Y - bx.Y2)));
    if (p.X < 0) then
      p.X := 0;
    if (p.Y < 0) then
      p.Y := 0;
    Result := Sqrt(Sqr(pt.X - p.X) + Sqr(pt.Y - p.Y));
  end else
    Result := 0.0;
end;