// determine if 2 line cross given their end-points
function LinesCross(LineAP1, LineAP2, LineBP1, LineBP2 : TPoint) : boolean;
Var
 diffLA, diffLB : TPoint;
 CompareA, CompareB : integer;
begin
 Result := False;
 diffLA := Subtract(LineAP2, LineAP1);
 diffLB := Subtract(LineBP2, LineBP1);
 CompareA := diffLA.X*LineAP1.Y - diffLA.Y*LineAP1.X;
 CompareB := diffLB.X*LineBP1.Y - diffLB.Y*LineBP1.X;
 if ( ((diffLA.X*LineBP1.Y - diffLA.Y*LineBP1.X) < CompareA) xor
  ((diffLA.X*LineBP2.Y - diffLA.Y*LineBP2.X) < CompareA) ) and
  ( ((diffLB.X*LineAP1.Y - diffLB.Y*LineAP1.X) < CompareB) xor
  ((diffLB.X*LineAP2.Y - diffLB.Y*LineAP2.X) < CompareB) ) then
  Result := True;
end;
function LineIntersect(LineAP1, LineAP2, LineBP1, LineBP2 : TPoint) : TPointFloat;
Var
 LDetLineA, LDetLineB, LDetDivInv : Real;
 LDiffLA, LDiffLB : TPoint;
begin
 LDetLineA := LineAP1.X*LineAP2.Y - LineAP1.Y*LineAP2.X;
 LDetLineB := LineBP1.X*LineBP2.Y - LineBP1.Y*LineBP2.X;
 LDiffLA := Subtract(LineAP1, LineAP2);
 LDiffLB := Subtract(LineBP1, LineBP2);
 LDetDivInv := 1 / ((LDiffLA.X*LDiffLB.Y) - (LDiffLA.Y*LDiffLB.X));
 Result.X := ((LDetLineA*LDiffLB.X) - (LDiffLA.X*LDetLineB)) * LDetDivInv;
 Result.Y := ((LDetLineA*LDiffLB.Y) - (LDiffLA.Y*LDetLineB)) * LDetDivInv;
end;
function Subtract(AVec1, AVec2 : TPoint) : TPoint;
begin
 Result.X := AVec1.X - AVec2.X;
 Result.Y := AVec1.Y - AVec2.Y;
end;