LÖVE

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function line_line(x1, y1, x2, y2, x3, y3, x4, y4)
  local uA = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
  local uB = ((x2-x1)*(y1-y3) - (y2-y1)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1));
  return uA >= 0 and uA <= 1 and uB >= 0 and uB <= 1
end

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function pseudoScalarMutiplication (ax, ay, bx, by)
	return ax*by-ay*bx
end

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AB = {x=Bx-Ax, y=By-Ay} -- where Ax, Ay is a position of point A; Bx, By - position of point B
AC = {x=Cx-Ax, y=Cy-Ay}
AD = {x=Dx-Ax, y=Dy-Ay}
-- check if points C and D are on the one side of line AB:
local value = pseudoScalarMutiplication (AB.x, AB.y, AC.x, AC.y) * pseudoScalarMutiplication (AB.x, AB.y, AD.x, AD.y)
if value > 0 then
	-- no intersection: both are positive or both are negative
else
	-- the intersection is _possible_
	-- check if points A and B are on the one side of line CD:
	CD = {x=Dx-Cx, y=Dy-Cy}
	CA = {x=Ax-Cx, y=Ay-Cy}
	CB = {x=Bx-Cx, y=By-Cy}
	local value = pseudoScalarMutiplication (CD.x, CD.y, CA.x, CA.y) * pseudoScalarMutiplication (CD.x, CD.y, CB.x, CB.y)
	if value > 0 then
		-- no intersection: both are positive or both are negative
	else
		-- 100% intersection!
	end
else
end

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function isIntersection (x1, y1, x2, y2, x3, y3, x4, y4)
-- line segments AB: x1, y1, x2, y2 and CD: x3, y3, x4, y4
	local abx, aby = (x2-x1), (y2-y1) -- main vector ab
	local acx, acy = (x3-x1), (y3-y1) -- vector ac
	local adx, ady = (x4-x1), (y4-y1) -- vector ad
	local u = (abx*acy - aby*acx)*(abx*ady - aby*adx)
	if u > 0 then return false end
	local bcx, bcy = (x3-x2), (y3-y2) -- vector bc 
	local dcx, dcy = (x3-x4), (y3-y4) -- main vector dc (vector ac is above)
	local v = (dcx*acy - dcy*acx)*(dcx*bcy - dcy*bcx)
	if v > 0 then return false end
	return true
end