Benutzer:Antonsusi/Streckenschnittpunkt

s(x2 - x1) - t(x4 - x3) = x3 - x1        s(y2 - y1) - t(y4 - y3) = y3 - y1
s(x2 - x1) = t(x4 - x3) + x3 - x1        s(y2 - y1) = t(y4 - y3) + y3 - y1 
s = (t(x4 - x3) + (x3 - x1))/(x2 - x1)   s = (t(y4 - y3) + (y3 - y1))/(y2 - y1)

(t(x4 - x3) +(x3 - x1))/(x2 - x1) =  (t(y4 - y3) + (y3 - y1))/(y2 - y1)

(t(x4 - x3) +(x3 - x1))*(y2 - y1) = (t(y4 - y3) + (y3 - y1))*(x2 - x1)

t(x4 - x3)*(y2 - y1) - t(y4 - y3)*(x2 - x1)   = (y3 - y1)*(x2 - x1) -(x3 - x1)*(y2 - y1)
t ((x4 - x3)*(y2 - y1) - (x2 - x1)*(y4 - y3))   = x2y3 -x2y1 -x1y3 +x1y1 -x3y2 +x1y2 +x3y1 - x1y1

    (x2 - x1)*(y3 - y1) -(x3 - x1)*(y2 - y1)
t = ----------------------------------------
    (x4 - x3)*(y2 - y1) -(x2 - x1)*(y4 - y3)

s =