Given two points and two vectors, find point of intersection [duplicate]

Answer 1

It's simple math.

But, first, check that you have intersection. If both vector are parallel you will fail to solve that:

// Edit this line to protect from division by 0 
if (Vy == 0 && Uy == 0) || ((Vy != 0 && Uy != 0 && (Vx/Vy == Ux/Uy)) // => Fail.

Then (I want show the calculation cause they long but):

R = (AxUy - AyUx + ByUx - BxUy) / (VyUx - VxUy)  
S = (Ax - Bx + RVx) / Ux  

Hope that helped you.