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.

Answer 2

Looks like an assignment problem to me. Here is the logic that will help you write the code.

Let us call the first Ray as R0.
Locus of a point on R0 is defined as P:

P = P0 + alpha x V0

For the second ray R1:

P = P1 + beta x V1

Since they should intersect:

P0 + alpha x V0 = P1 + beta x V1

alpha and beta are unknowns and we have two equations in x any y.

Solve for the unknowns and get back the point of intersection.

i.e.,

P0.x + alpha * V0.x = P1.x + beta * V1.x
P0.y + alpha * V0.y = P1.y + beta * V1.y

solve for alpha and beta.

If there is a real positive solution for both alpha and beta, rays intersect.
If there is a real but at least one negative solution for both alpha and beta, extended rays intersect.