# How to simulate collision of two balls?

There two balls, $B_1$ & $B_2$ with respective masses $m_1$ & $m_2$ traveling in two dimensions with velocities $v_1$ & $v_2$ in the directions $\theta_1$ & $\theta_2$. I also know the angle at which they are traveling. The collision is perfectly elastic and there is no friction or air resistance. How do I model the collision in order to find the direction and velocity of each ball after colliding. I know that momentum and kinetic energy will be conserved, but I am not sure how to combine the equations: $$m_{1}v_{1i}+m_{2}v_{2i}=m_{1}v_{1f}+m_{2}v_{2f}$$ $$\frac12m_{1}v_{1i}^2+\frac12m_{2}v_{2i}^2=\frac12m_{1}v_{1f}^2+\frac12m_{2}v_{2f}^2$$ I also don't know how to determine the direction the balls will move after the collision.

I am trying to make a simplistic computer simulation which can display realistic 2-dimensional physics.