GAMES101

Möller Trumbore Algorithm

$$ \vec{O}+t\vec{D} = (1-b_1-b_2)\vec{P}_0 + b_1 \vec{P}_1 + b_2 \vec{P}_2\\ \left[\begin{matrix}t\b_1\b_2\end{matrix}\right] = \frac{1}{\vec{S}_1\cdot \vec{E}_1}\left[\begin{matrix}\vec{S}_2\cdot \vec{E}_2\\vec{S}_1\cdot \vec{S}\\vec{S}_2\cdot \vec{D}\end{matrix}\right]\\ \begin{aligned}\text{Where}:& \vec{E}_1 = \vec{P}_1-\vec{P}_0\ & \vec{E}_2 = \vec{P}_2-\vec{P}_0\ & \vec{S} = \vec{O}-\vec{P}_0\ & \vec{S}_1 = \vec{D} \times \vec{E}_2\&\vec{S}_2 = \vec{S}-\vec{E}_1\end{aligned} $$