Ray-plane intersection ($\lambda =\frac{n\cdot (a-o)}{n\cdot r}$)

Intersection of $o+\lambda r$ with the plane $n\cdot (p-a)=0$, when $n\cdot r\ne 0$. For a ray, require $\lambda \ge 0$. A zero denominator requires separate parallel or coplanar handling.

A ray-plane intersection followed by an inside-triangle test, conveniently using nonnegative barycentric coordinates. Oriented surfaces may additionally require a front-facing hit through back-face culling.