Given a triangle defined by points _p0_, _p1_ and _p2_ and a ray given by its origin _o_ and direction _d_, the barycentrics of the hit point as well as the _t_-value of the hit can be obtained by solving the system:
We recommend that you implement the *Moller-Trumbore algorithm*, a fast algorithm
that takes advantage of a barycentric coordinates parameterization of the
intersection point, for ray-triangle intersection.
Where:
This system can be solved by Cramer's Rule, yielding:
In the above, |a b c| denotes the determinant of the 3x3 with column vectors _a_, _b_, _c_.
Note that since the determinant is given by:
you can rewrite the above as:
Of which you should notice a few common subexpressions that, if exploited in an implementation, make computation of _t_, _u_, and _v_ substantially more efficient.
