Möller-Trumbore intersection algorithm

The Möller-Trumbore algorithm is a fast method for finding where a ray meets a triangle in three dimensions. It is named after its inventors Tomas Möller and Ben Trumbore. Its main advantage is that it needs no precomputed equation of the plane containing the triangle, so it can be run directly on the three vertices of each triangle in a mesh. The method first tests whether the ray direction is parallel to the triangle plane by checking whether a dot product with the plane normal is zero. It then expresses the hit point in barycentric coordinates, using the weights of the triangle vertices, and checks that those coordinates are non-negative and sum to at most one, which means the hit lies inside the triangle. In computer graphics it is widely used to implement ray tracing over triangle meshes.