In the article you linked to, point P is obtained by first intersecting the ray with the plane containing the triangle. If you step back two slides you can see how it goes together.

Anyway, intersecting a vector (really, a line segment) with a triangle should be just a matter of doing a ray-triangle intersection and then checking if the returned ‘t’ value is in the [0, 1] interval, i.e. between the endpoints of the vector.

Does anybody know how to find

1. the point at where the vector crosses the triangle.

2. Vector does not touch the triangle/intersect the triangle.

I have found an explanation on this website

http://www.cs.princeton.edu/courses/archive/fall00/cs426/lectures/raycast/sld018.htm

but it does not explain how to find Point P.

Can anybody help me on this.