Intersection of a line with the infinity plane

Question

I would like to compute the intersection of a 3D line with the plane at infinity. I suspect it would be the same as taking the 3D direction of the line and setting the 4th vector coordinate to 0.

However, this is not enough. I would like to know the 2D position of the intersection in screen coordinates after the line is transformed and projected by a perspective camera.

This problem is equivalent to finding the vanishing point in a 2D image.

Answer 1

It seems that a vanishing point corresponds to a direction in 3D space. Hence, using a homogeneous vector of the form [x y z 0] in the rendering pipeline yields the 2D coordinates of the vanishing point on the screen.