Intersection between 2d image point and 3d mesh

Given: Mesh, Source Camera - I have intrinsic and extrinsic parameters, Image coordinate 2d

Output: 3D point, which is the intersection of a ray from camera center, through the 2d point on the image plane and the mesh. (I'm trying to find the 3d point on the mesh)

This is the process:

From Multiple View Geometry in Computer Vision book:

I have constructed the equation (6.14).

I'm not sure how to continue and get the 3d point that lies on the mesh (I also need the point that is closet to the camera).

I thought that it can be done in the following way:

Iterate over all the vertices and find the distance between the vertex and the line and the vertices that have the least distance lie on the line (if they're close to zero or zero), and finding the closet vertex is I guess finding the magnitude of between the center of the camera and the closet vertices, the smallest one will mean the point is the closest?

Quick update: This repo does seem to work with the rays: github.com/szabolcsdombi/python-mesh-raycast

I guess the bug now lies in getting the point D right..

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