Is it possible to draw objects which are sliced by the near clip plane in orthographic view?

If I have an object which is located between the clipping planes in orthographic view and I move the camera, such that the camera plane is parallel to one side of the object, I can see the object as if it was 2D. I would like to have the same effect, if the object is “sliced” by the near clip plane.

For example: If my orthographic camera is placed inside the floor, I can see objects above and below the floor but not the floor itself.

What I would like to get is: 2D (no depth) view of the world sliced by the camera plane.

Update: I think I can achieve what I would like to have with a Distance to Nearest Surface material as described here. If I place a static mesh plane with this material right infront of my camera, the intersections get highlighted. What I currently do not quite understand is why the highlighting is a sharp line for the floor but fuzzy for other objects.

Update 2: It seems like the Distance to Nearest Surface cannot provide me with the pixels inside a static mesh.