What does "in a direct line with" mean here?

This quote is from a book called The Scole Report concerning the scientific study of paranormal phenomena. The Group includes the investigators and mediums. The lights refer to "spiritual lights" that generated in the process of a seance. A particular section in this book is dedicated to describing the behaviors of the spiritual lights. Following this section the authors try to prove that these lights are not normal lights which are produced by secret man-made equipment but a production of spiritual energy.

This is the text:
However, the use of clandestine equipment would have required energetic and hence detectable movement by any of the arm-banded Group. The behaviour of the light or lights was generally inconsistent with the concept of a rod or manipulated wire or thread. Such hypothetical instruments or mechanism would not only have had to create the lights but enable them to change form, move at great speed, and describe perfect geometrical shapes in the air at such velocity that the shapes appeared unbroken. Then, when still producing the shapes, the lights would have to remove a segment from the view, replace it, then remove another segment. They would equally have to possess the competence to respond intelligently to requests, acting in places or on things which were not in a direct line with any member of the Group, visit apparently inaccessible sites with great precision despite the darkness, irradiate objects such as Pyrex bowls, cylindrical Perspex supports and sitters' feet, and simulate the floating figures.

1. Could you tell me what "in direct line with" means here?

2. What does "floating figures" refer to?

Thank you.