show scratch direction on the side of rolling box

Suppose I have a ground plane and a rolling and yawing and transforming box on top of it.
as the box rolls and yaws and transforms I would like to show the direction of the scratches on one of the sides of the box when that particular side touches the ground plane.
The scratches can be represented by one line on the side of box.
I would appreciate any suggestion on how to solve this problem.