Schematic drawing of 3D tumor motion in the coordinate system of the scanned ion beam. The tumor is depicted in its reference position (grey) and in a second position corresponding to a different motion phase (red). The scanning coordinate system consists of iso-energy layers (z in water-equivalent units) as well as grid positions within these layers (x, y). Motion of a grid position is indicated by a motion vector (white). Δ(x, y, z) are the parameters required for motion compensation.