Deriving data for calibration or improving the positioning of a computer-controlled machine involves a movable carrier for changing the position of a first machine part relative that of second machine part. The carrier is moved to a plurality of carrier positions. At each position, a pattern generator attached to the first machine part is illuminated such that at least one three-dimensional pattern of light is created in space. Position data is recorded and images of the three-dimensional pattern are recorded in at least two different optical configurations of the illuminator, the pattern generator, and at least one camera. The recorded image data is compared with image data of a reference database, and pairs of similar images are found. Image translation off set data is derived for each pair, and translation and rotation data are derived.