Example vector schemes for remapping sound into a goal-directed gaze shift. A, The head-centered scheme. The head-centered sound representation (TH, gray arrow) should be transformed into an oculocentric motor command (ΔG, bold black arrow), by subtracting eye-in-head orientation (EH, gray dotted arrow; Eq. 1). B, C, The world-centered scheme. B, Head-centered sound coordinates are transformed into a supramodal world-centered (TS, bold black arrow) reference frame, by incorporating head orientation at sound onset (HS,0, gray dotted arrow; Eq. 2). C, The world-centered sound (TS, gray arrow) is transformed into an oculocentric motor command (ΔG, bold black arrow) by incorporating both eye and head orientation (EH and HS, gray dotted arrows; Eq. 3).