Experimental design and participants groups—Experiment 1.

The experiment consisted of two sessions: Training (24 trials) and Test (48 × 8 trials). In the Training session, all targets were presented by rotating the initial cursor orientation around an axis that was aligned to either an intrinsic or an extrinsic reference frame. The Test session of the Separate cond. group contained four trial sets with aligned axes followed by four trial sets with misaligned axes. The Test session of the Mixed cond. group contained eight trial sets with mixed aligned and misaligned axes. In both groups, half of the trials initiated from two fixed initial hand orientations (o1 and o2 ), while the rest had two fixed target orientations (t1 and t2 ). (a) Legend for the different experimental conditions of each trial. (b) The order of the trials in the Separate cond. group. (c) The order of the trials in the Mixed cond. group. (d) Examples of trials from the experiment. In each box, the left column shows the initial cursor orientation and the right column shows the respective target orientation (the notations of the initial cursor and target orientations, and the transition quaternion are in the inset; see Table 1 for more details). α is the rotation angle, and q−δ is the inverse of the transition quaternion. The top row shows trials constructed using rotation axes that are either misaligned (box 1 and 3) or aligned (box 2 and 4) with an extrinsic reference frame (dark red, green, and blue arrows). The bottom row shows trials constructed using rotation axes that are either misaligned (box 1 and 3) or aligned (box 2 and 4) with an intrinsic reference frame (light red, green, and blue arrows).