Fig 1.
Examples of visual stimuli used.
In each stimulus, participants were asked to judge whether two objects matched or fit. (A): The present study refers to objects (connectors) with a ‘dip’ as U-type and those with a ‘bump’ as T-type, inspired by the shapes and meanings of the Japanese kanji characters for concave and convex. (B.1), (C.1): objects are rotated 60° on the left side. (B.2), (C.2): objects are rotated 60° on the right side. (B.1) represents the less-wall side, while (B.2) represents the wall side. The U-type and T-type objects fit together to make a whole cube. The objects to be matched or fit are wholly or partially shaped, respectively, yet they occupy the same space.
Table 1.
Demographics of study participants.
Fig 2.
Bisectional rotation axes in the study.
The yellow axes are bisectional between the local blue and red axes. The cross points of the local axes on both sides correspond to the geometric centers of whole cubes of 5 × 5 × 5 unit-cubes. The directions of the axial arrows and their rotations are aligned with the right-hand rule, where the thumb points in the direction of the bisectional axis, and the curled fingers indicate the rotational direction.
Fig 3.
Schematic of (A) the experiment workflow and (B) a single experiment trial.
(A) PreQ: handedness questionnaire, C/V: calibration and validation of eye-tracking, PostQ: tactics questionnaire. The fitting task (FT) and the matching task (MT) are randomly presented in every trial. The practice block included 16 trials without feedback, using unique stimuli to simulate the main block. The main block consisted of six subblocks, each containing 96 visual stimuli. A total of 576 stimuli were randomly assigned to each subblock, ensuring an equal distribution of conditions (task, congruency, rotation side, angle factors) across the first and last three subblocks. Questionnaires were completed on a tablet computer using custom applications developed in Android Studio® version 2022.2.1. (B) A fixation cross appeared randomly, lasting between 800 and 1,200 msec in increments of 100 msec, as a precaution against rhythmical responses. The size of the fixation cross differs from that used in the main experiment. Reaction time and eye-tracking data were measured at the third step.
Fig 4.
Schematic of eye-tracking analysis in a single trial.
Green rectangle: left AOI (area of interest), red rectangle: right AOI, yellow circle: fixation, magenta arrow: saccade, cyan arrow: the first saccade and transit saccade, and numerals: fixation sequence and dwell time. DTR: dwell time ratio. The fixation times within each AOI were tallied to calculate the DTR, which is the ratio of fixation time within the AOI on the rotation side to the total fixation time across both AOIs. A DTR value greater than 0.5 indicates a bias towards the rotated object’s side. The AOIs were standardized to capture the activity related to two objects located on the left and right sides of the screen, each sharing the same area (960 × 1,080 pixels). The fixations shown are illustrative.
Table 2.
Descriptive statistics of dwell time ratio (DTR).
Fig 5.
Functional differences in cognitive strategies.
Task differences at rotation-side levels (A) for dwell time ratio across angles and (B) for the proportion of positive responses in subjective matching/fitting direction. (A) Eye-tracking dwell time ratio (DTR) is the ratio of dwell time within an AOI on the rotation side to that within both AOIs combined. Values above 0.5 indicate more time spent fixating on the rotation side, associated with rotated U-type objects in the fitting task (FT) and T-type objects in the matching task (MT). (B) Questionnaire results show significant associations between Direction and Task on both rotation sides. The present study refers to indented object as ‘U-type’ and protruding object as ‘T-type.’ In FT, participants tended to match or fit T-type objects leftward toward U-type objects rotated on the left, and rightward toward those rotated on the right. ns: p ≥ .05, * p < .05, **p < .01, ***p < .001.
Table 3.
Descriptive statistics of subjective report.
Fig 6.
(A) Rotation-side differences for correct RT across angles after collapsing tasks. Correct RT across angles (B) at rotation-side levels after collapsing tasks and (C) at task levels after collapsing rotation sides. (D) Regression lines for correct RT in tasks across half-round angular disparity after collapsing rotation sides and half of angles. (B) Rearranged graph from (A). (D) Significant linear trends observed in the fitting task (FT) and the matching task (MT). Dashed lines indicate regression lines with equations; shaded areas represent 95% confidence intervals. ns: p ≥ .05, * p < .05, **p < .01, ***p < .001.
Table 4.
Descriptive statistics of correct RT.
Fig 7.
Behavioral differences between FT versus MT. Task differences for correct RT across angles at rotation-side levels (A) before and (B) after controlling for direction confounders.
(A) Significant main effect of Task observed. (B) Controlling for confounders: subjective matching/fitting direction (first and second levels) and both this direction and rotational direction (first and third levels). FT: fitting task, MT: matching task. ns: p ≥ .05, * p < .05, **p < .01, ***p < .001.
Table 5.
Descriptive statistics of error ratio (ER).
Fig 8.
Preprocessing of direction confounders.
Horizontal arrow in red: direction of matching, rotational arrow in green: direction of rotation. The first row displays the left rotation side in the fitting task. The second row shows the right rotation side in the matching task, controlling for the subjective direction. The third row further controls for the rotation direction by flipping the positions at 60° to 300° and 120° to 240° from the second row.
Fig 9.
Schematic of trajectories in mental jigsaw puzzles.
Dashed lines denote the degrees of represented routes. The present study refers to indented object as ‘U-type’ and protruding object as ‘T-type.’ The diagram is illustrative.
Fig 10.
Example combinations of directions in mental jigsaw puzzles.
Horizontal arrow in red: direction of translation, rotational arrow in green: direction of rotation. The head was selected as the starting point of rotation, given that this area may receive more biased fixation during the mental rotation of T-type objects [5,71]. Pairing a leftward comparison direction with a counterclockwise rotation from the head is coherent (leftness and leftness), compared to a leftward comparison with clockwise rotation from the head (leftness and rightness). This same asymmetry can be also achieved with the directions of translation and rotation switched. The same coherence behavior applies to object mental rotation tasks, achieved by visualizing T-type objects emerging from the blank spaces surrounding U-type objects. The present study refers to indented object as ‘U-type’ and protruding object as ‘T-type.’.