## 5 Discussion  
The experimental results showed that the main effects, the direction of operation and _ID_, significantly affected _MT_. It was shown that the steering tasks that follow the path in all 24 directions, evaluated in the experimental conditions, can be modeled by the steering law with a high coefficient of determination. [PERSON] et al. [20] evaluated the effect of direction on the pointing task by head motion. They reported that the relationship between _ID_ and _MT_ was represented by a Fits model with a coefficient of determination of 0.86 to 0.98. Our results also showed the applicability of the steering model with a similar coefficient of determination. Studies that evaluated steering tasks using manual straight and circular paths also reported that the relationship between _ID_ and _MT_ showed a high coefficient of determination. (R\({}^{2}\) = 0.986 \(\sim\) 0.999) [21]. As for the magnitude of _MT_, compared to the horizontal and vertical directions, the study by [20] showed that pointing tasks in the diagonal direction tended to take a little longer. We read from the data in their paper that the 315\({}^{\circ}\) direction had the highest _MT_, about 1.15 times higher than the 90\({}^{\circ}\) direction, which had the lowest _MT_. This ratio was relatively higher in our study, where a difference of about 1.94 times was found between horizontal-vertical and diagonal steering tasks. The simple positioning and steering operations showed a consistent trend in that they tended to take more time for diagonal movements. The difference in the ratios can be attributed to the intrinsic difference between the pointing task, which is to head in a free path to the target, and the steering task, which is to track the path without straying from it continuously. To evaluate the usefulness of ARHD as an endoscopic surgical communication support system, we compare the results obtained in the present study with the performance of cursor manipulation using existing input devices evaluated by the previous studies [21; 22] using the steering law. [PERSON] et al. [21] evaluated the performance of a steering task using five input devices (mouse, tablet, trackball, touchpad, and TrackPoint) with a trajectory in which the cursor is manipulated straight to the right horizontally (corresponding to \(\theta\) = 0\({}^{\circ}\) in our experiment). [PERSON] et al. [22] evaluated the performance of a steering task with a laser pointer in the same way as [21]. From the present study, the _IP_ of drawing operation by head movement in the direction of \(\theta\) = 0\({}^{\circ}\) was 4.941 s\({}^{-1}\), which is lower than the results of a mouse (14.3), tablet (14.4), trackball (5.30), touchpad (6.70), TrackPoint (8.70), and laser pointer (9.80). All of the interfaces used in this comparison are hand-operated interfaces, indicating that head manipulation is less precise than hand manipulation. This result is consistent with the trend reported by [PERSON] and [PERSON] [23], who found that _IP_ was lower in head manipulation than in hand manipulation, and that _IP_ was lower in large limb than in small limb pointing manipulation. Other than hand-operated interfaces, [PERSON] et al. [24] used a VR navigation interface called VirtuSphere to apply a steering model to the operation of moving in a VR environment. They reported that the _IP_ was 1.585 s\({}^{-1}\) for a linear path, which is lower than that of a manual gamepad operation (4.546). In their system, inertia was applied to start, stop, and change the direction during the tracking task, making it difficult to operate the system. The only device used in the present study was the AR glasses, which may have had relatively little effect on the operation compared to [24]. From the results of the _IP_ and subjective evaluation questionnaires, it was found that diagonal manipulation was more difficult than horizontal and vertical manipulation. This result is consistent with the results reported by [PERSON] et al. [20], who considered two factors: perceptual and kinematic.