## 4 Discussion
### Impact of Depth on Circular Tracking Movement  
Unlike 2D space, depth estimation is a significant control metric for depth perception and motor control in 3D space. In previous studies on target-tracking movements, particularly for circular tracking movements, no technology or system has been able to provide an accurate representation of the visual target. Therefore, the role of depth in 3D target-tracking movements, the relationship between target speed and depth in 3D target-tracking movements, and impact of depth on kinematic parameters, such as position, and velocity need to be explored further.  
Previously, we developed a 3D visuomotor control evaluation system in a VR environment [11]. By evaluating the Cartesian coordinate spatial error, we analyzed circular tracking movements on the frontal and sagittal planes. However, the evaluation using the Cartesian coordinate spatial error in that study could not clearly show the difference between circular tracking movements on the two planes. Consequently, we did not explore the role of depth information in motor control of 3D target-tracking movements. Furthermore, we confirmed that, regarding the Cartesian coordinate spatial errors, a significant difference was observed between the two circular tracking movement types even when the target speed was increased to a higher level (see Figure 6). Accordingly, we needed to propose a new analysis method for various circular tracking movement types and speeds in a 3D environment and for exploring the role of depth information in 3D target-tracking movement motor control. In this study, based on the three polar coordinate parameters, we quantitatively showed that the depth information is significant for the performance of circular movements, position control accuracy, and velocity control accuracy in 3D movements. Furthermore, it was established that the depth information is even more significant when the target is moving faster (Figures 3-5).  
Target motion cognition in 3D space is significant for 3D circular tracking movement motor control. In our previous study, using a rubber hand illusion in a VR environment, we showed that depth perception is easier in left to right motion for the same depth than for different depths [27]. Also, we found that the limb position visual feedback is most accurate in the azimuth and least accurate in the depth direction [28]. Those previous studies helped us interpret our results in these studies. In other words, because target motion cognition is better on the frontal plane than on the sagittal plane, performance, position control, and velocity control are better on the frontal plane in circular tracking movements. The faster the target speed, the clearer the trend (Figures 3-5). In future studies, we will quantitatively analyze the hand-arm system sensitivity as well as the impact of the target cognition level for both planes in 3D space by modifying the target visual feedback [23]. Further, we will  
Figure 6: Evaluation of the circular tracking performance based on \(\Delta\)3D (3D error; spatial errors in Cartesian coordinates). Note that, there was a statistically significant \(\Delta\)3D difference under \(V\)3 and \(V\)4 conditions between \(ROT(0)\) and \(ROT(90)\).  
quantitatively analyze the difference in the weight of the 3D tracking movements by experimentally recording and analyzing muscle activity.