## 3 Results
### Circular Tracking Movement Differences Based on \(\Delta\omega\) in 3D VR Space  
Figure 2C1,C2 show \(\Delta\omega\) on the frontal and sagittal planes, respectively, at each of the four target speeds.  
We compared \(\Delta\omega\) between the frontal and sagittal planes at each target speed to investigate the impact of depth on velocity control accuracy. Two-way repeated-measures ANOVA on the performance differences based on \(\Delta\omega\) revealed significant core impacts for the plane, \(F(1,15)=171.36\), \(p=0\), _partial_  
Figure 4: Evaluation of the circular tracking movement based on \(\Delta\theta\) in 3D VR space. (**A**) The graphs indicate the pairwise comparison of \(\Delta\theta\) analyzing the speed factor between \(ROT(0)\) and \(ROT(90)\). (**B**) The result of the pairwise comparison was indicated for \(\Delta\theta\), on the frontal plane (\(ROT(0)\)), at four target speeds. (**C**) The pairwise comparison was displayed for \(\Delta\theta\), on the sagittal plane (\(ROT(90)\)), at four target speeds.  
\(\eta^{2}=0.92\), and speed, \(F(1.07,16.03)=252.33\), \(p=0\), _partial_\(\eta^{2}=0.944\), as well as an interaction between the plane and speed factors, \(F(1.258,18.87)=38.1\), \(p=0\), _partial_\(\eta^{2}=0.717\) (item A in Table S3). This indicates that \(\Delta\omega\) in the circular tracking was affected by the plane and speed factors. Further, the interaction between the target speed and depth in 3D target-tracking movements would affect the \(\Delta\omega\) performance in evaluating the velocity-control precision in circular tracking movements.  
As shown in Figure 5A, the pairwise comparison of the plane and speed factors revealed a statistically significant \(\Delta\omega\) difference between \(ROT(0)\) and \(ROT(90)\) (item B in Table S3). This indicates that the subjects were more precise on the frontal plane (\(M=27.53\)\({}^{\circ}\) s\({}^{-1}\), \(SD=18.27\)\({}^{\circ}\) s\({}^{-1}\)) than on the sagittal plane (\(M=37.17\)\({}^{\circ}\) s\({}^{-1}\), \(SD=26.24\)\({}^{\circ}\) s\({}^{-1}\)) when synchronizing the target and tracer angular velocities (\(p=0\), \(r=0.855\); item C in Table S3).  
Next, we examined the \(\Delta\omega\) and target speed relationship for both planes using pairwise comparison. As shown in Figure 5B, there was a significant \(\Delta\omega\) difference in target speeds for the \(ROT(0)\) phase (item D in Table S3). The values of \(\Delta\omega\) were \(9.65\pm 1.61\), \(15.17\pm 2.05\), \(31.23\pm 4.8\), and \(54.07\pm 10.13\)\({}^{\circ}\) s\({}^{-1}\) for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. \(\Delta\omega\) increased significantly on the frontal plane (\(ROT(0)\)) as the target speed increased. In shows that it is increasingly difficult to control the frontal plane (\(ROT(0)\)) circular tracking movement velocity as the speed increases.  
As shown in Figure 5C, there was a significant difference in target speeds \(\Delta\omega\) for the \(ROT(90)\) phase (item E in Table S3). The values of \(\Delta\omega\) were \(12.09\pm 1.5\), \(19.93\pm 3.01\), \(42.15\pm 5.35\), and \(74.54\pm 18.66\)\({}^{\circ}\) s\({}^{-1}\) for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. Furthermore, \(\Delta\omega\) increased significantly on the sagittal plane (\(ROT(90)\)) as the target speed increased.  
Figure 5: Evaluation of the circular tracking movement based on \(\Delta\omega\) in 3D VR space. (**A**) The graphs indicate the pairwise comparison of \(\Delta\omega\) analyzing the speed factor between \(ROT(0)\) and \(ROT(90)\). (**B**) The pairwise comparison was performed for \(\Delta\omega\), on the frontal plane (\(ROT(0)\)), at four target speeds. (**C**) The pairwise comparison was performed for \(\Delta\omega\), on the sagittal plane (\(ROT(90)\)) at four target speeds.  
We found that as the speed increased, the subjects had more difficulty controlling the circular tracking movement position on the sagittal plane (_ROT_(90)) compared with that on the frontal plane (_ROT_(0)).