## 3 Results
### Circular Tracking Movement Differences Based on \(\Delta\theta\) in 3D VR Space  
Figure 2B1,B2 show \(\Delta\theta\) at the four target speeds on the frontal and sagittal planes, respectively. First, we compared \(\Delta\theta\) between the frontal and sagittal planes at each target speed to investigate the impact of depth (distance from the subject) on \(\Delta\theta\). Two-way repeated-measures ANOVA on \(\Delta\theta\) performance-based differences revealed significant main impacts for the plane, \(F(1,15)=156.89\), \(p=0\), _partial_\(\eta^{2}=0.913\), and speed, \(F(1.07,16.12)=64\), \(p=0\), _partial_\(\eta^{2}=0.81\), as well as plane and speed interaction factors, \(F(1.542,23.13)=6.72\), \(p=0.008\), _partial_\(\eta^{2}=0.309\) (item A in Table S2). This shows that the plane and speed factors affected \(\Delta\theta\) in circular tracking movements. Also, the interaction between the frontal and sagittal planes at each target speed affected the \(\Delta\theta\) performance in evaluating the precision of circular tracking movement position control.  
Therefore, we performed a pairwise comparison analyzing the speed factors of \(ROT(0)\) and \(ROT(90)\). As shown in Figure 4A, there was a statistically significant difference in \(\Delta\theta\) between \(ROT(0)\) and \(ROT(90)\) (item B in Table S2). Unlike \(\Delta R\), \(\Delta\theta\) has a significant difference with respect to circular tracking accuracy on \(ROT(0)\) and \(ROT(90)\) over 0.125 Hz. This indicates that the subjects found it more  
Figure 3: Evaluation of the circular tracking movement based on \(\Delta R\) in 3D VR space. (**A**) The graphs indicate the pairwise comparison of \(\Delta R\) analyzing the speed factor between \(ROT(0)\) and \(ROT(90)\). (**B**) The result of the pairwise comparison was indicated for \(\Delta R\), on the frontal plane (\(ROT(0)\)), at four target speeds. (**C**) The pairwise comparison was displayed for \(\Delta R\), on the sagittal plane (\(ROT(90)\)), at four target speeds.  
difficult to synchronize the target and tracer positions on the sagittal plane (\(M=7.48^{\circ}\), \(SD=5.81^{\circ}\)) than on the frontal plane (\(M=5.52^{\circ}\), \(SD=4.44^{\circ}\)) at all target speeds (\(p=0\), \(r=0.845\); item C in Table S2).  
Next, we examined the relationship between \(\Delta\theta\) and target speed for each plane. Figure 4B shows that the pairwise comparison had a significant \(\Delta\theta\) difference in target speeds for the \(ROT(0)\) phase (item D in Table S2). The values of \(\Delta\theta\) were \(1.95\pm 0.74^{\circ}\), \(2.79\pm 0.85^{\circ}\), \(5.84\pm 1.91^{\circ}\), and \(11.51\pm 4.26^{\circ}\) for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. As is the case with \(\Delta R\), \(\Delta\theta\) increased significantly on the frontal plane (\(ROT(0)\)) as the target speed increased. This indicates significant difficulty in circular tracking movement position control on the frontal plane (\(ROT(0)\)) as the speed increases.  
Next, as shown in Figure 4C, there was a significant \(\Delta\theta\) difference in target speeds for the \(ROT(90)\) phase (item E in Table S2). The values of \(\Delta\theta\) were \(2.95\pm 0.95^{\circ}\), \(4.12\pm 1.2^{\circ}\), \(7.93\pm 2.19^{\circ}\), and \(14.91\pm 6.46^{\circ}\) for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. Also, with increased target speed, \(\Delta\theta\) increased significantly on the sagittal plane (\(ROT(90)\)).  
The results indicate that as the speed increased, the subjects had substantially more difficulty with circular tracking movement position control on the sagittal plane (\(ROT(90)\)) compared with the frontal plane (\(ROT(0)\)).