## 3 Results
### Differences in Circular Tracking Movement Based on \(\Delta R\) in 3D VR Space  
Figure 2 shows typical circular tracking movement examples at four target speeds (\(V1\): 0.125 Hz, \(V2\): 0.25 Hz, \(V3\): 0.5 Hz, and \(V4\): 0.75 Hz; each with \(n=16\)). Figure 2A1,A2 show the circular tracking movement \(\Delta R\) on the frontal and sagittal planes at each target speed. For the circular tracking movement on both the frontal and sagittal planes, the difference between target trajectories and the tracer tended to increase as the target speed increased. Further, there is a higher sagittal plane difference compared to the frontal plane at each target speed, as shown in Figure 2A1,A2. Hence, we examined the 3D space circular movement at the four target speeds using \(\Delta R\).  
Two-way repeated-measures ANOVA on the \(\Delta R\) performance differences revealed significant key impacts for the plane, \(F(1,15)=47.53\), \(p=0\), _partial_\(\eta^{2}=0.76\), and speed, \(F(1.43,21.46)=76.15\), \(p=0\), _partial_\(\eta^{2}=0.835\), as well as an interaction between the plane and speed factors, \(F(3,45)=7.4\), \(p=0\), _partial_\(\eta^{2}=0.33\) (item A in Table S1). This indicates that the plane and speed factors affected the circular tracking movement \(\Delta R\). Further, the interaction between the target speed and depth in 3D target-tracking movements would affect the \(\Delta R\) performance in estimating the spatial motor control characteristics in the task.  
Therefore, we performed a pairwise comparison to analyze the speed factor between \(ROT(0)\) and \(ROT(90)\). As shown in Figure 3A, there was a statistically significant \(\Delta R\) difference between \(ROT(0)\) and \(ROT(90)\) (item B in Table S1). The results show that the subjects found it particularly difficult to track the sagittal plane target radius (\(M=11.77\) mm, \(SD=5.2\) mm) than that on the frontal plane (\(M=8.93\) mm, \(SD=3.90\) mm) at target speeds of 0.25 Hz and higher (\(p=0\), \(r=0.656\); item C in Table S1).  
Next, we examined the \(\Delta R\) circular tracking movement on each plane at the four target speeds. Figure 3B shows that the pairwise comparison had a significant \(\Delta R\) difference for \(ROT(0)\) phase target speeds (item D in Table S1). The values of \(\Delta R\) were \(6.01\pm 3.53\), \(6.95\pm 3.24\), \(9.67\pm 1.72\), and \(13.11\pm 2.36\) mm for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. This indicates that \(\Delta R\) increased significantly on the frontal plane (\(ROT(0)\)) as the target speed increased.  
As shown in Figure 3C, there was a significant \(\Delta R\) difference in target speeds for the \(ROT(90)\) phase (item E in Table S1). The values of \(\Delta R\) were \(7.35\pm 3.23\), \(8.62\pm 2.54\), \(13.25\pm 2.45\), and \(17.86\pm 4.19\) mm  
Figure 2: Typical examples of circular tracking movements for 0.125 Hz, 0.25 Hz, 0.5 Hz, and 0.75 Hz. **(A1)** Absolute values of \(\Delta R\) for the frontal plane (\(ROT(0)\)) and **(A2)** the sagittal plane (\(ROT(90)\)). **(B1)** Absolute values of \(\Delta\theta\) for \(ROT(0)\) and **(B2)**\(ROT(90)\). **(C1)** Absolute values of \(\Delta\omega\) for \(ROT(0)\) and **(C2)**\(ROT(90)\).  
for 0.125, 0.25, 0.5, and 0.75 Hz, respectively. No significant \(\Delta R\) difference between \(V1\) and \(V2\) was noted on the sagittal plane (\(ROT(90)\)) (\(t(15)=2.143\), \(p=0.29\), \(r=0.484\)). This suggests that the subjects found it more difficult to track the sagittal plane (\(ROT(90)\)) target radius for speeds over 0.25 Hz.  
We found that the circular tracking movement that maintains a constant distance from the circle center can be more accurately tracked on the frontal plane (\(ROT(0)\)) compared with that on the sagittal plane (\(ROT(90)\)).