## 2 Materials and Methods
### Data Analysis  
For data analysis, we transformed the Cartesian (X, Y, Z) data to radial displacement, angular displacement, and angular velocity on polar coordinates; \(R\), \(\theta\), and \(\omega\), respectively.  
\[\Delta R\ [\text{mm}]=\frac{\sum_{t=1}^{n}abs\big{(}R_{tracer}(t)-R_{target}(t) \big{)}}{n}, \tag{1}\]  
where \(\Delta R\) is defined as the radial position difference absolute value between the target and tracer from the origin.  
\[\Delta\theta\ [\text{deg}]=\frac{\sum_{t=1}^{n}abs\big{(}\theta_{tracer}(t)- \theta_{target}(t)\big{)}}{n}, \tag{2}\]  
where \(\Delta\theta\) represents the angular displacement difference absolute value between the target and tracer.  
\[\Delta\omega\ \bigg{[}\frac{\text{deg}}{\text{s}}\bigg{]}=\frac{\sum_{t=1}^{n}abs \big{(}\omega_{tracer}(t)-\omega_{target}(t)\big{)}}{n}, \tag{3}\]  
where \(\Delta\omega\) denotes the angular velocity difference absolute value between the target and tracer. These parameters were normalized with total time \(n\) of three trials for each target speed.  
The units of \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) are mm, deg, deg/s, respectively. We calculated the absolute difference averages of \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) on three trials for each subject. Next, the mean (\(M\)) and standard deviation (\(SD\)) were calculated by using the \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) averages for the 16 subjects.  
Statistical analysis and data visualization were performed by SPSS Statistics V26, IBM and MATLAB, MathWorks. In general, [PERSON]'s \(\alpha\) indicates the overall data reliability; it is understood that a value around 0.8 is respectable [15]. The reliability analysis for \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) data was measured by [PERSON]'s \(\alpha\) (Reliability Analysis function in SPSS Statistics, IBM), with values of 0.87, 0.82, and 0.84, respectively.  
This study verified a relationship between the target speed and depth in 3D target-tracking movements. Therefore, we investigated the parameter differences of \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) between frontal and sagittal plane circular tracking movements. In addition, we examined the visuomotor control differences for four different parameter-based target speeds. For the analysis of circular tracking movement differences based on \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\), we carried out a two-way repeated-measures analysis of variance (ANOVA), with a two-level plane factor (\(ROT(0)\), frontal plane; and \(ROT(90)\), sagittal plane) and a four-level speed factor (\(V1\): 0.125 Hz, \(V2\): 0.25 Hz, \(V3\): 0.5 Hz, and \(V4\): 0.75 Hz; each with \(n=16\)). The total sample size was 128, calculated by a priori power analysis [16]. The main impacts and interaction of plane and speed factors in \(\Delta R\), \(\Delta\theta\), and \(\Delta\omega\) parameters were assessed by the Repeated Measures function in SPSS Statistics, IBM. We performed [PERSON]'s sphericity test to validate the ANOVA results. When sphericity was assumed (\(p>0.05\)), the values corrected with Sphericity Assumed were used. When sphericity was not assumed (\(p<0.05\)), the values corrected with Greenhouse-Geisser were used.  
A posthoc test was conducted by pairwise comparison of the Bonferroni corrections. Except where noted, we describe data using M and SD; considering comparisons yielding \(p<0.05\) as statistically significant and those yielding \(p<0.01\) as highly significant differences. This analysis corresponds to the statistical tests shown in Tables S1-S3.