2.1.2. Task & Procedure

To test the users' horizontal and vertical common range, we set visual cues to let the user move their hands horizontally and vertically while selecting the target block. First, the user pressed the "Start" button, and a green target block appeared randomly in a horizontal or vertical direction, as shown in Figure 2a,b. Taking the spatial position corresponding to the target block as a reference, when the user's hand moved to the spatial position in front of the screen corresponding to the target block, the block would turn red. A second target block would then randomly appear. In this and subsequent target selection tasks, the target block was always displayed in red when a gesture was made toward it. When the user thought their hand overlapped the target block, they could select the target by pressing the left Ctrl button. At the same time, the position of the users' hand was saved into an Excel file, and the next target selection task began.

**Figure 2.** The beginning interface of the pilot experiment: (**a**) the horizontal experiment; (**b**) the vertical experiment.

Prior to the formal experiment, the participants were allowed to warm up by practicing until they understood and performed the task correctly. Taken together, these two experiments included the following: 12 subjects × 8 block levels × 14 repetitions × 2 directions = 2688 target selection trials.

#### 2.1.3. Result

We analyzed the frequency of the user's hand position at each interval. We then were able to reach a conclusion regarding the user's vertical and horizontal common range, which was used as the study object of the following experiments.

After analyzing the collected data, we found that individuals manipulated their hands horizontally within the range (−220, 240) and vertically over the range (30, 370). The effective horizontal range was an interval of (−190, +190), and the vertical range was an interval of (50, 350), as Figure 3a,b show. We then chose 80% of this interval as the most common operational range, which was defined as a rectangle. The vertical interval was (80, 320), and the horizontal interval was (−152, +152). So the common operational region was an area of 240 mm × 304 mm, located 80 mm above the desktop.

**Figure 3.** The results of the pilot study: (**a**) the results of the horizontal experiment; (**b**) the results of the vertical experiment.

Based on these results, we set this common operational region as a study object and divided it into differently sized target arrays and target regions through even spatial partitioning. The common operational region was divided into four evenly sized sections, as shown in Table 1. There were six target-size levels, as shown in Table 2. We then designed experiments in which the participants attempted target selection tasks at different target-size levels, and with target positions within the different regions.

**Table 1.** The position of each region.


**Table 2.** The target size (length × width) at each level of the experimental condition.


In addition, differences between sighted and visually impaired individuals were also considered. The participants finished target selection tasks under both visual and non-visual scenarios. We then analyzed the data collected, including the average time and error rate. The contributions of this work are:


#### **3. Experiment 1: Visual Scenario**

To test the users' performance accuracy when conducting the interaction task, we set a visual cue for sighted users.

#### *3.1. Participants & Apparatus*

The participants and apparatus in Experiment 1 were the same as in the pilot study.

#### *3.2. Task & Procedure*

In Experiment 1, the current position of the users' hand mapping to the current block was shown on the experiment screen in real time. The target block turned from green to red while the current block overlapped with it, as shown in Figure 4. The user sat in a chair at the desk before the computer as they did in the pilot study.

**Figure 4.** The experiment interface of Experiments 1 and 2: (**a**) experiment interface of the 5 × 5 level; (**b**) experiment interface of the 8 × 8 level.

To maintain consistency in the experimental data, we saved the data to an Excel file at the end of a single target selection task, which was the moment the left Ctrl button was pressed. In addition, the experiment recorded a standard timestamp for an incremental time in the Unity 3D program. Once the user pressed the left Ctrl button to complete a target, the next target selection task began timing. To ensure an equal time for task selection, the user always placed their left index finger on the left Ctrl button. Before the formal experiment, participants were allowed a warm-up practice session until they could understand and perform the task correctly. In total, the experiment consisted of the following: 12 subjects × 6 target size levels × 4 target regions × 2 blocks × 3 repetitions = 1728 target selection trials.

#### *3.3. Results*
