# Movement Time for Pointing Tasks in Real and Augmented Reality Environments
## 2 Methods
### AR Device and Pointing Tasks  
A Microsoft(r) Hololens 2 headpiece (Microsoft Inc., Redmond, WA, USA) was used. This device has been reported as the most commonly adopted one in the medical community to display virtual objects [49]. It has a weight of 566 g. The Windows Holographic Operating System was installed. The glasses use see-through holographic lenses. The resolution of the display is 2 k with 3:2 light engines. The holographic density is 2.5 k radians (light points per radian) or higher with eye-based rendering. This device tracks hand location and gestures using built-in cameras and a two-handed fully articulated model with directional manipulation. The world-scale positional tracking and real-time environment mesh are employed in the system for six-degrees-of-freedom tracking and spatial mapping purposes, respectively. The app Graph Calculator (Microsoft Inc., Redmond, WA, USA) was adopted for the pointing tasks. The pointing tasks were performed in both real (or physical) and AR (or virtual) environments. In the AR environment, the participant wore the Hololens headpiece. The virtual calculator panel appeared in the vision of the participant (see Figure 1). The size, location, ratio of the horizontal to the vertical dimension, and tilt angle of the keyboard were adjustable using hand gestures. The inclined angle of the panel to a flat surface was adjusted to either 90\({}^{\circ}\) or 30\({}^{\circ}\). These angles were confirmed using a goniometer. Hand movements of the pointing task included horizontal and vertical movements. There were three sizes (large, medium, and small) of the keys on the panel (see Table 1). Each pointing task was performed by moving the tip of the index finger from the original key to touch a target key. There were three target keys in each of the horizontal and vertical movement trials. Figure 1: Virtual calculator panel. For horizontal pointing tasks, the key at origin was \"C\" on the upper left corner of the keypad (see Figure 1). For each of the three key sizes, the third (or \"In\"), fifth (or \"(\"), and seventh (or \") keys in the same row were selected as one of the target keys. The sizes (W) of the original and the three target sizes were the widths of the marks on these keys. An averaged \(W\) (\(W_{\text{ave}}\)) was the averaged width of the marks of the origin and each of the target key. For vertical pointing tasks, the original key was the \"In\" on the first row on the keypad (see Figure 1). For each of the three key sizes, the second (or \"sinh\"), fourth (or \"tanh\"), and sixth (or \"0 \(\times\) 16\") keys on the same column were selected as one of the target keys. The sizes (W) of the original and each of the three target sizes were the heights of the marks on these keys. The \(W_{\text{ave}}\) was also the average height of the marks of the origin and each of the target key and was 4 mm, as the height of the marks on all the original and target keys were this height. The distance between the origin and target key was the distance between the middle of the marks on the two keys. The distance between the origin and a target key, \(W_{\text{ave}}\), and ID calculated using Equation (2) of the pointing tasks were summarized in Table 2. The sizes, locations, distances between the origin and end point of the pointing tasks, and distance between each key to the participant were measured using a measuring tape. The angles of the virtual panel were measured using a goniometer. For the pointing tasks in the real environment, the calculator panels mimicked those of the virtual ones and were drawn on plastic boards. These boards were attached on a wood panel that was positioned on a workbench (see Figure 2). The inclined angle of the wood panel was also 30\({}^{\circ}\) or 90\({}^{\circ}\). The sizes and distances of the keys and the angles of the