## 6 Improving Projection Stability  
### Causal Analysis of Projection Stability Degradation  
Polygon meshes are one of the main approaches for representing 3D objects in computer graphics and visualizations [37]. Meshes represent a 3D object using an interlinked collection of polygons (i.e., triangles or rectangles), which in turn are composed of edges and vertices. The simple and repetitive representation format makes computation highly efficient, especially when using Graphical Processing Units (GPUs) to handle graphic displays in computing devices.  
AROS_x uses triangle meshes to represent and project 3D objects of interest (prefab format). The total number of vertices for a given object determines its resolution. According to [PERSON]'s formula, 2n triangles are created when the number of vertices is n [38]. As the number of vertices increases, an object can be expressed more accurately, but it requires additional computational power to process and display. So, an excessive increase in the number of triangle meshes can result in hardware overload, which occurs more frequently on mobile devices which are limited in their graphics specifications.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Distance** & \multicolumn{2}{c}{**3 m**} & \multicolumn{2}{c}{**6 m**} & \multicolumn{2}{c}{**9 m**} & \multicolumn{2}{c}{**12 m**} & \multicolumn{2}{c}{**15 m**} & \multicolumn{2}{c}{**Mean (Total)**} \\ \hline
**Standard Plane** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** & **x-z** & **x-y** \\ \hline
1 & 0.180 & 0.140 & 0.150 & 0.100 & 0.150 & 0.100 & 0.180 & 0.120 & 0.150 & 0.120 & 0.162 & 0.116 \\
2 & 0 Therefore, it is necessary to set the appropriate number of vertices according to the device and purpose of use. The process of increasing and decreasing the resolution of 3D meshes is referred to as'refinement' and'simplification,' respectively (Figure 5).  
Based on investigations into the specifications of iPad Pro and Unity 3D, the recommended range for optimal rendering performance in terms of mesh numbers was between 300 and 1500 (Unity3D (version 2020.3) recommends this range, assuming that the latest high-end hardware is used in mobile devices ([[https://docs.unity3d.com/560/Documentation/Manual/ModelingOptimizedCharacters.html](https://docs.unity3d.com/560/Documentation/Manual/ModelingOptimizedCharacters.html)]([https://docs.unity3d.com/560/Documentation/Manual/ModelingOptimizedCharacters.html](https://docs.unity3d.com/560/Documentation/Manual/ModelingOptimizedCharacters.html)) (accessed on 17 October 2022))). The two most representative high-end mobile devices are Apple's iPad Pro (4 th generation, A12Z Bionic chip with 64-bit architecture, 6 GB RAM) and Samsung's Galaxy S8 Ultra (Qualcomm Snapdragon Gen 1 SM8450, 16 GB RAM). As a result of comparing the two devices, the rendering performance of the iPad Pro was superior, and LiDAR was also embedded, so this study utilized an iPad Pro as AR implementation hardware). However, the number of triangle meshes for the bridge model included over 2200 meshes (red box in Figure 6) and exceeded these specifications. This was identified as a primary cause for deterioration in projection stability.  
Figure 5: Trade-offs based on the number of vertices.  
Figure 6: Number of triangle meshes in the AR model.