## 4 Results
### Performance Analysis: Resolution vs. Frame Rate  
#### 4.1.1 Resolution-Based Performance Test  
To evaluate the real-time performance of the proposed GPU-PBD-based cloth simulation, a comprehensive performance test was conducted by comparing it with Unity's built-in Cloth component across various cloth resolutions. All experiments were performed in a standalone XR environment using the Meta Quest 3 device.  
Performance was measured based on frames per second (FPS) across five different cloth resolutions: \(8\times 8\), \(16\times 16\), \(32\times 32\), \(64\times 64\), and \(128\times 128\). Each test involved creating a static cloth mesh at the specified resolution and applying only gravity forces, without any desk collision experiments. FPS was measured using the Meta Quest Developer Hub Performance Analyzer. The numerical results are summarized in Table 3, and a graphical comparison is illustrated in Figure 4.  
The results demonstrate that Unity's Cloth component consistently maintains 72 FPS across all tested resolutions, likely benefiting from advanced internal optimizations. The proposed GPU-PBD system achieves comparable performance up to a \(32\times 32\) resolution for both single-sided and double-sided configurations. At higher resolutions, the single-sided GPU-PBD maintains relatively high performance (65 FPS at \(64\times 64\), 42 FPS at \(128\times 128\)), whereas the double-sided GPU-PBD experiences greater performance degradation (40 FPS at \(64\times 64\), 16 FPS at \(128\times 128\)). Nonetheless, even the double-sided implementation maintains sufficient real-time performance for XR applications at resolutions up to \(64\times 64\)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Purpose** & **Test Setup** & **Compared Systems** \\ \hline \multirow{2}{*}{1} & Measure FPS performance across & Gravity-only cloth drop in static & Unity Cloth vs. GPU-PBD (Single \& Double-sided) \\  & resolutions (\(8\times 8\) to \(128\times 128\)) & space using Meta Quest 3 & \& Double-sided) \\ \hline \multirow{3}{*}{2} & Test physical interaction accuracy & \multirow{3}{*}{SubMesh from controller-selected} & Unity Cloth vs. GPU-PBD \\  & between cloth and & RoomMesh region & (Double-sided) \\  & real-world surface & & \\ \hline \multirow{2}{*}{3} & Evaluate hand interaction realism & Hand sweeps across cloth using & Unity Cloth vs. GPU-PBD \\  & using 19 capsule colliders & capsule colliders & (Double-sided) \\ \hline \multirow{2}{*}{4} & Evaluate natural deformation via & Real-time hand mesh in push and & \\  & hand mesh geometry & two-hand stretch interactions & GPU-PBD (Double-sided) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Overview of experimental scenarios: (1) resolution vs. frame rate, (2) RoomMesh collision, (3) hand capsule collider collision, (4) hand mesh collider collision.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Resolution** & **Unity Cloth (FPS)** & \
\begin{tabular}{c} **GPU-PBD** \\ **(Single-Sided)** \\ \end{tabular} &
\begin{tabular}{c} **GPU-PBD** \\ **(Double-Sided)** \\ \end{tabular} \\ \hline \(8\times 8\) & 72.0 & 72.0 & 72.0 \\ \(16\times 16\) & 72.0 & 72.0 & 72.0 \\ \(32\times 32\) & 72.0 & 72.0 & 72.0 \\ \(64\times 64\) & 72.0 & 65.0 & 40.0 \\ \(128\times 128\) & 72.0 & 42.0 & 16.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance comparison by resolution: average FPS over five trials (single and double).