## 6 Conclusions and Future Works  
VBD, which was introduced in 2024, is an improved algorithm over the previously published methods. In this study, the existing VBD algorithm, originally implemented in C++, was integrated into Unity, a physics engine, for simulation. Despite being conducted in a CPU-only environment without GPU acceleration, VBD demonstrated better fps performance than PBD. In the hanging scenario, as the number of nodes increased, VBD achieved up to 82.9% better fps, showing a clear performance advantage over PBD. In the object-to-object collision scenario, VBD provided up to 31.1% higher fps with the same number of nodes. As node counts increased, the computational load grew rapidly, and the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time Step** & **0.01 s** & **0.02 s** \\ \hline VBD & 100–101.5\% & 100–101.8\% \\ PBD & 100–101.1\% & 100–107.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Changes in hanging cloth area by time step. Figure 8: The 16 \(\times\) 16 node, 0.1 s time step cloth simulation using PBD (**left**) and VBD (**right**). Figure 7: The 64 \(\times\) 64 node, 0.02 s time step cloth simulation using PBD (**left**) and VBD (**right**). performance gap between VBD and PBD widened further than in the hanging scenario. In the self-collision scenario, the difference in performance between VBD and PBD was smaller than in the previous cases, likely due to the increased computational complexity, which limited performance in the CPU-only environment. These results are based on identical parameters, time steps, and node counts for both algorithms. Additionally, the maximum number of nodes that could sustain real-time performance was measured for each scenario. In this study, 30 fps was established as the minimum standard for real-time performance, representing the lowest frame rate at which games and animations can maintain real-time responsiveness across various graphic content types. However, studies by [PERSON] et al. [39] suggest that lower frame rates in VR and AR environments can lead to motion sickness. Therefore, a minimum frame rate of 60 fps is recommended for VR and AR content to ensure a smoother and more comfortable user experience. In the hanging simulation, PBD could maintain real-time performance with up to 93 \(\times\) 93 nodes, while VBD supported up to 120 \(\times\) 120 nodes. For object-to-object collisions, the limits were 92 \(\times\) 92 nodes for PBD and 80 \(\times\) 80 nodes for VBD. In self-collision simulations, PBD and VBD could sustain real-time performance with up to 21 \(\times\) 21 and 23 \(\times\) 23 nodes, respectively. As expected, as the operations became more complex, the limitations in the CPU-based simulations became more noticeable. This study proposed a simulation design methodology utilizing only CPU resources, excluding compute shaders, implemented in C# within Unity. This approach may demonstrate improved results on devices relying solely on CPU computation, particularly if advancements in memory or CPU performance are achieved. Furthermore, since VBD is optimized for parallel processing, it is expected to achieve significantly better performance with GPU acceleration through compute shaders. Future research will focus on improving computational processes and implementing a variety of physical simulation algorithms, including VBD, PBD, the Mass-Spring System, and Extended Position-Based Dynamics (XPBD), on GPU platforms. Comparative studies will further optimize these algorithms. Future work will also explore real-time simulations for augmented reality (AR), virtual reality (VR), and resource-constrained platforms, such as mobile and web environments, using optimized algorithms tailored for these platforms. Conceptualization, J.M. and M.H. ; methodology, J.M. ; software, J.M. ; validation, J.M. and N.-J.S. ; formal analysis, J.M. and M.-H.C.; investigation, J.M., N.-J.S., and M.-H.C.; resources, N.-J.S. ; data curation, J.M. ; writing--original draft preparation, J.M. ; writing--review and editing, M.H.