## 3 System Information
### Real-Time Physics Simulator  
The physical simulator is divided into a rigid body simulator whose shape does not change when the force is applied, and a soft body simulator whose shape does change. The model on the left in Figure 8 shows after the collision of the rigid body, and the model on the right shows after the collision of the soft body.  
Figure 6: Result of Method (**Left**: Color Image, **Middle**: Depth Image, **Right**: Calibrated Image).  
Figure 7: Find Squares in Video Frame (for Interacting with Physics Model).  
The rigid body simulator has the advantage that the simulation speed is fast; however, the reality is low. The soft body simulator has the advantage of showing realistic motion; however, the simulation speed is slow. While most of the augmented reality content that performs simple augmentation uses rigid body simulators, it is preferable to use soft body simulators for content for physics education. Therefore, we developed a soft body simulator that can simulate real-time simulations, and applied it to augmented reality systems.  
To perform soft body simulation, most researchers adopt deformation computing methods, such as the Finite Element Method (FEM), Mass Spring System (MSS), and Position Based Dynamics (PBD). Table 2 shows the advantages and disadvantages of each calculation method [17; 18; 19]:  
FEM is chosen if precise simulation accuracy is required, while PBD is chosen if relatively fast speeds and inaccurate simulation accuracy are required. Without this extreme situation, most researchers choose MSS to perform soft body simulation. We implemented a soft body simulator by selecting MSS, which is a method of guaranteeing simulation accuracy and speed.  
The MSS has the structure shown in Figure 9, in a way that the object is constituted by a point (node) having a mass and an imaginary line (spring) connecting it. When constructing a cloth model, all spring structures are used, but when constructing a volume model, only a structural spring is used.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **FEM** & **MSS** & **PBD** \\ \hline
**Simulation Speed** & low & **mid** & mid \\
**Simulation Accuracy** & high & **mid** & low \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of Each Calculation’s Advantages and Disadvantages (low, mid, high).  
Figure 8: Behavior Comparison (**Left**: Rigid Body, **Right**: Soft Body).  
Figure 9: Structures of MSS (Node, Structural Spring, Shear Spring, Bend Spring) [20].  
The MSS consists of a node and three springs (Structural, Shear, and Bend), and each component has the following data. The node has mass, position, velocity, and force basic data for each point. The spring has an initial length (_RestLength_), associated with the number of two connected nodes (_Index1 & Index2_), a spring constant (_Ks_), and a damping constant (_Kd_) representing the characteristics of the spring as basic data. The MSS calculates the spring force through Hooke's Law based on the information of the node and the spring to express the strain. The force of the spring is used as an intermediary for tracing the position of the object through various numerical integration methods, such as the implicit Euler method, or the 4 th order Runge-Kutta method. The deformation of the soft body is finally calculated through the prediction of the position of the object. Our soft body simulator satisfies at least 60 fps, and satisfies the constraints even when it performs in the augmented reality environment.  
In this paper, we implemented a real-time MSS based on GPU parallel processing in the environment shown in Table 3.