## 3 Results
### Verification on Stanford Bunny Simulation  
The proposed framework was verified in terms of latency caused by data transmission and the accuracy of transmitted surface meshes in the simulation. We have applied the proposed framework to a simulation involving interaction with a deformable Stanford Bunny model and the VE training simulation. Position-based dynamics [20] were used to compute the deformation of an object in both simulations. The latencies were compared in both cases when surface vertices and normals are sent and control points are sent instead of surface meshes. The accuracy was measured by root mean square (RMS) position error between the original mesh and a reconstructed mesh from received control points. Measuring end-to-end latency from user input to visual response in AR requires external sophisticated devices [21]. Instead of end-to-end latency, we recorded the time when data were sent to the HMD on the PC and the time when data were received on the HMD to measure latency caused by data transmission. We assumed that a constant communication lag between the PC and HMD was zero to analyse latency caused by data transmission separately from any inherent delay in the network. This means that if a signal is sent to the HMD without data, then the transmission time is assumed to be zero. The initial time difference, \(t_{0}\) caused by unsynchronised clocks between the PC and HMD, and an inherent delay of the network was measured. Empty data were sent to the HMD 100 times. The time when the data were sent from the PC and the time when a signal was received at the HMD were measured on the PC and HMD, respectively as shown in Figure 9. The average difference was calculated and used as the initial time difference, \(t_{0}\). Time differences were measured for \(n\) steps: \((t_{1},\ t_{2},\ t_{3},\ \ldots,\ t_{n})\) and then the latency was calculated by subtracting the initial time difference \(t_{0}\) from all measured times: \((t_{1}-t_{0},\ t_{2}-t_{0},\ t_{3}-t_{0},\ \ldots,\ t_{n}-t_{0})\). In the simulation of the Stanford Bunny model, we grabbed and moved some points of the model that comprised 524 vertices and 950 triangular surface meshes, as shown in Figure 10. A total of 48 control points (4 \(\times\) 4 \(\times\) 3) were placed to embed the model. Figure 9: Measurement of latency caused by data transmission from the PC to the HMD. In the proposed framework, 48 control points were transmitted to the HMD, and a surface mesh was reconstructed from the received control points. Global deformation was not transmitted in this simulation because no specific scenario was defined. A total of 524 pairs of vertices and normals are needed to directly render the Stanford Bunny model on the HMD without the proposed framework, which will result in 1048 vectors sent to the HMD for 400 steps. The average and maximum latency caused by sending 1048 vectors are 281 and 315 ms, respectively. In the case of the proposed framework, only 48 control points are needed to render a virtual scene. The average and maximum latency over 400 simulation time steps caused by sending 48 control points are 6 and 51 ms, respectively. The average and maximum latency are summarised in Table 1.  
The accuracy of the proposed method was verified by the RMS position error between the original mesh in the server and the reconstructed mesh in the client. RMS error was measured for 400 simulation steps. Figure 11 shows the RMS error over time and the snapshots of the simulation. The initial RMS error of 4 mm was caused by an error in the inverse mapping matrix. The error was 4% compared to the longest length of the model, 100 mm. The error increased by up to 7.5 and 29 mm when the head was pressed down, and the ear was pulled to the right, respectively. The relative errors compared to the longest length are 7.5% and 29%, respectively. The error increases as the shape of the model changes from the initial shape. This is because the global deformation was not transmitted as target shapes were not predetermined in this simulation.