## 3 Results  
### Round-Trip Time and Processing Time  
The proposed framework was verified in terms of the time taken to deliver the deformed mesh and the accuracy of the transmitted mesh in a vaginal examination training simulation. The analysis and verification were carried out using a server PC with Intel(r) Core(tm) i7-6700K CPU, NVIDIA GeForce GTX 1080, 5G Wi-Fi by NetGear, and a HoloLens 1 st Generation. The Mixed Reality Toolkit (MRTK) was used to establish the network communication between the PC and the HMD. Latency occurs when data are transmitted to the HMD through the network, and the HMD processes these current data to receive the next data, as shown in Figure 6. Even if data transmission can be performed without latency, if the processing takes time, latency between visual feedback and user input can increase. We used the round-trip time (RTT) and processing time, \(t_{process}\), as shown in Figure 6 to analyse the tendency of latency against the number of vectors in a server-client model. RTT has been used as a metric to indirectly measure latency in the network [18]. It is defined as the time taken to send data from a server and receive a confirmation signal from the HMD. Three-dimensional vectors, such as surface vertices and normals required for visual feedback, are transmitted to the HMD.  
Figure 7 shows the average RTT when the data were sent five times as a function of the number of vectors transmitted. The number of vectors increases by 100 from 0 to 10,000.  
Figure 5: The overall process of the proposed framework.  
Figure 6: The overall process of the proposed framework.  
RTT is around 225 ms, even if the number of vectors is zero. This is because RTT includes the latency of the update loop at the server, and there is an inherent latency in the network communication established on Web Real-Time Communication (WebRTC) [19]. As the number of vectors increases, the latency fluctuates around 200 ms up to 5000 vectors, when the latency begins to increase consistently.  
From Figure 7, we can conclude that the number of three-dimensional vectors must be smaller than 5000 to avoid additional latency in data transmission. This is in addition to the inevitable latency present in the communication network. RTT involves not only data transmission time but also processing time, which is analysed separately from RTT. The time difference between when the data are received in the HMD and when a confirmation signal is sent to the PC is measured as shown in Figure 6. The number of vectors increases by 50 from 0 to 1000, and the average processing time of 10 times data communication is computed for each number of vectors. Figure 8 shows how the processing time increases proportionally to the number of vectors. The processing time is less than 1 ms up to 1000 vectors, which means that data transmission is dominant in the latency. The processing time, however, must be small enough as a virtual scene needs to be rendered at a refresh rate of at least 30 Hz for smooth visual feedback. Accordingly, all the computations on the HMD, such as processing data to obtain control points, computing surface meshes from the control points, and rendering a scene, must be performed at at least a 30 Hz update rate.  
Figure 8: Processing time over the number of vectors.  
Figure 7: Round-trip time (RTT) against the number of vectors.  
A pair of surface vertex and normal is required to render a 3D object in the virtual world. The total number of vectors must be as small as possible to provide more computational margin in the HMD, where computational power is lower than the PC. The number of vertices in our cervix model and vulva model used in the simulation are 2160 and 2400, respectively. Therefore, a total of 9120 vectors would need to be transmitted in real time without latency to render the 3D scene on the HMD directly. Our framework can reduce this total number of vectors by only transmitting the control points of the cervix and vulva model.