# SINDVis: User-Centered Dynamic Interactive Visualization System for Space Information Networks
## 3 Theory and Methods
### TopoView Methods
#### 3.4.3 P&Z Interaction  
Interaction technology is inseparable from the visual analysis, and all interaction technologies are only meaningful when combined with a visual interface. There are some representative technologies of interactive visual analysis of detailed information, and most of them are based on deformation technology.  
As shown in Table 1, the current interactive techniques commonly used in the field of visualization can be summed up by the following categories: 1) fisheye views, 2) focus and context, 3) overview and details, 4) panning and zooming, 5) multiple coordinated views, and so on [23]. We carried out a detailed review of the above-mentioned methods in previous research work [4; 13], and we do not elaborate much on it in this section. Admittedly, the canvas area used to draw the network dynamic topology is limited, and the nodes and edges of the SIN topology have a certain scale. To clearly display all the information in the TopoView, we used the panning and zooming (P&Z) interactive technology to realize the dynamic interactive function of the user.  
P&Z is an interactive technology, and it solves the problem of fitting large amounts of data onto a smaller screen [24]. In this study, we borrowed the P&Z interaction model proposed by [PERSON] and [PERSON] to implement the TopoView; the basic principles are shown in Figure 11.  
As shown in Figure 11, path \(s\) represents the reduction from 0 to \(s_{A}\), that is, from \((u_{0},w_{0})\) to \((u_{0},w_{m})\). Path \(s\) is translated from \(s_{B}\) to \(S\), that is, from \((u_{1},w_{m})\) to \((u_{1},w_{1})\). [PERSON] and [PERSON] completed path optimization work based on the above-mentioned basic principles, as shown in the following equations [25]:  
\[u(s)=\left\{\begin{array}{cc}u_{0},&s\in[0,s_{A})\\ \frac{w_{m}(s-s_{A})}{\rho}+u_{0},&s\in[s_{A},s_{B})\\ u_{1},&s\in[s_{B},S]\end{array}\right. \tag{12}\]  
\[w(s)=\left\{\begin{array}{cc}w_{0}exp(\rho s),&s\in[0,s_{A})\\ w_{m},&s\in[s_{A},s_{B})\\ w_{m}exp(\rho(s_{B}-s)),&s\in[s_{B},S]\end{array}\right. \tag{13}\]  
\[\left\{\begin{array}{cc}s_{A}=\frac{ln\left(\frac{w_{m}}{w_{0}}\right)}{ \rho}\\ s_{B}=s_{A}+\frac{\rho(u_{1}-u_{0})}{w_{m}}\\ S=s_{B}+\frac{ln\left(\frac{w_{m}}{w_{1}}\right)}{\rho}\end{array}\right., \tag{14}\]  
where, \(u(s)\) means to pan along a straight line, and \(w_{m}=max\big{(}w_{0},w_{1},\rho^{2}(u_{1}-u_{0})/2\big{)}\). \(\rho\) depends on the user's subjective feelings, and when the value of \(\rho\) is different, the moving path is different when moving from point A to point B, and the gap is more obvious.  
In summary, based on the smooth and efficient P&Z method proposed by predecessors [25; 26], we analyzed the visualization interaction problem of TopoView in SIN. To implement the TopoView  
Figure 11: Diagram of the 2D space of panning and zooming (P&Z) reduction, translation, and amplification (adopted from [PERSON] et al. [25]).  
based on the P&Z method, we used the improved FDA and the FAT method described above. Next, we describe the specific implementation of GeoView and the TopolView.