# A Modified Methodology for Generating Indoor Navigation Models
## 3 Results  
A zigzag line in the corridor (Figure 3a) and the segmentation of corridor space with the use of the VD algorithm are shown in Figure 3b to present the results of the proposed methodology. An indoor navigation model was generated in the corridor based on the segmented corridor space (Figure 4a). The model was developed with the MPRSS method based on neighborhood relations (SS-SS). The network occupies the middle of the corridor based on its midpoints \(\{P_{Mil}\}\). In a straight corridor, network fragments are straight lines. Network elements have a more complex structure at turns in the expanded corridor space (Figure 4a). If the identifiers [SS] were segment centroids C\({}_{\text{SEG}}\), the generated line would not be straight because \(\{C_{SEG}\}\
eq\{P_{Mil}\}\) (Figure 4b).  
Figure 4: Network model in the corridor: (**a**) network generated based on topological relations in dataset [SS], where midpoints \(\{P_{Mil}\}\) are the nodes, (**b**) differences in the location of midpoints \(\{P_{Mil}\}\) and segment centroids.  
Figure 3: Segmentation of corridor space: (**a**) base points and Triangulated Irregular Network (TIN) edges, (**b**) zigzagging in corridor space and generation of midpoints \(\{P_{Mil}\}\), (**c**) corridor segmentation with Voronoi diagrams (VDs) based on dataset \(\{P_{Mil}\}\).  
Three models were developed in the process of constructing indoor navigation models that account for corridors and rooms:  
1. The MPRSS model (Figure 5a) based on (segment-segment), (segment-room), or (segment-stairs) relations,
2. The MPRSSE model (Figure 5b) based on (segment-segment), (segment-entrance), (entrance-room), or (segment-stairs) relations,
3. The MPRSSEM model combining the relationships from models 1 and 2 (Figure 5c).  
The MPRSSEM model was generated by modifying the MPRSSE algorithm. The (segment-room) relations from the MPRSS model were presented as (segment-entrance-room) relations in the MPRSSE model. As a result of the modification (Figure 5c), five edges of the MPRSSEM model do not fit the corridor space (marked in white) and had to be removed by the algorithm. An edge can also be added between each entrance and the adjacent segment of the corridor. In this case, there would be no edges marked in white in Figure 5c.  
The network model in Figure 5a could be useful if there were no partition walls on the side of the corridor. The models that account for entrances are more practical. The MPRSSE and MPRSSEM models are similar, but the MPRSSEM model is more extensive in corridor space.  
Indoor navigation models facilitate traffic in buildings. The MPRSSE and MPRSSEM models were used to generate paths between selected rooms. Two rooms that were most distant from one another were selected in the first example (Figure 6). Rooms that were located closer to each other were selected in the second example (Figure 7).  
The above approaches produced different solutions. The MPRSS model would be useful if there were no partition walls on the side of the corridor. However, such solutions are rarely encountered in practice. The MPRSSE model is suitable for navigation despite the fact that (segment-entrance) and (segment-segment) edges form nearly straight or even acute angles along the routes. The MPRSSEM model supports the generation of routes that approximate natural paths. These routes do not have acute or straight angles. The MPRSSEM model generates the shortest routes.  
Figure 5: Three models of an indoor navigation network generated with the use of different methods: (**a**) Middle-Point Relation Structure Segment (MPRSS) network model; (**b**) Middle-Point Relation Structure Segment Entrance (MPRSSE) network model; (**c**) Middle-Point Relation Structure Segment Entrance Modification (MPRSSEM) network model.