## 5 Results
### Results of the Study Using NMT, NMPT  
The photogrammetric method is one of the methods of acquiring data concerning the heights of the terrain for later use in creating the numerical model of its surface. The photogrammetric measurements of aerial photographs or satellite images on digital stations allow us to determine the heights of a selected point in space. The process of acquiring height data on the basis of the model can be carried out automatically on a large area or under the user's control. This is an undoubted advantage of this way of collecting data for DTMs. Another strength of this method is the speed of data acquisition and the possibility of developing large areas. The most interesting effects of the spatial modeling process can be observed in areas that are heavily diversified in terms of topography. Based on this belief, a fragment of the municipal commune of Mszana Dolna, along with the village of Kasinka Mala, was adopted as the study area. The research area is characterized by the high potential in terms of the construction of the digital terrain model. When choosing the research area of this study, the possibility of emphasizing the relationship between the terrain shape and the objects present in it, as well as with land use and spatial development, were taken into account. The analyzed area includes, among others, compact forest complexes, agricultural areas, green areas, and urban and rural development areas, together with road and rail infrastructure. The occurrence of these elements gave an opportunity to create a digital terrain surface model (DSM), taking into account their connection with the relief. To create the digital terrain model, a method of triangulation of acquired data was used to create a vector model in the form of a triangulated irregular network (TIN). The model created in this way was supplemented with three-dimensional models of buildings, trees, and road infrastructure, thanks to which the digital terrain surface model was created (Figure 15). A digital terrain surface model was used as a basis for carrying out additional research on the applications of 3D models in the fields related to the branch of geoinformation engineering. The creation of the DTM required the construction of an irregular grid of TIN triangles. The creation of a regular grid could result in the omission of some details of the relief due to the high variability of the terrain configuration of the selected study area. The digital terrain model of the Mszana Dolna and the surrounding area was created as the TIN grid surface (Figure 16). Figure 15: Digital terrain surface model—Kasinka Mala. On the basis of the pre-formed TIN grid, the vectorized contours of mountains and the slopes of embankments were projected onto the created surface. The final version of the DTM is shown in Figures 17 and 18. Figure 16: Digital terrain model of the research area—TIN grid, draft version, view from above. Figure 17: Digital terrain model—view from the side of Mszana Dolna, Phong type rendering. Figure 18: Digital terrain model—view from above, Phong type rendering with solar lighting from the southeast side. The mean square error of the height determination for the model was equal to \(\pm\)0.56 m. It was calculated from the Ackermann formula, Equation (2). \[\text{m}_{\text{NMT}}\ ^{2}=\text{m}^{2}{}_{x}+(\ \alpha\text{-d}\ )^{2}=0.56\ (\text{m}) \tag{2}\]  
where:  
m\({}_{x}\)--the mean square error of the height of the point determination, adopted as 0.1 (m) due to the accuracy of the heights given on the source map,  
\(\alpha\)--coefficient describing the nature of the terrain. It was assumed as \(\alpha=0.022\) difficult terrain (mountainous with high slopes)  
d--the average distance between the measurement points was adopted as 25 m according to the original TIN grid triangulation options. To build the land cover model, it was necessary to conform the previously created DTM model to the original model, not only in terms of the shape but also the appearance.