## 3 Results  
The result of the creation of a forest structure from data obtained from the original forest (see Figure 8) by generating random tree positions is shown in Figure 9. The size of the analyzed forest area was 140 \(\times\) 80 m (11,200 m\({}^{2}\)). The length of the vehicle's passage was 212 m. The direct path between the starting point and the target is shown by a black line. This path is generally unrealistic due to the tree stem obstacles (displayed as green points). All possible paths (blue closed Voronoi polygons) that match the tree distances and vehicle parameters have been computerized using Dijkstra algorithm and displayed in Figure 8 using our own software tools. Unfinished Voronoi polygons (ending between trees) are nonbinding paths where the width of the vehicle does not allow passage between trees. We can choose any of these blue passable routes, but only one will be the shortest (fastest)--the red highlighted route. This route traverses around (between) the burning forest polygons. The simulation of the polygons displaying the fire areas was done completely at random by adding the points around the impassable zones (orange areas). These areas can be complemented e.g., by satellite images or aerial photos. If we wanted to avoid these risky places, we would have to create a security zone around the burning polygons--so-called buffers--using GIS tools.  
Figure 7: The relationship between the Delaunay triangulation and Voronoi graph (scale 1:200). (**a**) Set of trees generated from average \(MTS\) values. (**b**) The area is divided into elementary triangles using Delaunay triangulation (each reference tree has its two closest neighbors). (**c**) Axes of triangle sides create so-called Voronoy edges and Voronoy cells. (**d**) Voronoy edges represent the safest.  
There are also displayed the routes inside the areas of fires (blue lines inside the orange polygons)--see Figure 9. These routes can be used later when the fires end, but they are primarily not included into the calculation of the shortest route. For some types of vehicles, such as tanks, we can also choose the route through the burning area and calculate the route segments inside the orange polygons. The influence of other elements of the terrain (slope gradient, soil properties, terrain surface roughness, forest paths, etc.) are not calculated.  
The above-mentioned result of seeking an optimal forest path partially affected by a fire may be modified in case when the forest structure is regular triangular or rectangular. There are displayed all the possible routes and the shortest route--red line in the triangular forest structure in Figure 10.  
Figure 8: The Sitka spruce forest near Utechov, where the heights of trees and \(DBH\) data were measured (scale 1:1000, center coordinates: \(\varphi=49.282744\), \(\lambda=16.632918\))—(Ortophoto Mappy-cz).  
Figure 9: Navigation on the shortest vehicle route (red track) avoiding the burning forest (orange areas). Randomly spaced trees, approx. scale 1:1000.  
The methodology for finding the optimal rescue vehicle path was based on verifying the input data. Determining a forest structure from DSM data can be very unreliable, especially when LiDAR data are obsolete. Therefore, the use of growth curves of trees and derived vegetation parameters were used. These parameters were determined on a relatively small area. Verification of the vegetation parameters by photogrammetric and geodetic pathways lasted several months. The results of the presented model are valid for the designated coniferous forest. The general application of the optimal vehicle route determination will depend on the type of trees (coniferous, deciduous, and mixed). The author assumes that the presented model for finding the optimal route of a vehicle will be better utilized with the development of mapping methods aimed at determining the exact coordinates of the trees.