# Characterization of Dynamic Blockage Probability in Industrial Millimeter Wave 5G Deployments
## 4 Individual Machine LoS Blockage Probability  
In this section, we formulate the individual machine blockage probability by utilizing photogrammetric approach.  
To assess the blockage probability of an individual machine we will utilize photogrammetric approach. At the glance, the procedure consists in observing the animated model over the full period of action at different yaw and pitch angles and creating the associated static transparency maps. A transparency map consists of 0 s and 1 s, where 1 represents the blocked LoS while 0 corresponds to the non-blocked conditions. Blocked and non-blocked conditions are distinguished based on the background color serving as a template. A timestamp \(t_{i}\in(0,T)\), where \(T\) is the fill action period of a model, and yaw and pitch angles \(\alpha\) and \(\beta\) fully define a blockage probability of an individual machine in time and space. Note that in the case of D2D communications, the only pitch angle is sufficient. The rest of the procedure is performed by utilizing binary transparency maps. Specifically, to obtain an average transparency map, we average individual maps based on the timestamps and angles.  
To perform this, step we utilize a free and multi-functional 3D modeling program--Blender Modeller [28]. This tool allows the creation and animation of 3D models of realistic industrial environments, namely, perfectly implemented animation of solids, several built-in visualization tools with various renderers, a large selection of tools for 3D modeling, a wide selection of textures, and shader sets. The transformation of illustrations into matrices was performed in the Matlab/Simulink software environment using the MATLAB language.  
The step-by-step methodology is as follows:  
1. _Setting up the scene._ By utilizing Blender, we place the model at the starting point of the coordinate system. Next, we install the camera at the selected height that depends on the heights of UE/BS and the analyzed UE and fix the middle frame to the center of our object. Then, we rotate the camera 360 degrees around the model. We select the correct focal length to fully capture the dynamics of the object in each picture. As a result, a minimum bounding rectangle can be calculated for each device, considering the viewing angle, see Figure 1(a).
2. _Tracing the objects._ For each model, we run a dynamic animation lasting the full operational period of a machine with a well-distinguishable background, and take pictures with a frequency of 60 frames per second. Thus, we obtain \(N\) static illustrations. See an example in Figure 1(b).
3. _Characterizing LoS paths._ By utilizing Matlab, we calculate the static blockage probability for a given space-time coordinate \((t_{i},\alpha,\beta)\). For each image and each pixel, we get the color value. If the color is equal to the background value, then we write the value 0 for this image to the pixel matrix, i.e., there is unobstructed LoS path. Otherwise, we write the value 1, i.e., there is no LoS path through an object in this direction. At the output, we obtain \(N\) binary matrices consisting of 0 and 1. Then, for each pixel, we calculate the sum of ones and divide by the number of images to obtain the average blockage probability. The stage is shown in Figure 1(c).
4. _Averaged blockage probability._ We repeat this procedure for \(M\) \"typical\" angles of view per model in 45 degree increments. Having superimposed the results of different angles of view on each other, i.e., having found the average in the angles of view, we obtain the LoS blockage value by one industrial device, see Figure 3.  
Figure 2: _Cont._