## 3 Results
### The Experiments  
After setting up the environment, the experiment was started. For each type of calibration, five sample collections of spatial coordinates were performed at each point. Each collection consisted of running the application developed for the experiment, performing the calibration procedure, moving toward the point in question, collecting 500 samples of spatial coordinates from the marker, and closing the application. To ensure equality of conditions in the behavior of the application, each time that collection was started at one of the points, the HoloLens mapping information was deleted.  
The experiment generated 2500 samples for each point, resulting in 10,000 samples for each type of calibration. To evaluate the accuracy (the mean distance between the virtually measured position and the real measured position) and the precision (the dispersion of the samples) of the simple and two-step calibrations, the following values were measured:  
1. Euclidean distance between the virtual coordinates and the real coordinates;
2. Magnitude of the error in the evaluation of distances, which in this study is defined as the difference between the absolute value of the measured vector (the actual distance from the origin to the chosen point) and the distance from the origin to the chosen point returned by the HoloLens.  
To visualize the angular dispersion of the error, we also mapped the value of the angle formed at the origin between the corresponding vector to the coordinates provided by the HoloLens and the real coordinates of the points (Figure 5). This angle, of course, is determined by the Euclidean distance obtained in (1) and by the absolute values of the real distances and those provided by the HoloLens.  
For the Euclidean distance of the samples relative to the real point, magnitude is the difference between the absolute value of the measured vector (the actual distance from the origin to the chosen point) and the distance returned by the HoloLens. Angular distance is the angle formed at the origin between the corresponding vector of the coordinates provided by the HoloLens and the real coordinates of the points.  
Figure 6 depicts the graph containing the dispersion and the median of the Euclidean distances between the virtual coordinates and the real coordinates obtained from the samples. The graph shows that the two-step calibration was always more precise than the simple calibration at all points. Thus, we conclude that the two-step calibration contributes significantly not only to reducing the Euclidean distance between the virtual and the real coordinates but also to reducing the dispersion of the results.  
Figure 7 shows the dispersion of the difference between the magnitude of the samples and the measured magnitude. Note that at some moments, the two-step calibration had a lower magnitude and/or dispersion; in others, the simple calibration was less dispersed and more precise. This seems to indicate that the error associated with the magnitude is not influenced by the calibration method.  
Figure 8 shows how much the two-step calibration contributes positively to reducing the size and dispersion of the angles obtained in the samples.