## 4 Discussion
In this test, the best elliptical representation of a set of points was obtained for sets in which \(\Delta P\) was close to 0.5; areas with PM 2.5 concentrations <20 \(\mu\)g/m\({}^{3}\) and <17 \(\mu\)g/m\({}^{3}\) demonstrate this. In their case, the value of ratio \(\Delta P\) was 0.58 and 0.59. The least accurate mapping of the set of points with ellipse was obtained for a PM 2.5 concentration of <14 \(\mu\)g/m\({}^{3}\). For this set of points, the value of the ratio \(\Delta P\) was 0.79. The presented example of applying the method on data describing PM 2.5 particulate matter emission has demonstrated the advantage of the described method consisting of simplicity to determine the area occupied by the analyzed set of points. Using this method, determining the area of presence of the analyzed points requires only calculating the area of an ellipse with two known parameters defining the lengths of the semiaxes \(a\) and \(b\). The results obtained during the verification of the method confirm that the highest emission of air pollutants is closest to the emission source, i.e., the internal combustion engine [51; 52]. The experiments carried out to verify the operation of the method checked how the distribution type and the number of measurement samples affect its applicability. The experiment testing the effect of the number of points on the dimensions of the ellipse showed that, when analyzing a set characterized by a normal distribution, the number of points has little effect on changes in the dimensions of the ellipse. When measuring the variation of gravity center position for the human body propelling the wheelchair, using the set consisting of 230 points, the dimension of semiaxis a was 61.46 mm, while it was 16.00 mm for semiaxis \(b\). However, for the same measurement test measured with the frequency enabling to measure 1835 points, the dimension was 61.37 mm for semiaxis \(a\) and 15.83 mm for semiaxis \(b\). Having included these results, it is noticeable that the mapping accuracy of the point presence area increases with the increase in the number of points. Despite that, the obtained small difference in the dimensions of the semiaxes confirms the thesis saying that the increase in the number of points of the analyzed set has little effect on the final dimensions of the ellipse. Based on that, it was found that the method is characterized by high flexibility when the analyzed set of points demonstrates variable size. Additionally, using the example of data from the measurement of the human body's gravity center position, it was found that, for the distribution of points characterized by the uniformity ratio \(\Delta_{P}\) at the level of 0.57-0.61, there is an average of 84.08% of all points delivered to the algorithm of the method included in the ellipse. The data on the center of gravity position used for verification during wheelchair propulsion were consistent with the results of other tests measuring and analyzing this parameter in a different aspect [53; 54]. An experiment conducted on motion capture data was supposed to demonstrate the effect of the distribution type on the representation of a set of points by an ellipse. Points characterized by a uniform distribution were used in this data set. In the case of such distributions, determining the length of the ellipse semiaxis as a value of double standard deviation is not very precise. It ensures covering over 95.4% of the points with the area plotted by the ellipse, but the plotted area is noticeably larger than the area of presence for the set of analyzed points. In order to also fit this method to uniform distributions, the method of calculating the semiaxis ellipse dimensions was modified. In this case, they are the quotient of the conformity coefficient \(\varrho\) value of ellipse semiaxis dimensions and the standard deviation value.