## 2 Materials and Methods
### Procedures for the Verification of the Method

Table 1: Summary of measured parameters and evaluated criteria for analyzed data sets, where \(a\)—length of the longer semiaxis of the ellipse, \(b\)—length of the shorter semiaxis of the ellipse, \(\alpha\)—angle of inclination of the directional line of the ellipse, \(x_{COG}\)—mean position on the horizontal axis of the analyzed set of points, \(y_{COG}\)—mean position on the vertical axis of the analyzed set of points, \(\Delta_{P}\)—distribution uniformity ratio, \(k\)—percentage of analyzed points inside the area plotted by the ellipse \(\Delta R\)—difference between the standard radius of curvature and the mean radius of curvature of the ellipse, \(A\)—area of the plotted ellipse \(\sigma_{a}\)—standard deviation of the semiaxis a, and \(\sigma_{b}\)—standard deviation of the semiaxis b.  
Figure 3: Test stand for the implementation of biomechanical tests with the specified elements for measuring the position of the center of gravity (**A**) and the test stand during the test (**B**), where 1—weighing pan, 2—strain gauges supporting the test stand, 3—linear guides stabilizing the weighing pan, and 4—rollers that connect the wheel of the wheelchair with the weighing scales. cycles. However, because of the type of evaluation performed, this measurement sample was recorded with eight different frequencies f, taking the following values: 25 Hz, 29 Hz, 33 Hz, 40 Hz, 50 Hz, 67 Hz, 100 Hz, and 200 Hz. The variation in sampling frequency during the test translated into the number of points provided to the algorithm of the verified method. The effect of the conformity coefficient value of the semiaxis dimensions for the distribution of points \(\varrho\) on the percentage of points contained inside the plotted ellipse was evaluated with the example of data obtained from the motion capture measurement of the point ID1 position in space (SAMPLE 2), moving with constant speed v on a circle of constant radius d [37]. The test station (Figure 4) used to generate the data consisting of a measuring wheel with a fixed reference diameter d of 520 mm. The ID1 marker was placed on this wheel moving with a constant velocity v of 0.2 m/s\({}^{2}\). The position data collected were the coordinates of the ID1 marker's position relative to the ID0 marker. These data were obtained after processing the image recorded by a camera capturing video at 240 fps, with original software. An application example of the method for describing a set of points with elliptical areas for real operational tests of technical devices is presented using the example of measuring PM 2.5 particulate matter concentration (SAMPLE 3) and measuring the muscular activity of upper limb muscles (SAMPLE 4). The concentration of PM 2.5 particulate matter was measured in a city park, simulating the performance of greenery maintenance using equipment driven by an internal combustion engine (Figure 5). The test was performed in a circular working area (WA) with a 17 m diameter. In the center of this area, there was a Lifan internal combustion engine, with a power of 10 KW, 390 cm\({}^{3}\) capacity, powered by gasoline, which was a particulate matter emitter [38]. Measurement of PM 2.5 concentration was performed in different points of WA area using an ATMON FL sensor. Muscle activity (SAMPLE 4) was measured on a wheelchair dynamometer (Figure 3), where a manual-hybrid wheelchair [39] was tested (Figure 6). In these tests, a wheelchair user propelled the wheelchair on a dynamometer that generated three different moments of resistance to motion: 8.14 Nm, 9.67 Nm, and 11.19 Nm. The procedure for propelling the wheelchair was to push off the push rings using the upper limb. During this propulsive movement, an electric motor built into the hub of the drive wheel additionally supported the propulsive force generated by the upper limb. During the performed measurement tests, the electric motor assist gain factor was 0%, 25%, 30%, 40%, 50%, 60%, 70%, and 75%.