## 4 Results and Discussion  
To prove the thesis of approximately 25 points being enough for a section measurement, this theory was verified in practice on a Zeiss (Oberkochen, Germany) Accura II, Calypso 2019 (Zeiss, Oberkochen, Germany) software with curve and freeform modules, and Vast XT and Vast XXT probe heads. Different scenarios from 10 to 1000 measuring  
Figure 10: Serious discontinuities on a 999 points interpretation of overall airfoil section. Red straight line, ideal shape; green dashed line, tolerance zone; blue dot line, deformed unacceptable shape with error. Figure 9: Spline interpretation based on 10 significant points (red-dashed), 25 (blue-straight) vs. the original spline (green dotted-dashed). (**a**) Turbine guide vane. (**b**) Turbine blade. points are presented in Table 2 and drawn in the chart in Figure 11. The chart shows the same level of error for all the measurements, which proves the theoretical assumptions. Thus, it transpires that within the boundaries of the specified part tolerances it has been proved that smaller point groups can drastically reduce the overall measuring time for part inspection. Based on theoretical speculations, a production part was measured by CMM using three sections and one trend line. Data was collected on all the measured points and deviations calculated from the original 2D spline. Sample results are presented in Table 3. The result including two almost perfect sections and one which varies greatly from the desired specification but is still within tolerance. This is part-specific, based on curvature changes in the configuration, but also shows an interesting fact about part castability. Twenty-five points per section and 16 for the trend line gave us satisfactory results with an average error similar to the theoretical one. The total number of measured points can slightly fluctuate around this number; there is no difference whether we use 23 or 28 for a \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Part A** & \begin{tabular}{c} **Maximum Distance** \\ **Error (mm)** \\ \end{tabular} & \begin{tabular}{c} **Average Distance** \\ **Error (mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard Deviation (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Points Outside the** \\ **Tolerance Zone** \\ \end{tabular} \\ \hline
1000 & 0.122 & 0.059 & 0.024 & 0 \\ \hline
500 & 0.122 & 0.059 & 0.024 & 0 \\ \hline
250 & 0.122 & 0.059 & 0.024 & 0 \\ \hline
125 & 0.122 & 0.059 & 0.024 & 0 \\ \hline
75 & 0.122 & 0.059 & 0.024 & 0 \\ \hline
50 & 0.120 & 0.059 & 0.024 & 0 \\ \hline
**25** & **0.103** & **0.060** & **0.024** & **0** \\ \hline
15 & 0.121 & 0.066 & 0.018 & 0 \\ \hline
10 & 0.103 & 0.068 & 0.023 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculations of measured CMM points for one section and deviation to CAD B-Spline shape for vane example. Figure 11: Average distance error between 10 and 1000 control points based on real CMM measurements for a part without defects. curve. Twenty-five was chosen as it seems to be a good compromise between the maximum and average distance error, giving a reliable result. This proves the thesis about shape inspection simplification. The sample standard deviation is acceptable, as its value is at the same level as for 1000 points. All tests were repeated on about 50 guide vanes as a first attempt at a prototype set and then released to production for other sets. All results are very similar and confirm the method for the real parts. An additional check was performed using a 3D scan aligned with the best fit related to the data. The results were computed using Geomagic Control X [16]. The calculated error is within the desired overall tolerance, which confirms that the simplified CMM inspection is enough to accelerate the verification process. Previously, for a qualified process, all parts met the intent of the checking process, so additional checks were introduced on the parts rejected before qualification.