## 4 Results of Comparison of Proposed MVD Algorithm with Existing Algorithms
Subsequently, the final \(SD_{\text{final}}\) measure for each simplified line was determined and is presented in Table 1.  
The proposed maximal vertical distance algorithm performs better than the Visvalingam Wyatt algorithm in terms of the finally obtained stress deviation percentage (\(SD_{\text{fin}}\)) for all combinations of studied material constants and maximal stress deviations (\(SD_{\text{lim}}\)). For different numbers of initially given points, the discretized polyline obtained from the Visvalingam Wyatt algorithm obtains varying \(SD_{\text{fin}}\) measures, making it less reliable. When comparing the obtained \(SD_{\text{fin}}\) values with the maximal requested limit \(SD_{\text{lim}}\), the VW algorithm yields values exceeding the limit for the same number of points as those obtained by the MVD algorithm. Determining the optimal number of initial discretization points for the VW algorithm is challenging, given the variability in \(SD_{\text{fin}}\) limits. Also, a considerable number of points is needed for the discretized polyline to closely resemble the original curve. As the VW algorithm iteratively removes points starting from the complete set, it demands a greater computational effort with finer initial discretization. The equal-intervals algorithm occasionally exhibits a lower percentage of stress deviation compared to the MVD algorithm. However, it is inconsistent, as it does not comply with the limit of stress deviation in every observed case, making predictions unreliable. In contrast, the MVD algorithm stops once it achieves the minimum number of points required to meet the stress deviation criterion, ensuring consistent adherence to predefined limits. To visually illustrate the multilinear curves obtained using the compared algorithms, only specific parameter combinations from Table 1 were chosen. Here, the focus is on results corresponding to \(SD_{\text{lim}}\) of 5% and a fixed number of initial points for VW discretization \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**K = 549 MPa**} & \multicolumn{2}{c}{**K = 1435.7 MPa**} \\
**Stopping** & **Algorithm** & **Number of Initial Points** & **n = 0.038** & **n = 0.276** & **n = 0.002** & **n = 0.002** \\ \cline{3-6}  & & & **SDfin, \%** & **Final Number of Points** & **SDfin, \%** & **Final Number of Points** \\ \hline \(SD_{\text{lim}}\) = 2\% & MVD & 1.1 & & 1.9 & \\ \hline \multirow{3}{*}{Number of simplified points *} & EI & 0.8 & & 3.18 & \\ \cline{2-6}  & VW & 500 & 2.49 & 5 & 5.05 & 9 \\ \cline{1-1}  & VW & 1000 & 2.52 & & 5.29 & \\ \cline{1-1}  & VW & 10,000 & 2.02 & & 3.24 & \\ \hline \(SD_{\text{lim}}\) = 5\% & MVD & 4.57 & & 4.57 & \\ \cline{1-1} \cline{2-6}  & EI & 2.85 & & 6.65 & \\ \cline{1-1} \cline{2-6} Number of simplified points * & VW & 500 & 5.94 & 3 & 12.69 & 6 \\ \cline{1-1}  & VW & 1000 & 5.94 & & 12.82 & \\ \cline{1-1}  & VW & 10,000 & 5.38 & & 10.46 & \\ \hline \hline \end{tabular}  
* The VW and EI algorithms stop when the same number of simplified points that were obtained with MVD algorithm are reached.  
\end{table} 
Table 1: Comparison of MVD, VW, and EI algorithms on different materials. set at 10,000. This visual representation includes both materials and all three algorithms and is depicted in Figure 9, with the left side illustrating material 1 and the right side illustrating material 2. The upper graphs showcase the final multilinear curves obtained from all algorithms, while the bottom graphs illustrate the percentage of stress deviation, \(SD\), obtained for the values of the plastic strain. Notably, the peaks of stress deviation (\(SD_{\text{fin}}\)) are most pronounced at smaller values of plastic strains. It is evident from the figure that the EI algorithm can occasionally yield even lower values of \(SD_{\text{fin}}\) than the MVD algorithm, particularly notable for material 1. However, since it exceeds the limit of stress deviation for material 2, it is clear that it is failing to adhere to the initial condition.