## 4 Results
### Computational Efficiency  
The estimation of the computational efficiency of the proposed technique was considered separately for geometric and materials layers. In theory, the faulting algorithm complexity should be interpreted as \(O(m\times n^{2})\) for square height-fields defined as two-dimensional matrices (side \(n\)). It depends on the model size (\(n\times n\)) and \(m\) as the number of faults (data processing needs two nested loops for introducing each fault). Our experiments, with the practical implementation for large models, showed that the faults number has much less influence on computation time in comparison to model size. This lead us to further examinations and the introduction of the concept of height-field as a one-dimensional vector (only one loop is required then to process data for each fault). With a limited constant value of \(m\), it may be assumed that the overall cost of the (practical) method can be considered as linear dependency. The CFF geometry modelling performance was tested in comparison to the LFF and the impact of the model size. For both methods, the test sample consisted of 100 models per \(n\)-size, where \(n=(1,\ldots,9)\times 10^{6}\) and \(n\in\mathbb{N}\). All models were seeded by randomised value with a uniform distribution and generated by 1000 faults with a constant height (1.0). The radius for circular fault was also constant and set to \(r=250\). The results indicate the linear character of the method in terms of the size of the model. The results presented in Table 2 and in Figure 22 show that for the largest models tested, the working time did not exceed 0.3 s. In general, the CFF method is faster than the LFF technique due to the fact that the fault area is definitely smaller. Only in the worst case scenario, the efficiency of the proposed method will be equal to the linear one. However, the choice of the radius for which the faults would cover an area comparable to the LFF method is not the purpose of the publication. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Model Size**} & \multicolumn{2}{c}{**Geometry**} \\
**Elements** & **Resolution** & **LFF** & **CFF** \\ \hline \(\times 10^{6}\) & \(\times 10^{3}\) & **t [ms]** & **t [ms]** \\ \hline
1 & \(1\times 1\) & 53 & 38 \\
2 & \(2\times 1\) & 99 & 69 \\
3 & \(2\times 1.5\) & 145 & 100 \\
4 & \(2\times 2\) & 191 & 132 \\
5 & \(2.5\times 2\) & 236 & 163 \\
6 & \(3\times 2\) & 281 & 195 \\
7 & \(7\times 1\) & 327 & 227 \\
8 & \(4\times 2\) & 372 & 258 \\
9 & \(3\times 3\) & 416 & 290 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational efficiency of the CFF method depending on the model size compared to the LFF variant. Figure 22: Computational efficiency of the CFF method depending on the model size compared to the LFF variant. The experiments also include the influence of the model size on the materials' classification. Within it, 100 models were examined per \(n\)-size, where \(n=(1,\ldots,9)\times 10^{6}\) and \(n\in\mathbb{N}\). All models were generated for 1000 faults with a constant radius \(r=250\) and seeded by randomised value with a uniform distribution. The initial models consist of materials for \(mat=(2,\ldots,255)\), where \(mat\in\mathbb{N}\). In total, \(2277\times 10^{4}\) models were tested. The results show the linear nature of the classification method in terms of the model size and for the largest models tested, the working time did not exceed 0.02 s. The results are summarised in Table 3 and shown in Figure 23a. The influence of the model size on the erosion modifier was also examined. Within it, 100 models were tested per \(n\)-size, where \(n=(1,\ldots,9)\times 10^{6}\) and \(n\in\mathbb{N}\). All models were generated by 1000 faults with constant radius \(r=250\) and seeded by randomised value with a uniform distribution. For the procedure, \(mat=9\) as the materials number was selected. The initial models were eroded for \(E=(0.1,0.2,\ldots,0.9)\), where \(E\in\mathbb{R}\). In total, 8100 models were tested.