## 2 Materials and Methods
### Micro-Scale Cylindrical Surface Modeling via Genetic Algorithm  
The micro-scale cylindrical surface modeling is performed by a genetic algorithm via surface coordinates, which are retrieved via micro laser line projection. To carry it out, a cylindrical surface model is constructed by means of surface coordinates, which are retrieved from a rectangular cylindrical surface. The surface coordinates are shown in Figure 3, where, the surface coordinates are represented by \((x_{i,j},y_{i,j},z_{i,j})\), and the sub-indices \((l,j)\) are defined in the \(x\)-axis and \(y\)-axis, respectively. Thus, the rectangular surface provides the surface points \((z_{0,0},\,z_{1,0},\,\ldots,\,z_{n,0},\,z_{n,1},\,\ldots,\,z_{n,m})\) in the \(x\)-axis, where, the sub-indices \((n,m)\) depict the number of surface points in the \(x\)-axis and \(y\)-axis, respectively. The origin coordinates are represented by \((x_{0,j},\,k_{0},\,l_{0})\), the direction coordinates are depicted by \((x_{n,j},\,k_{n},\,l_{n})\), and the ratio is defined by \(r\). In this way, the cylindrical surface model is defined based on the circumference equation via ratio \(r\) by means of the next expression  
\[(y_{i,j}-k_{i})^{2}+(z_{i,j}-l_{i})^{2}=r^{2} \tag{12}\]  
For this equation, the coordinates \((k_{i},\,l_{i})\) are determined based on the surface geometry shown in Figure 3 by means of the next expressions  
\[k_{i}=\frac{(k_{n}-k_{0,})}{(x_{n,j}-x_{0,j})}(x_{i,j}-x_{0,j})+k_{0} \tag{13}\]  
\[l_{i}=\frac{(l_{n}-l_{0})(k_{i}-k_{0})}{(k_{n}-k_{0})}+l_{0} \tag{14}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Parameter** & \(\mathbf{f}\) & \(P_{1}\) & \(P_{2}\) & \(P_{3}\) & \(P_{4}\) & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) & \(C_{6}\) & \(C_{7}\) & \(C_{8}\) \\ \hline \(h\) & 1 & 33.5896 & 29.1142 & 31.1072 & 28.2664 & 24.8035 & 30.58 & 33.3301 & 35.1367 & 27.9462 & 28.6664 & 31.0478 & 32.0006 \\ \(k\) & 1 & 44.2103 & 40.3246 & 38.2204 & 39.1703 & 37.6548 & 42.0848 & 43.1417 & 47.8128 & 36.1213 & 38.5753 & 38.8636 & 44.1221 \\ \(l\) & 1 & 21.46 & 31.1081 & 35.0979 & 25.7211 & 20.0535 & 21.7505 & 30.3015 & 34.3909 & 23.018 & 30.1367 & 32.9515 & 37.372 \\ \hline _fitness_ & & 1.9963 & 0.5305 & 1.4442 & 0.9236 & 1.9747 & 1.1481 & 1.9987 & 4.5804 & 1.774 & 0.9567 & 0.9154 & 2.9193 \\ \hline \(h\) & 2 & 29.1142 & 30.58 & 28.2664 & 31.0478 & 24.1021 & 29.2203 & 30.1932 & 25.8899 & 24.7351 & 29.657 & 29.8396 & 28.2141 \\ \(k\) & 2 & 40.3246 & 42.0848 & 39.1703 & 38.8636 & 40.0788 & 41.0045 & 41.4932 & 41.898 & 35.5124 & 38.9784 & 39.0833 & 38.8631 \\ \(l\) & 2 & 31.1081 & 21.7505 & 25.7211 & 32.9515 & 20.5784 & 24.3133 & 27.9526 & 28.4532 & 21.9167 & 27.3088 & 32.5313 & 30.1781 \\ \hline _fitness_ & & 0.5305 & 1.1481 & 0.9236 & 0.9154 & 1.872 & 0.8474 & 0.7176 & 1.7872 & 2.4692 & 0.6377 & 0.6918 & 0.9849 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spherical model parameters generated via genetic algorithm for first and second generation. These equations are computed via origin and direction coordinates. In this way, the cylindrical surface model is performed by determining the coordinates \((k_{0},l_{0})\), \((k_{n},l_{n})\) and the ratio \(r\) via genetic algorithm. To do so, the genetic algorithm determines the origin and direction coordinates via Equation (12), and surface coordinates \((x_{i,j},y_{i,j},z_{i,j})\). This procedure is carried out in five steps, which are described as follows:  
The first step is to determine the initial population via surface data.