## 4 Example Analysis
### Mesh Quality Analysis and Runtime Comparison  
After five cycles of the Delaunay-TCOGIM algorithm with 1.52 times the average value of the boundary triangles, Table 1 compares the mesh average quality coefficient \(q_{M}\) and the mesh association quality coefficient \(q_{I}\) (see the Appendix A for specific formulas). After one cycle, there was a notable enhancement in the mesh quality and reduced aberration. After three runs, the average and association quality coefficients tended to reach a stable state. The combined Delaunay-TCOGIM algorithm produced a Delaunay triangular mesh with an average quality of 0.8766 and a degree of distortion of 0.8558. Figure 11: The effect of the triangular mesh is compared using (**a**) the Delaunay–TCOGIM algorithm and (**b**) the Delaunay method. Figure 10: Delaunay triangle network. Next, we will appropriately adjust the selection of contour discrete point sets by reducing the number of sets for the higher three contours to one-fifth of their original number while keeping the number of sets for the other contours unchanged. It compares the triangular mesh generated by cycling five times with the average value of the boundary triangles, 1.52 times, with that caused by the Delaunay method. It reaches the quality of the Delaunay triangular mesh generated by the two ways in Table 2. Refining the triangular grid cells improved the grid quality, allowing it to better meet the wind resource study requirements. In contrast, the triangular grid generated by the Delaunay method produces more deformed grid cells, which degrades the grid quality. Mesh cell regularity p quantifies the proximity of individual triangles to positive triangles. In contrast, mesh geometric irregularity \(p_{G}\) quantifies the irregularity of the mesh geometry (see the Appendix A for specific formulas). As shown in Table 3, a significant proportion of the triangular meshes generated by this algorithm are close to or reach the positive triangles (\(p\geq 0.46\)), and the number of meshes that deviate from the positive triangles to a greater extent decreases (\(p\leq 0.4\)). In this algorithm, the percentage of meshes close to or reaching the positive triangles is 46.36%, and the portion of meshes deviating from the positive triangles is 19.83%. In contrast, in the Delaunay method, the percentage of meshes close to or reaching the positive triangles is 17.08%. The portion of meshes deviating from the positive triangles is 61.05%, a significant decrease from the part of meshes varying from the positive triangles. This algorithm has significantly enhanced the quality of the triangular Delaunay mesh. The CPU time is an essential indicator of the efficiency of the algorithms. With the area-to-boundary triangle ratio set at 1.5 in both algorithms, the discrete points in the final mesh are the same or similar. The comparison of CPU running times between the two algorithms is shown in Table 4. The CPU time comparison in Table 4 shows that the algorithm's running time in this paper is smaller than that of the Delaunay method when the number of loops is \(\leq\)3. However, this trend reverses when the loop count exceeds 3. It  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Aithmetic**} & \multirow{2}{*}{ \begin{tabular}{c} **Total** \\ **Meshes** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **\(p=0\)–0.3** \\ **0.3–0.4** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **\(p=0\)–0.4** \\ **0.4–0.42** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **\(p=0\)** \\ **0.42–0.44** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **\(p=0\)** \\ **0.44–0.46** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **\(p=0\)** \\ **0.46–0.48** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular}{c} **\(p=0\)** \\ **0.48–0. can be inferred that when the final mesh's discrete points remain constant, the algorithm in this paper gradually inserts fewer discrete points as the loop count increases.