# Build Orientation Optimization Based on Weighted Analysis of Local Surface Region Curvature
## 5 Case Study
To observe key regions of Fan-duct intuitively, the facets are extracted from the original model shown in Figure 12c. The detailed comparison parameters are shown in Table 2. It should be noted as different models have its dimension scale, the volume error is bigger when the dimension of the model is bigger. For example, the model size of Impeller is 400 mm in the \(y\)-dimension as the Rocket hardware is just 30 mm in the \(y\)-dimension. Therefore, the volume error of Impeller is obviously bigger than the Rocket hardware. In addition to the dimension scale, the operation time of the program is mainly depended by the mesh density. The more points per unit volume, the greater the time it takes. For example, there are 24,310 points in impeller as there is only 8358 points in Fan duct. There is no doubt the time cost is bigger in testing the impeller. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Orientation** & \(\delta\) (\({}^{\circ}\)) & \(\psi\) (\({}^{\circ}\)) & \(e\) ( mm\({}^{3}\)) & **Time (s)** \\ \hline Orientation 1 & 89.127 & 70.714 & 138.873 & \\ Orientation 2 & 89.383 & 19.277 & 55.419 & 4.132 \\ Orientation 3 & 52.068 & 46.040 & 29.417 & \\ EWO & 49.881 & 52.511 & 35.656 & 1.827 \\ Default & 0.00 & 90.00 & 51.818 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Volume error comparison in different methods. Figure 10: Comparison of candidate build orientation: (**a**) Original model, (**b**) orientation 1, (**c**) orientation 2, (**d**) orientation 3, (**e**) orientation determined by EWO method. The model has different sizes under various build orientations. The size means the minimum enclosing rectangle parallel to the axis plane. The length is the Consumables in PLA. Weight is the mass of final printed model. The cost is material costs and the time is the whole printing process takes. The comparison of three orientations in size, length, weight, cost and time is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Faces (k)** & **Algorithm** & \(\delta\) (\({}^{\circ}\)) & \(\psi\) (\({}^{\circ}\)) & \(e\) (mm\({}^{3}\)) & **Time (s)** \\ \hline \multirow{2}{*}{Hardware} & \multirow{2}{*}{7.488} & EWO & 77.571 & 43.962 & 21.872 & 2.638 \\  & & Proposed & 75.891 & 51.988 & 17.275 & 2.873 \\ \multirow{2}{*}{Fun duct} & \multirow{2}{*}{12.708} & EWO & 57.562 & 0.030 & 35.925 & 5.255 \\  & & Proposed & 65.564 & 3.068 & 25.070 & 4.813 \\ \multirow{2}{*}{Impeller} & \multirow{2}{*}{48.614} & EWO & 45.539 & 1.041 & 207.354 & 45.561 \\  & & Proposed & 36.404 & 18.318 & 153.305 & 62.909 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Volume error comparison in different methods via more models. Figure 11: Comparison of the proposed algorithm and the EWO method. Figure 12: Curvature shift on the fan duct. If we choose the Z-axis as the default build orientation, the cost is maximum. Compared with the EWO, the length, weight, cost and time are all reduced to some extent when the method proposed is applied. Meanwhile, the volume error also reduced from the Table 2 in spite of the program execution time increased a bit. Therefore, the proposed method not only reduces the costs but improve the surface quality of the fabricated model. Finally, the Fan duct model was printed in three orientations using the H2000A Printer (Figure 13a) produced by Himalaya 3D company. Although the cost and time may be different by Cura and H2000A, the print result is consistent with our proposed method. The actual printing time is shorter than EWO despite of the little longer execution time of algorithm shown in Figure 13 (The printing time is included in parentheses). In order to see the details more clearly, we also magnified the original model by 1.8 times. The local magnification region which is marked by a black rectangular box shows the results under three build orientations in Figure 14. The local average surface roughness [32] is measured by TR200 roughness meter, a hand-held roughness measuring instrument.