# Build Orientation Optimization Based on Weighted Analysis of Local Surface Region Curvature
## 5 Case Study  
To execute the whole framework, we tested the model shown in Figure 7(a). The free-form model was reconstructed by Solidworks, which is used in the engine of aircraft. The edge and free-form patch of the blade are all key regions which are needed to print more accurately. The key points (the read points) were detected by the algorithm proposed as shown in Figure 7(b). Those key points are distributed a bigger weight factor to build volume error function so that the optimal build orientation is dependent more on the key points. In the printing process, the model can be fabricated in a high quality especially in those regions. Curvature map is used to help find the surface changes of the turbine blade. To simplify the analysis process, we extract the point cloud from the STL file. Each point curvature is obtained based on the NURBS reconstructed by the local sample. In addition to the edges, some inside points of the blade also appear. The curvature map is shown in Figure 7(c). Once the curvature map is obtained, weight factor is distributed for calculating the curvature shift vector. Gaussian weight is applied in determining the weight distribution. In our test, 1-ring points are chosen under the bandwidth 3. In addition to the curvature, distance combined with Gaussian weight is also considered into the calculation for the weight distribution. The Gaussian weight map based on curvature and Euclidean distance are respectively shown in Figure 8(a),b. In the calculation of the optimal build orientation, the key step is determining the normal weighted region. Once key points are obtained, the key region of the model is taken into account when determining the optimal build orientation. Only if given a high weight factor can the part have a high surface quality. Therefore, the weight distribution, including two parts: cluster weight and local weight, is needed for calculating the volume error function too. The optimal build orientation is chosen from three candidate orientations by the one which minimizes the volume error function. The orientation which minimizes the volume error function, is the desiring build orientation. As a comparison, the Equal Weight Optimization (EWO) proposed in reference [13] is adopted. The comparison of build orienta  
Figure 8: Curvature map of the turbine blade. Figure 9: Gaussian weight map based on curvature and Euclidean distance. The comparison of data is shown in Table 1. The default, volume error, Zenith and Azimuth angles are referred to as Z-axis orientation, \(e\), \(\delta\) and \(\psi\), respectively. The time is the running time of the program. From Table 1, orientation 3 is the optimal build orientation based on proposed method. Zenith angle and azimuth angle are 52.068\({}^{\circ}\) and 46.040\({}^{\circ}\). As a contrast, the result calculated by reference [13] is 49.881\({}^{\circ}\) and 52.551\({}^{\circ}\). As for the volume error function, the facets in key points (Figure 10) play a more important role than the other facets. EWO method Ref. [13] regards all facets equally important. The facets in key regions bring greater errors, so those facets are given different weight in this paper. Despite that the program execution time is longer than that in [13], the volume error is obviously smaller. To further confirm the validity of proposed method, more different models were tested in the following comparisons shown in Figure 11, the model in the left panel of Figure 11 is the default orientation, the medium is optimized by EWO method and the right is determined based on the algorithm proposed in this paper. Curvature shift is processed on Fan duct as shown in Figure 12. The curvature distribution is obtained shows the regions with big curvature are main concerned in boundary-edges and free-form surface. Small curvature change at the surface transition. Based on the curvature map and weight distribution, all the clusters are shown in different color. Key regions can be further acquired more reasonably in each cluster.