# Build Orientation Optimization Based on Weighted Analysis of Local Surface Region Curvature
## 1 Introduction  
3D printing or additive manufacturing (AM, rapid prototyping, layer manufacturing, free-form fabrication, rapid manufacturing) is a process where parts are manufactured according to a digital 3D model by adding material, usually layer by layer along the build orientation, as opposed to subtractive manufacturing methodologies such as traditional milling [1]. The original CAD model of the fabricated part can be designed by commercial CAD software or reconstructed via reverse engineering. Once the CAD model is available, layer slice program is applied to deal with the model and output all the 2-D contour layers, then 3D printers print the model layer by layer. The build orientation needs to be determined first before printing. Only when the build orientation is already known can we set the other necessary printing parameters, slice the model and print it by 3D printing.  
We all know that the inherent defect of 3D printing technique: the staircase effect [2, 3, 4] occurs in the process of layer by layer addition shown in Figure 0(a). If the nozzle size is smaller and the layer thickness is thinner, the surface quality can be greatly improved, however it takes a long time to fabricate. It is actually a contradiction between efficiency and surface quality. When the hardware parameters of the 3D printer are determined, the build orientation has a great influence on the surface accuracy caused by the staircase error. Therefore, this paper will focus on reducing the staircase error in the pre-processing of 3D printing models. As for the effect of printing, process parameters and material shaping on the surface accuracy of the model are not involved.  
If the build orientation is parallel or vertical to the surface facet of the model printed, the staircase effect disappears. If the angle \(\theta\) (shown in Figure 0(b)) between the surfacenormal \(\vec{n}\) and the build orientation \(\vec{d}\) is between 0 and 90 degrees, the staircase effect occurs and the surface quality decreases. The build orientation determines surface quality of the part and even its mechanical properties [5]. However, for most part models, the normal direction of the surface is rarely perpendicular or parallel to the build orientation, and the staircase error is unavoidable. Therefore, it is very necessary to improve the accuracy of certain regions of the printed part by adjusting the build orientation [6]. Based on the principle of generation, we add the regional weight to the staircase error function, and obtain the candidate build orientation through eigenvalue decomposition to improve the surface quality of the region. The objective of this article was to find local regions with obvious curvature changes in the surface of the printed part from a geometric point of view, which is then given a high weight factor. Of course, according to the different application scenarios and performance of the fabricated part, different regions of the part require different surface quality. However, this article does not consider this problem.  
In this paper, a novel optimization of part build orientation based on weighted analysis of local surface region curvature is proposed. The rest of this paper is structured as follows: Section 2 presents the related studies of the optimization of build orientation. Section 3 presents a detailed explanation of the methodology based on the curvature shift process. This is followed by case study on test models in Section 4. Finally, the conclusions and future scope of this work are presented in Section 5.