# Build Orientation Optimization Based on Weighted Analysis of Local Surface Region Curvature
## 2 Literature Review  
Due to the importance of build orientation in AM, intensive researches are conducted to provide feasible solutions. An attempt is made to achieve minimum average part surface roughness (best overall surface quality), minimum build time and support structure for stereo lithography (SL) and selective laser sintering (SLS) processed parts by determining optimum part build orientation [7; 8; 9; 10]. For most simple models, the direction parallel to a coordinate axis is used as the build orientation [11]. It cannot be the same as complicated models. Most researchers usually chooses single or multiple factors to construct a single-object or multi-object optimization function and find the best build orientation from the feasible solution by determining the weight and range for the optimization target [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. On the research of a single target method, most researchers take one factor such as volume deviation or surface roughness to build the object function, which can get the optimal build orientation under the specific factor chosen [12; 13; 14; 15; 16; 17]. [PERSON] et al. [12] determines the optimal build orientation based on the position of normal vectors of the original CAD model. All the normal vectors are considered as the candidate orientation. It is certainly feasible to adopt an exhaustive approach, but subject to the existing surface normals. It is difficult to get the optimal build orientation. [PERSON] et al. [13] used a new volume error model. The biggest problem is that all normal-weighted regions are weighted equally. The geometry features of the model itself are neglected and the weighted optimization process essentially belongs to normal weight, which means all facets contribute equally  
Figure 1: Staircase effect analysis: (**a**) 3D printing process. (**b**) Volume error between two layers. (**c**) Estimation of volume error. to the optimal build orientation. [PERSON] et al. [14] proposed a new method to determine the optimal build orientation using Gauss Map, which collects all facet normals in a unit sphere. The unit vector from the center of the sphere to the center of the bottom circle of the spherical crown is the optimal build direction. Although just considering the facet normal, it effectively decreases the volume of support structure. It should be noted that the algorithm is not versatile especially for some more complex parts which contain open concave loops or non-sharp edges. [PERSON] et al. [15] researched the effect of different build orientations on Ti-6 Al-4V for microstructural and mechanical property evaluation. However, printing performance is more affected by material properties and cooling deformation after thermoforming. Relatively speaking, the build orientation has relatively little influence. [PERSON] et al. [16] used particle swarm optimization [17] to search an optimal build orientation owing to its ease of programming, convergence speed and computational efficiency. If the initial particle is not good, it may be biased by a certain particle. The algorithm is easy to converge prematurely and fall into a local optimal solution. In addition, the complexity of the algorithm increases, resulting in reduced efficiency. The multi-object method chooses multiple factors such as surface quality, construction time and material consumption to determine the optimal build orientation [18]. The proportion of each factor is determined empirically or based on the demand [19; 20; 21]. [PERSON] et al. [19] applied the genetic algorithm to solve the parameter optimization of multiple objects (staircase error, heights and materials cost). The method distributed different weight to the three factors and obtained the optimal orientation. A constrained non-linear multi-object optimization model is constructed based on the eight parameters [20]. The model is solved by global search algorithm in MatLAB. Different parameter weight is based on which parameter is more important.