**3. Multidirection slicing**

Most of the current AM processes involve slicing a 3D CAD model into a set of 2.5D layers with a constant or adaptive thickness along the build-up direction as mentioned in unidirection slicing. However, to fabricate parts with complex shapes the unidirectional slicing strategies are generally limited by the need for support structures to deposit overhangs. **Figure 8a** shows a component and its usual build direction *B*. It is clear that to fabricate the component in direction *B*, support structures (refer **Figure 8b**) are required due to overhangs. The deposition of supports results in the wastage of materials and the removal of these supports requires costly post-processing.

**Figure 8.** (a) The component and its usual build direction *B*; (b) support required (parts colored in orange); (c) multi‐ direction slicing and various build directions *B1*, *B2*, and *B3* [3].

Some of the additive manufacturing techniques are able to deposit materials along multiple directions. The application of multidirection deposition could eliminate or significantly decrease the usage of supports for complex components. As shown in **Figure 8c**, the component can be fabricated in multiple directions, for example, *B*1, *B*2, *B*3, without support structures. Such a multidirection deposition system furthers the capability of layered manufacturing by reducing the need for supports.

A key challenge in multidirection AM is to develop robust algorithms capable of automatically slicing any 3D model into a set of layers which satisfy support-less and collision-free layered deposition. The following sections review some existing multidirection slicing strategies.

Silhouette edges projection [4]: This strategy firstly identifies the unbuildable surface features of a model by projecting silhouette edges along the user defined original build direction. Then the part is decomposed into buildable and unbuildable sub-volumes using the silhouette-edgebased method. For the unbuildable sub-volume, a new suitable build direction is determined using the Gauss and Visibility maps. With the new build direction, the unbuildable subvolume is further decomposed through repeating the same projection procedures. This projection method is recursively used to decompose the sub-volume as shown in **Figure 9**. The framework for the multidirection slicing and some essential problems have been addressed and discussed by the authors. However, the implementation of the strategy could be compli‐ cated and computationally expensive for complex components with inner cavities.

**Figure 9.** (a) Model; (b) Decomposition tree; (c) Supports [4].

**Figure 7.** Case III. (a) A Triceratops STL model; (b) Resulting slices.

Case I 1076 12 ms Case II 1584 34 ms Case III 172,122 352 ms

**Table 1.** The computing time of the program.

**3. Multidirection slicing**

8 New Trends in 3D Printing

costly post-processing.

**No. Facets Computing time**

Most of the current AM processes involve slicing a 3D CAD model into a set of 2.5D layers with a constant or adaptive thickness along the build-up direction as mentioned in unidirection slicing. However, to fabricate parts with complex shapes the unidirectional slicing strategies are generally limited by the need for support structures to deposit overhangs. **Figure 8a** shows a component and its usual build direction *B*. It is clear that to fabricate the component in direction *B*, support structures (refer **Figure 8b**) are required due to overhangs. The deposition of supports results in the wastage of materials and the removal of these supports requires Transition wall [5]: The key idea of this strategy is to identify the overhang layers by computing the difference between the current layer and the previous layer. Then, as shown in **Figure 10**, to build an overhang structure, the machine is turned 90° to start depositing a transition, namely thin wall. After the deposition of the first few layers, the wall is finished and the subsequent overhang structures can be deposited in the vertical direction again. Although this strategy is simple, it is only suitable for a subset of part geometries. In some cases, the deposition of the transition wall is difficult or impossible to implement due to deposition nozzle collision, such as the part shown in **Figure 8a**.

**Figure 10.** Illustration of building the transition wall through rotating 90 degree. (a) Overhang; (b) Vertical deposition; (c) Horizontal deposition [5].

Centroid axis extraction [6]: The first step in this strategy is to extract the centroid axis of the model as shown in **Figure 11**, which provides a global perspective on the geometry, allowing the slicing procedure to be conducted on an optimal sequence. Through analyzing the topological information from the centroid axis, the splitting surface is identified and the subsequent decomposition operation is conducted. For each subcomponent obtained from decomposition, multiaxis slicing is performed and the collision-free slicing sequence is finally generated. The centroid axis extraction method decomposes the component by detecting the change of centroid of presliced layers, making the geometry analysis process easier. However, in some cases it will be difficult to decompose components efficiently as required since the centroid axis does not always indicate the change of the geometry.

**Figure 11.** Example of centroidal axis extraction [6].

Other multidirection slicing methods have been proposed that are either adaptations or combinations of a few techniques from the above strategies, such as adaptive slicing algorithm [7], offset slicing [8], skeleton method [9], and modular boundary decomposition [10]. How‐ ever, each method is only suitable for a subset of part geometries. In addition, these methods are not efficient for processing parts with holes and depression features. As shown in **Figure 12**, the part is decomposed into buildable volume and unbuildable volume due to the direction of hole, H, is vertical to the build direction, B, of its associated volume. The part is firstly decomposed into buildable and unbuildable sub-volume [4]. The unbuildable sub-volume could be further built by offset slicing strategy [8] with the direction as shown in **Figure 12b**. However, unbuildable volume also exists due to the holes. It is clear that holes would hamper implementing multidirection slicing algorithm.

Transition wall [5]: The key idea of this strategy is to identify the overhang layers by computing the difference between the current layer and the previous layer. Then, as shown in **Figure 10**, to build an overhang structure, the machine is turned 90° to start depositing a transition, namely thin wall. After the deposition of the first few layers, the wall is finished and the subsequent overhang structures can be deposited in the vertical direction again. Although this strategy is simple, it is only suitable for a subset of part geometries. In some cases, the deposition of the transition wall is difficult or impossible to implement due to deposition

**Figure 10.** Illustration of building the transition wall through rotating 90 degree. (a) Overhang; (b) Vertical deposition;

Centroid axis extraction [6]: The first step in this strategy is to extract the centroid axis of the model as shown in **Figure 11**, which provides a global perspective on the geometry, allowing the slicing procedure to be conducted on an optimal sequence. Through analyzing the topological information from the centroid axis, the splitting surface is identified and the subsequent decomposition operation is conducted. For each subcomponent obtained from decomposition, multiaxis slicing is performed and the collision-free slicing sequence is finally generated. The centroid axis extraction method decomposes the component by detecting the change of centroid of presliced layers, making the geometry analysis process easier. However, in some cases it will be difficult to decompose components efficiently as required since the

centroid axis does not always indicate the change of the geometry.

**Figure 11.** Example of centroidal axis extraction [6].

nozzle collision, such as the part shown in **Figure 8a**.

(c) Horizontal deposition [5].

10 New Trends in 3D Printing

**Figure 12.** Illustration of the impact of holes on multidirection slicing strategy [3].

Decomposition–regrouping method [3]: Differing from these existing slicing approaches, which are mainly focused on finding an optimal volume decomposition strategy, a recent study proposed simplification of holes and a decomposition–regrouping method. A model simplification step is introduced before CAD decomposition to significantly enhance the capability of the proposed multidirection strategy. The CAD model is then decomposed into sub-volumes using a simple curvature-based volume decomposition method and consequent‐ ly a depth tree structure based on topology information is introduced to merge them into ordered groups for slicing. The proposed strategy is proven to be simple and efficient on various tests parts. As an example shown in **Figure 13**, the part is decomposed and regrouped, then sliced in multiple directions with holes been filled. Since there is no robust multidirection slicing algorithm validated for any complex geometry, the proposed multidirection slicing algorithm is not versatile also, while it is particularly useful for components with large number of holes.

**Figure 13.** Example of decomposition–regrouping method for multidirection slicing. (a) Volume decomposition; (b) Sub-volume regrouping; (c) Slicing in multiple directions [3].
