**11. Hybrid and continuous path**

**8. Spiral path**

14 New Trends in 3D Printing

**9. Hybrid path**

The spiral tool-path generation, as shown in **Figure 14d**, has been widely applied in numeri‐ cally controlled (NC) machining, especially for 2D pocket milling and uniform pocket cutting [17, 19]. This method can also be used to solve the problems of zigzag tool paths in AM process,

The hybrid path planning strategy is promising as it shares some merits of various approaches. A combination of contour and zigzag pattern is commonly developed to meet both the geometrical accuracy and build efficiency requirements. Zhang et al. [20] applied a new image algorithm for welding-based AM. The planned approach includes one inner zigzag path which is faster and more universal, and one outline vector path which is very helpful for maintaining the surface accuracy and quality. Jin et al. [18] proposed a mixed tool-path algorithm to generate contour and zigzag tool path for AM of biomedical models, as shown in **Figure 14e**. The zigzag tool path is employed to fill the interior area of the part to improve the efficiency, while the contour tool path is used to fabricate the area along the boundary of the contours to

Continuous path planning can be considered as another tool-path generation method. Hilbert filling curve applied by Bertoldi et al. [21] is a continuous path, which can cover a region of space without intersecting itself as shown in **Figure 15a**. It has been found to be particularly useful in reducing shrinkage during AM fabrication processes. However, the large number of path direction turning motions that are produced by using this strategy are not suitable for AM. Wasser et al. [22] introduced a fractal-like build style using a simulated annealing algorithm. This method is able to generate filling patterns that allow the continuous deposition of a single path to fill arbitrarily shaped areas, as shown in **Figure 15b**. In this method, the area to be deposited is firstly decomposed into nodes, with the number of the nodes determined by the accuracy requirement of the AM process. However, when the area to be filled is large and the accuracy requirement is high, the processing time required would be unacceptably long. Moreover, highly convoluted paths may result in accumulation of heat in certain regions, therefore inducing excessive distortion of the part. Frequent alternations of tool-path travel

but is only suitable for certain special geometrical models.

improve the geometrical quality of the model.

directions are also not preferred in AM.

**10. Continuous path**

Dwivedi et al. [23] developed a continuous path planning approach which combines the merits of zigzag and continuous path patterns, as shown in **Figure 15c**. In this method, the 2D geometry is firstly decomposed into a set of monotone polygons. For each monotone polygon, a closed zigzag curve is then generated. Finally, a set of closed zigzag curves are combined together into an integrated continuous torch path.

The continuous path planning approach significantly reduces the number of welding passes. However, purely employing zigzag-based curves would have a surface accuracy issue, as Zhang et al. [20] point out the importance of filling the outline of the image with vector motions in wire and arc additive manufacturing (WAAM). Recently, we proposed another continuous path pattern which leverages the advantages of zigzag, contour, and continuous path patterns, as shown in **Figure 15d** [24]. It is indicated that this continuous path pattern is suitable for WAAM of solid structures.
