**12. Medial axis transformation (MAT) path**

Kao [25] has proposed an alternative methodology of using the medial axis transformation (MAT) of the geometry to generate the offset curves by starting at the inside and working toward the outside, instead of starting from the boundary and filling toward the inside. This approach is able to compute paths which can entirely fill the interior region of geometry as the paths are generated from interior to the boundary. This strategy avoids producing gaps by depositing excess material outside the boundary, as illustrated in **Figure 16**. The extra material can subsequently be removed by post-processing. Therefore, the traditional contour path patterns from outside to inside is natural for machining whereas MAT path starting from inside and working toward the outside is suitable for AM of void-free components.

**Figure 16.** Illustration of path generated from MAT. (a) up: original geometry (green region) and the MAT of the ge‐ ometry (black line); down: contour path patterns with gaps in middle are clearly seen; (b) up: red region is deposition of excessive materials; down: the MAT path patterns without gaps [25].

However, the previous authors limit their discussion to geometries with simple MAT paths. Recently, Ding et al. [26, 27] developed a methodology of generating MAT-based paths for an arbitrary geometry, either thin-walled or solid structures.

The following are the main steps for generating MAT-based paths:

Compute the medial axis: The cross section of a sliced layer with a thin-walled structure is shown in **Figure 17a**. The medial axis or skeleton of the geometry is computed and represented using red lines. The computed skeleton is the crucial information, which describes the shape of the geometry.

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

Kao [25] has proposed an alternative methodology of using the medial axis transformation (MAT) of the geometry to generate the offset curves by starting at the inside and working toward the outside, instead of starting from the boundary and filling toward the inside. This approach is able to compute paths which can entirely fill the interior region of geometry as the paths are generated from interior to the boundary. This strategy avoids producing gaps by depositing excess material outside the boundary, as illustrated in **Figure 16**. The extra material can subsequently be removed by post-processing. Therefore, the traditional contour path patterns from outside to inside is natural for machining whereas MAT path starting from inside

**Figure 16.** Illustration of path generated from MAT. (a) up: original geometry (green region) and the MAT of the ge‐ ometry (black line); down: contour path patterns with gaps in middle are clearly seen; (b) up: red region is deposition

However, the previous authors limit their discussion to geometries with simple MAT paths. Recently, Ding et al. [26, 27] developed a methodology of generating MAT-based paths for an

and working toward the outside is suitable for AM of void-free components.

WAAM of solid structures.

16 New Trends in 3D Printing

**12. Medial axis transformation (MAT) path**

of excessive materials; down: the MAT path patterns without gaps [25].

arbitrary geometry, either thin-walled or solid structures.

The following are the main steps for generating MAT-based paths:

**Figure 17.** Illustration of MAT-based path planning. (a) The medial axis computing (red lines). (b) Domain decomposi‐ tion (each domain is described in one different color. (c) Path generation for domain 3. (d) MAT-based paths at the crossing area [27].

Decompose the geometry: Using the computed medial axis, the geometry is decomposed into several domains. As the geometry with N holes will be decomposed into N+1 domains, this geometry is decomposed into 10 domains as shown in **Figure 17b**. As displayed in different colors, each domain is bounded by a portion of medial axis (red lines in **Figure 17a**) and a boundary loop (black line loop in **Figure 17a**).

Generate path for the domain: Deposition paths for each domain are generated by offsetting the medial axis loop (red line loop in **Figure 17c** for domain 3) toward the corresponding boundary loop (black line loop in **Figure 17c**) with an appropriate step-over distance. The offsetting is repeated and terminates when the domain is fully covered. Green line loops in **Figure 17c**, represent the generated deposition paths.

Complete the deposition paths: A complete set of MAT-based deposition paths is obtained by repeating step 3) for all the decomposed domains. The generated paths are a set of closed-loop lines without start/stop sequences, which is preferred for the arc welding system.

From the above description, the MAT path planning algorithm for an arc welding process is able to be automated for any complex geometry; just as the existing commercially available raster and contour path planning strategies have been automatically applied to powder-based AM. MAT path is particularly preferred for void-free AM. Example of MAT path generation for a solid structure with holes is shown in **Figure 18**.

**Figure 18.** Example of a solid structure with holes. (a) Geometry is represented by black lines, MAT represented by dotted red lines, and red solid lines stand for branches. (b) Generated trimmed path [26].
