## 3 Results
### Determining the Optimal Layer Height by Printing Tubular Structures  
In this paper, the layer height is defined as the prescribed gap between successive layers. The layer height parameter can be controlled by precise motion along the z-axis between printed layers. To systematically explore the optimal single layer height within a multilayered print construct using a liquid hydrogel precursor in a support bath medium, a set of tubular structures is printed to test the preservation of shape fidelity. First, by following the G-code path created by the customized toolpath generation algorithm, the tubular structure design (5 mm internal diameter and 10 mm height) shown in Figure 5 is printed and post-processed. This experiment aims to determine the effect of layer height on the printed construct shape quality under certain constant parameters (flowrate is 4.8 mL/h, travel speed is 200 mm/min, bath temperature at 23 \({}^{\circ}\)C). In Figure 5, the (i) of (a)-(e) are images of printed tubular structures with different layer heights. The (ii) of (a)-(e) are binary images circumscribed with  
Figure 4: The cross-section geometry of the printed filament within a support bath medium with travel speed from 160 mm/min-400 mm/min, at flowrate of 4.8 mL/h: (**a**) the image of the filaments (laid flat, side view); (**b–d**) cross section view of three selected filaments. The length increases as the travel speed decreases; (**e**) measurements of the cross section length as a function of travel speed; (**f**) schematic shows the cross section of printed filament. The filament is elongated in z direction due to the slow travel speeds; (**g**) the cross section of the filament printed at travel speed of 200 mm/min; (**h**) binary image of the cross section view; (**i**) the schematic shows 2 filament with overlap that enables the fusion; (**j**) the 3D model of a 4 layers of helical structure with overlap of two adjacent layers. a red boundary box. A decrement in the total height is observed for the 5 printed tubular structures going from (a) to (e). The smaller layer heights result in higher total heights due to the more extruded material. Layer heights equal to or larger than 0.8 mm result in disconnected layers. Figure 5f illustrates an example of a disconnected tubular structure with layer height of 0.8 mm. In this paper, a metric is defined to compute the irregularity of the printed structures, which measures the roughness of the binary image outline. In Figure 5g, the irregularity of (a)-(e) is plotted. In Figure 5h, a segment of the binary image in (c) shows the detailed edge of the printed tubular structure. The red dashed line is the fitted linear model that represents the reference line, which avoids the accumulated errors due to the image incline. Figure 5i is the plot of the projected edge curve without the effect of the image incline. The curve is de-noised by using Fast Fourier Transform (FFT) to remove high-frequency wave patterns. The blue and red dots are the detected local maximum and minimum points. The irregularity (or roughness) is defined as the average vertical distance between the successive local maximum and minimum points. The results show that the irregularity decreases as the layer height approaches an optimal value (0.3 mm to 0.7 mm). Printed structures with a layer height of 0.7 mm exhibit more uniform surface characteristics compared to its smaller layer height counterparts. However, when the layer height is set to be larger than 0.7 mm, the successively printed layers are disconnected due to large gaps. Furthermore, although the surface quality is the optimized at the larger layer height (0.7 mm), this is accompanied by weaker connections between layers. As a result, the 0.5 mm or 0.6 mm prints are preferred over the 0.7 mm print.