## 4 Results
### Evaluation of Algorithm  
One way of demonstrating the correct functionality of the proposed algorithm is generating a printing trajectory on an analytical target surface and then comparing these values to those obtained using the algorithm by projecting the trajectory into the tessellated equivalent target surface. In this manner, the Hilbert curve explained in Section 3.2 was chosen as the printing trajectory, producing 319 principal points ordered in sequence on a \(XY\) plane (\(45\leq x\leq 115\), \(42\leq y\leq 118\), \(z=50\)) [mm]. The target surface or mandril was chosen to be the analytical saddle surface defined by Equation (6), generated using the software Mathematica and saved as a tessellated STL file with two different resolutions: one low-resolution consisting of 33,240 triangles and another high resolution of 99,816 triangles. Having the Hilbert printing trajectory (x,y) and the curved target surface (saddle), an analytical curved printing trajectory was created by the substitution of each value (x,y) of the Hilbert pattern into the saddle surface, using Equation (6), obtaining the \(Z_{analytical}\). At the same time, the algorithm for conformal printing proposed here and described in Section 3.1 was executed, having as inputs the same printing trajectory (Hilbert), the tessellated equivalent target surface (saddle STL) and a projection vector in the \(-z\) direction. Before projecting the points of the printing trajectory, the algorithm generated extra points as subdivisions, having a total of 1655 sequential points for the Hilbert trajectory. The obtained algorithm output was named \(Z_{projected}\) for each \((x,y)\) value. Figure 11 shows the printing trajectory before and after being conformed on the saddle surface and the normal vector for each projected point. The absolute relative error, defined as \(\frac{|Z_{analytical}-Z_{projected}|}{Z_{analytical}}100\%\), was used to measure the accuracy of the algorithm. Figure 12 shows the error found for each point \((x,y)\) of the Hilbert printing trajectory projected on the tessellated saddle structure with 33,240 triangles (low-resolution), having a mean error of 0.025853, and a maximum error of 0.287034% occurred at \((X=80,\ Y=42)\). Figure 13 shows the same points, but this time projected on the 99,816 triangle polygonal mesh (high-resolution structure), the mean error was 0.007551, and the maximum error found was 0.075592%, which occurred at \((X=83,Y=42)\). Finally, Figure 14 shows the actual 3D-printed piece: first, the target structure (mandrel) is printed using the slicing software Cura (planar printing), then the G-code generated by the algorithm allows the continuous conformal deposition of material following the Hilbert pattern on the target structure, being noticeable the contrast between the stair-stepping effect due to the planar slicing printing process for the target structure and the conformal Hilbert curved printing trajectory. Figure 11: Points of trajectory before and after being mapped on a tessellated surface. Figure 12: The absolute relative error for each point of trajectory with a maximum error of 0.287034% occurred at \((X=80,Y=42)\) and a mean error \(=\) 0.025853; the error was caused mainly by the resolution polygonal mesh. Plot generated using the script of [48]. Figure 13: The absolute relative error for each point of trajectory on higher resolution polygonal mesh with a maximum error of 0.075592% occurred at \((X=83,Y=42)\) and a mean error \(=\) 0.007551. Plot generated using the script of [48]. Two lattice examples were also simulated and 3D printed. In Figure 15, a re-entrant trajectory is projected on a random target tessellated structure generated, as explained in Section 3.2, similar to that used in [43]. The re-entrant trajectory initially consisted of 432 main points that define the pattern.