## 2 Materials and Methods
### Development of Procedures for Verifying Geometrical Accuracy  
In developing procedures for verifying the accuracy of the geometry of the part of a pelvic model manufactured in one piece and in three separate fragments, two coordinate optical systems were used: a measuring arm with laser head (Nikon Metrology, Leuven, Belgium) and an Atos II Triple Scan (Carl Zeiss AG, Jena, Germany). The entire process consisted of three steps:  
* Conducting the systems calibration process;
* Development of a geometry measurement procedure that enables accurate and complete digitization of the geometry of anatomical structures;
* Development of a procedure to evaluate the geometrical accuracy. The laser head measurement is based on the laser triangulation method, one of the best-known techniques for measuring 3D object geometry. With the measurements performed, we directly obtain data representing a 3D point cloud, which can be saved to STL format [16; 42]. The calibration process used three tests to check the measuring arm under the American standard ASME B89.4.22 [43] and one to check the laser head under ISO 10360-8 [44]. Effective Diameter Test (EDT) measured nine points on a standard sphere's surface. The procedure was performed three times, and the maximum absolute deviation from the certified value given on the standard was noted as the test result. The final deviation between the measured diameter of the sphere and the standard value was determined using the method of least squares based on Equation (1):  
\[EDT=D_{measured}-D_{calibrated}; \tag{1}\]  
Figure 3: Additive manufacturing is a part of the pelvic model for patient no.1 in one piece and is divided into three parts. The Single Point Articulation Performance Test (SPA) probe is placed in a conical socket. Individual points were measured from multiple angular positions of the arm. Each point measurement was analyzed as a range of deviation from the mean value using Equation (2):  
\[SPA=Range/2, \tag{2}\]  
The Volumetric Performance Test (VPT) is the most suitable test for determining the accuracy and repeatability of a coordinate measuring arm. It consisted of repeatedly measuring a certified length standard at several locations and orientations and comparing the resulting measurements with the actual length. The result was the maximum deviation between the measured and standard length values, which was determined according to Equation (3):  
\[VPT=L_{measured}-L_{calibrated}, \tag{3}\]  
In the case of the laser head, its accuracy was checked by scanning the calibration plate from different directions. The procedure result was the maximum standard deviation of the scanned data relative to the matched plane elements. The final value was determined by using the least squares method. After calibrating the system, we measured the models manufactured using 3D printing. We first selected the measurement parameters for the laser head (Table 1). It was crucial to match the measurement resolution to the accuracy of the manufactured models. We established a condition that the measurement resolution should not exceed 10% of the tolerance range of the scanned model. Based on available data, the maximum deviation values are usually within \(\pm\)0.3 mm for models manufactured on the Prusa MK3s 3D printer using PLA material [16]. Therefore, we assumed a tolerance of 0.6 mm for the accuracy of the manufactured models. With this in mind, we set an acceptable measurement resolution of 0.06 mm. To minimize errors in fitting individual scans, markers were applied to the surface of the measured models (made as a single piece and three separate pieces) before measurement. Additionally, due to the nature of the material from which the models were made, a matting layer was required to be applied to their surface. The thickness of the matting layer was measured on Alicona's InfiniteFocusG4 microscope and was about 10 \(\upmu\)m. The measurements of the models were carried out manually (Figure 4).