## 2 Materials and Methods
### Change of Provisionals and Scans  
Both the internal and external portions of the 30\({}^{\circ}\) provisional were scanned outside the oral cavity using an intraoral scanner (True Definition; 3M\({}^{\text{TM}}\)), thereby obtaining the STL_30 file. (Figure 7a). Figure 5: 30\({}^{\circ}\) provisional crown after 2 weeks of healing. Figure 6: 60\({}^{\circ}\) provisional crown after 2 weeks of healing. Figure 7: Geometries in 3D obtained in the different scans: (**a**) 30\({}^{\circ}\) provisional (STL_30), (**b**) 30\({}^{\circ}\) provisional cemented after 2 weeks in the mouth (STL_30_arch), (**c**) 60\({}^{\circ}\) provisional (STL_60), and (**d**) 60\({}^{\circ}\) provisional cemented after 2 weeks in the mouth (STL_60_arch). The 30\({}^{\circ}\) provisional was cemented (Temp Bond Clear, Kerr Dental, Orange, CA, USA), and 2 weeks later it was scanned together with its adjacent teeth, thereby obtaining the STL_30_arch file (Figure 7b). Both the internal and external portions of the 60\({}^{\circ}\) provisional were scanned outside of the oral cavity using an intraoral scanner (True Definition; 3M\({}^{\text{TM}}\)), thereby obtaining the STL_60 file (Figure 7c). The 30\({}^{\circ}\) provisional was removed, and in its place, a 60\({}^{\circ}\) provisional was cemented; 2 weeks later, it was scanned together with its adjacent teeth, thereby obtaining the STL_60_arch file (Figure 7d). In this first phase, 4 STL models were obtained; these corresponded to the 2 provisionals scanned outside of the oral cavity with their complete contouring (STL_30 and STL_60) and their position once cemented in the oral cavity together with the teeth and adjacent gingival tissue structure after 2 weeks (STL_30_arch and STL_60_arch). Alignment of the 3D Geometries Obtained in the Different Scans in Consideration of a Global Coordinate System  
The STL_30 file was imported into reverse engineering software (Geomagic Studio; 3D Systems, Rock Hill, South Carolina, USA), and three reference points were created: the apical buccal point (B), the apical lingual point (L), and the incision point (I) (Figure 8a). Once those 3 points were created, a plane through the 3 points was drawn up, thereby obtaining Plane B-L.  
To establish the tooth's axis, 2 points were selected. The first was the incision point (I). To create the second point, a line that linked point B and point L was created; using a mathematical calculation, the software devised a point located at the centre of this line, thereby obtaining the apical centre point (AC) corresponding to the mid-point between point B and point L (Figure 8b). Once points I and AC were established, a line that united them (AXIS) was created, thereby corresponding to the tooth's axis. Making use of the software, the plane created in step 4 (plane B-L) was aligned with plane XY of the global coordinate system, whereby the AXIS line coincides with axis Y (Figure 8c). The file corresponding to the 30\({}^{\circ}\) crown cemented together with its adjacent teeth (STL_30_arch) was imported into the software, and the alignment was made through the best-fit algorithm with the STL_30, which was oriented with respect to the coordinate axis in the previous step. For this purpose, the common surfaces in both 3D geometries were selected, i.e., the surfaces of the 30\({}^{\circ}\) provisionals (Figure 9a,b). Figure 8: Alignment of the 3D geometry of the 30\({}^{\circ}\) provisional in relation to the global coordinate system. (**a**) Plane B-L was created through the B, L, and I points. (**b**) The axis was created through the AC and I points. Note that the transparency of the provisional offers a better view of the Axis. (**c**) Plan B-L becomes parallel to the global XY coordinate system plane, and the tooth’s axis becomes parallel to the Y axis of the global coordinate system. The quality of the alignment was checked by carrying out a three-dimensional comparison (Figure 9c), where the green colour denotes a correct alignment.