## 2 Materials and Methods
### Protocols for Scanning  
The four experimental models were sprayed with a minimum amount of powder, immobilized, and automatically scanned with the reference scanner, Sensable S3 (Solutionix Inc., Seoul, Korea). In order to validate the reliability of the reference scanner, the Ideal model was digitized five times with the reference scanner. These images served as the standard data once the reliability of the reference scanner had been confirmed. Then, the four experimental models were each scanned 10 times with both iTero(r)1 iTero(r) Orthodontic ver. 5.2.1.290 (Align Technology Inc., Santa Clara, CA, USA) and Trios(r)2 3 Shape Trios(r) ver. 1.3.2.1 (3 shape Dental Systems, Copenhagen, Denmark) in the same manner. Geomagic Verify superimposed scanned images from the experimental scanners with those from the reference scanner to obtain 10 superimposable pairs of data. Simple linear regression analysis was performed, and deviation was calculated. Based on the Shapiro-wilk test applied to the repeated scanned data, a \(p\) value of 0.276 confirmed that the data was normally distributed. In addition, the Wald-Wolfowitz test showed a \(p\) value of 0.314, proving that the data was mutually independent. These values indicate that the same results are expected with any additional data. Using iTero(r), the full mandibular arch was scanned in Invisualign mode. The left side of the arch was scanned first, following the instruction manual, starting with the occlusal surface of the most distal molar. The same sequence of scanning was repeated from the right to the left side of the arch to construct a complete image. The following images from both sides of the arch were combined in the anterior region to generate an image of a single full arch; the areas of deficiency were scanned again to construct a complete image (Figure 2A). Using Trios(r), the left side of the arch was scanned first, following the manufacturer's guidelines. A calibration was performed prior to the experiment, with the calibration function incorporated in the scanner. This time, the incisor region was scanned slowly in a zigzag pattern. The second phase started from the last-scanned location on the right side, scanning toward the lingual surface to scan up to the most distal molar on the left side. In this process, the wand was turned 45-90 degrees. In the third phase, the wand was rolled up towards the buccal surface to scan the buccal side of the arch, from left to right. The areas of deficiency were scanned again to complete the whole image (Figure 2B). The four models (Ideal, Mild, Moderate, and Severe) were scanned 10 times, each with iTero(r) and Trios(r); two sets of 40 images were produced by scanning the models with iTero(r) and Trios(r), separately. In this process, five severely distorted images were produced; they have been excluded from the data in order to avoid potential discrepancies (Figure 3). Figure 1: The experimental models with different interdental spaces in the anterior dentition. Ideal has no spacing (0 mm); Mild has 1 mm spacing; Moderate has 3 mm spacing; Severe has 5 mm spacing. A total of 80 scanned images were then superimposed with the reference image. All data were configured into Standard Tessellation Language (STL) files to standardize the collected data, and Geomagic Verify superimposed the images using the best-fit algorithm. This method aligned the reference data with the scanned experimental data by using the overlapped regions until the overall mean deviation between the surfaces was the smallest. The reference plane was formed by connecting the resin-balls located at the apices of the bilateral canines and first molar in each type of model. Bases of the superimposed model were trimmed using the reference plane (Figure 4). Deviations from superimposing the reference image and the scanned image were quantified as the shortest mean in three dimensions, which was used as a reference point for the accuracy of superimposed data (Figure 4F).