Researches [14, 15] have shown that the anterior teeth play an important role in smile aesthetics. Previous studies of lateral incisors indicated that the width ratio of lateral incisors to central incisors should correspond to the golden ratio [1, 16]. However, many studies later reported that the golden ratio of lateral incisors to central incisors has negligible effect on the smile aesthetics . For example, Bukhary et al. showed that lateral incisors with a width of 67–72% of the central incisors and a length 1.5 mm shorter than central incisors were considered attractive. Pani et al.  demonstrated that most people preferred short, broad lateral incisors, and they could tolerate a small mesial inclination of lateral incisors. Brunzel et al.  compared different aesthetic changes brought by different teeth inclination and suggested that a slight amount of mesial inclination of both lateral incisors symmetry had a positive effect on an attractive smile.
Studies mentioned above only included the changes of teeth in 2D plane, whereas in orthodontic cases, the inclination and displacement of the teeth in 3D plane were quite common. Schlosser et al.  studied different anteroposterior (AP) positions of the maxillary central incisors, showing that people were more tolerant to labial protrusion of the maxillary central incisors than lingual retrusion. Analogously, Cao et al.  found that the labial inclination and lingual retrusion of maxillary central incisors were relatively unacceptable. Chirivella et al.  studied the labiolingual inclination and anteroposterior position of maxillary incisors in three different facial patterns on profile, showing that different facial pattern led to different aesthetic criterion, but consistent with previous studies, the tolerance of the labiolingual movement of maxillary central incisors was lower than labiolingual inclination.
The Little's Irregularity Index (LII), the sum of the distances between four anterior teeth’s anatomic contact points, is an important index used in the previous study of dentition crowding . However, researches argued that the LII index did not have enough repeatability [23, 24], so it could not meet the research requirements. Studies indicated that scanning models had better reliability than LII index . Sirona intraoral scanner was used to obtain the volunteer’s digital dentition models and used iOrtho7.0 software to change the position of maxillary lateral incisors in this study. The 2D photos was created based on the visual effect of the 3D models, so that the changes took place in 3D direction were transformed into 2D images. As orthodontists face more cases of 3D malformation of teeth or dentition in clinic, our research methods may provide references for future research. The angle used in taking the photographs should be matched with the angle to view the dental cast in iOrtho7.0 software, which is worth noting in future research. Moreover, we found that when we change the position of lateral incisors, since we fixed the adjacent teeth in the 3D modle, the space between the lateral incisor and its adjacent teeth was magnified on photographs + 1.0 mm and + 1.5 mm, which was somewhat different from the actual situation. In the future study, we will seek a better balance between controlling single variable and simulating actual situation, making the study more valuable.
VAS can be used for the questionnaire analysis of various factors affecting smile aesthetics due to its convenience and repeatability . Some studies asked participants to rank photos in the order of attractiveness to find which photo was the most or the least attractive.  And some studies combined ranking orders and VAS scores together and evaluated their consistency . In our study, since the changes were made bidirectionally, it was not difficult to speculate that a large amount of labial or lingual movement would be both considered unacceptable, so ranking the photos was impractical in this study.
Gender may be one of the factors influencing smile aesthetics , but some studies [1, 26] have shown that, there was no significant difference between male and female in evaluating the smile aesthetics, which is consistent with our study. Studies have shown that the gender of the subject could also influence the perceived smile aesthetics [27, 28]. In our study, only one photograph of a man’s smile was used, and only the part of mouth was retained to minimize the effects of the subject’s gender. Therefore, the evaluation of different maxillary lateral incisors’ labiolingual position in different genders can be explored in subsequent studies.
Our study indicated that orthodontists and laypersons both awarded the highest score to the control group (0 mm), and they gave lower scores as the moving distance of maxillary lateral incisors increased. Compared with laypersons, orthodontists had a lower tolerance for lateral incisors moved labially (P < 0.05), and also assigned lower scores to the images of lingual movement of maxillary lateral incisors (though there was no significant difference), which indicated that orthodontists had higher aesthetic standards, and orthodontists are more sensitive than laypersons when the lateral incisors were moved labially. For both laypersons and orthodontists, the intolerance of labial movement was generally higher than lingual movement with the same distance. This is in contrast to the study of Cao et al.  which reported that the lingual movement and labial inclination of the maxillary central incisors were more unacceptable. The divergence of the conclusions may result from that different labiolingual position of the maxillary central incisors tends to change the position of entire dentition, and the receding dentition could make the smile look less full , while people tend to appreciate fuller smile more. But our study was based on the position of the maxillary lateral incisors, which changed position independently with the entire dentition. What’s more, front-view picture was used in our research instead of profile, which can also cause difference.
In addition, our study showed that, orthodontist did not tell difference between 0 mm and − 0.5 mm, while laypersons did. This was not in favor of the previous view that orthodontist were more likely to distinguish between subtle changes in dentition [1–3]. Therefore, before orthodontic treatment, communication and discussion between orthodontists and patients is needed to achieve a better therapeutic outcome.