Fig. 1

a The components of the model; b The attachment designs of different groups; c Three different set of canine tipping angles; d Diagram of the bone remodeling simulation method (Notice the deformation of periodontal ligament in the red circles); e The automatic clear aligner morphology changing method based on the temperature changing method: the process began with the determination of the center point of dental crowns in the occlusal view, denoted as (Ci, Cj). Margin points of dental crowns on the line connecting Ci and Cj were established as (Pi, Pj), and the center point of Pi-Pj (Pc) was then calculated. A selected area, both mesial and distal to Pc, perpendicular to the Ci–Cj line, was identified as the deformation region during staging. Deformation within this area was constrained along the Ci–Cj line. Where in the formula U refers to the preset deformation quantity, k refers to the coefficient of linear expansion, Δ refers to the amount of deformation in previous steps, d refers to the width of the area, and t refers to the change of temperature. f Two coordinate systems were used in this study to evaluate tooth displacements. PDL, periodontal ligament