Orthodontic Treatment Based on Wearable Mirror-Type Oral Prosthetic Tongue Flap without Bracket Correction

White teeth can make people full of confidence and satisfy the concept of modern life from the love of beauty. Due to the fusion of computer-aided design and teeth, invisible orthodontics has become the focus of research. Invisible orthodontic treatment technology can predict the results of orthodontics. How to automatically calculate the position and posture of the teeth in the middle stage of orthodontics is the key point of the treatment technology. In order to solve this problem, this article is divided into two parts to start research. Aiming at the problem of tooth orthodontic path planning, quaternion is used to define the tooth posture, combined with the initial posture and target posture of the tooth. A two-stage method is given to plan a collision-free path for the orthodontic tooth. In the first stage, the quaternion spherical linear interpolation and position linear interpolation are used to obtain the intermediate posture of the tooth during orthodontics, and the initial value of the orthodontic stage is obtained, and the obtained intermediate posture is used as a sampling node to apply to the next stage. In the second phase, considering the problem of orthodontic collision and interference, a scheme for calculating the priority of orthodontics is proposed, and the random node expansion part in the RRT (Rapid-exploration Random Tree) algorithm is improved. The initial value of the orthodontic phase is used to calculate the initial value of the iteration. Finally, a path with no collision and the least number of orthodontic stages is searched from the random tree of each tooth node. The experimental results and analysis show that this method can quickly and effectively solve the orthodontic path of teeth, and it is used clinically. The clasp-free invisible correction technology pushes the molars far away to leave gaps for treating patients with mild to moderate overcrowding. The treatment time should be reduced by at least 30%; the stability of the gaps and the long-term healing effect of the treatment provide a reference.