Systems and methods for determining orthodontic treatments

A system of determining an orthodontic treatment for a subject, the system comprising a processor of a computer system, the processor arranged to execute a method comprising:

• obtaining a 3D model of upper teeth of an upper archform and lower teeth of a lower archform of a subject, the 3D model representative of a simulated position of the upper teeth and the lower teeth following a simulated orthodontic treatment, the 3D model comprising a point cloud representation of the upper teeth and the lower teeth, the point cloud representation comprising a plurality of vector points representative of the upper teeth and the lower teeth;
• identifying whether there is collision between the upper teeth and the lower teeth in the simulated position by:
• in a 3D grid in a simulation space onto which the plurality of the vector points representative of the upper teeth and the lower teeth have been mapped,
• determining if there is at least one cell in the 3D grid which includes vector points representative of the lower teeth and the upper teeth;
• and selectively executing:
• if the 3D grid does not include at least one cell which includes vector points representative of the lower teeth and the upper teeth, determining that there is no collision between the upper teeth and the lower teeth, and determining the simulated orthodontic treatment as the determined orthodontic treatment,
• if there is at least one cell in the 3D grid which includes vector points representative of the lower teeth and the upper teeth, determining that there is collision between the upper teeth and the lower teeth, and adjusting the simulated orthodontic treatment.