Methods of determining an orthodontic treatment comprising: obtaining 3D model of simulated position of teeth following proposed orthodontic treatment； the 3D model comprising a point cloud representation having vector points representative of teeth surface； generating an axis aligned boundary box around each tooth； identifying a pair of tooth-tooth bounding boxes of adjacent teeth that intersect； defining an area of overlap of the pair of tooth-tooth bounding boxes； mapping the area of overlap onto the plurality of vector points, the plurality of vector points populating a 3D grid, having cells, of a simulation space； identifying a subset of the cells including the mapped overlap area, and for only the subset of the cells determining a distance between the vector points relating to adjacent teeth； and determining the proposed orthodontic treatment as the determined orthodontic treatment if the determined distance is more than a predetermined distance.
