A system for generating a treatment plan for repositioning a plurality of teeth comprises instructions to receive a digital data set representing the plurality of teeth, and determine a movement trajectory for repositioning, each tooth from an initial position and orientation towards a target position and orientation. The movement trajectory of at least one tooth comprises movement along a plurality of different directions. A movement velocity is determined for repositioning each tooth along the corresponding movement trajectory. The movement velocity is determined independently for each tooth, and the movement velocity for the at least one tooth is determined independently for each direction.
