Abstract: Systems and methods are disclosed for matching computer models of two sets of teeth includes calculating a difference for two sets of teeth shapes; finding the position of one set of teeth with respect to the other set of teeth; calculating a positional difference of the corresponding teeth; and finding a corrective path to bring one set of teeth to the other set of teeth.

Abstract: Systems and methods are disclosed to prepare a malocclusion treatment plan by selecting a tooth treatment pattern from a library of predetermined tooth treatment patterns; and generating the malocclusion treatment plan implementing the selected tooth treatment pattern.

Abstract: A band cable comprising a tie having a plurality of grooves, a head having a tie passing slot into which the tie is inserted, and a stopper located in a one-body with the tie passing slot to fixedly secure the tie, is characterized in that there is formed in both sides of the tie passing slot an inclined path which makes the stopper separated from the groove of the tie, in case that a sort of force is given in one part of the tie so as to release the tie under such as a situation that the tie is bound by the tie passing slot of the head.

Abstract: A band cable having a tie through hole which is formed within a head, a stopper which is protrudedly formed on the top surface of the tie through hole, and a tie, on which a plurality of first grooves are formed, which is formed as a unitary body with the head, the band cable including a second groove formed on the lower portion of the tie through hole; and an elastic supporting member whose left and right side surfaces are separated from the inner side surface of the head, thus to move upwardly and downwardly, whereby after the tie is inserted into the tie through hole and is coupled with the head, if the tie coupled with the head is to be released, a user grasps the tie and then presses downwardly it with his thumb, and thereby, as the elastic supporting member is pushed in the downward direction of the second groove, the stopper is easily deviated from the first grooves formed on the tie.