An orthodontics virtual modeling system for modeling teeth of a patient, comprising: a server including processing circuitry configured to receive a virtual modeling file encoded with an orthodontic treatment plan such that encoded information of the virtual modeling file allows all of a plurality of treatment steps of the orthodontic treatment plan to be displayed without a separate file for each treatment step; download a first treatment step of the plurality of treatment steps of the virtual modeling file; receive gingiva geometries and teeth geometries corresponding to the first treatment step; display the first treatment step; transmit a request for a selected treatment step of the plurality of treatment steps to be displayed; determine if the selected treatment step is the first treatment step; when the selected treatment step is the first treatment step, display the gingiva geometries and the teeth geometries corresponding to the first treatment step; when the selected treatment step is not the first treatment step, download the selected treatment step of the virtual modeling file, receive a plurality of teeth transformation matrices and gingiva transformation vectors for each of a maxillary arch and a mandibular arch corresponding to the selected treatment step, apply a predetermined transformation matrix for each tooth of the teeth based on the selected treatment step, convert gingiva geometries of a currently displayed treatment step to the gingiva geometries corresponding to the first treatment step when the currently displayed treatment step is not the first treatment step, apply transformation vectors to the gingiva geometries corresponding to the first treatment step based on the selected treatment step, and display the gingiva geometries and the teeth geometries corresponding to the selected treatment step based on information encoded in the virtual modeling file without creating a separate file for each treatment step. receive a virtual modeling file encoded with an orthodontic treatment plan such that encoded information of the virtual modeling file allows all of a plurality of treatment steps of the orthodontic treatment plan to be displayed without a separate file for each treatment step; download a first treatment step of the plurality of treatment steps of the virtual modeling file; receive gingiva geometries and teeth geometries corresponding to the first treatment step; display the first treatment step; transmit a request for a selected treatment step of the plurality of treatment steps to be displayed; determine if the selected treatment step is the first treatment step; when the selected treatment step is the first treatment step, display the gingiva geometries and the teeth geometries corresponding to the first treatment step; when the selected treatment step is not the first treatment step, download the selected treatment step of the virtual modeling file, receive a plurality of teeth transformation matrices and gingiva transformation vectors for each of a maxillary arch and a mandibular arch corresponding to the selected treatment step, apply a predetermined transformation matrix for each tooth of the teeth based on the selected treatment step, convert gingiva geometries of a currently displayed treatment step to the gingiva geometries corresponding to the first treatment step when the currently displayed treatment step is not the first treatment step, apply transformation vectors to the gingiva geometries corresponding to the first treatment step based on the selected treatment step, and display the gingiva geometries and the teeth geometries corresponding to the selected treatment step based on information encoded in the virtual modeling file without creating a separate file for each treatment step. download the selected treatment step of the virtual modeling file, receive a plurality of teeth transformation matrices and gingiva transformation vectors for each of a maxillary arch and a mandibular arch corresponding to the selected treatment step, apply a predetermined transformation matrix for each tooth of the teeth based on the selected treatment step, convert gingiva geometries of a currently displayed treatment step to the gingiva geometries corresponding to the first treatment step when the currently displayed treatment step is not the first treatment step, apply transformation vectors to the gingiva geometries corresponding to the first treatment step based on the selected treatment step, and display the gingiva geometries and the teeth geometries corresponding to the selected treatment step based on information encoded in the virtual modeling file without creating a separate file for each treatment step.