Preventing interference between tooth models

1. A method for mounting at least two physical tooth models on a physical dental arch model, comprising:

acquiring coordinates of a plurality of points on the surfaces of each of the two physical tooth models;

digitally representing the surfaces of each of the two physical tooth models as a mesh of points in three dimensions using the acquired coordinates, wherein the meshes representing the surfaces of the two physical tooth models intersect at least at one point to form an overlapping portion; and

calculating the depth of the overlapping portion between the two meshes to quantify the interference of the two physical tooth models.

2. The method of claim 1 , wherein acquiring the coordinates of a plurality of points on the surfaces of each of the two physical tooth models includes measuring the positions of points on the surfaces of an impression representing a patient's teeth.

3. The method of claim 1 , further comprising digitally representing the surfaces of each of the two physical tooth models by a triangular mesh in three dimensions.

4. The method of claim 1 , wherein at least one of the meshes comprises at least one mesh opening having three, four or five nodes.

5. The method of claim 1 , further comprising adjusting the positions or the orientations of at least one of the two physical tooth models in accordance with the depth of the overlapping portion between the two physical tooth models to prevent the interference between the physical tooth models.

6. The method of claim 1 , further comprising selecting the configurations of a first feature to be affixed to the undersides of the two physical tooth models in accordance with the depth of the overlapping portion between the two physical tooth models to prevent interference between the two physical tooth models when they are mounted to a base with the assistance of the first feature.

7. The method of claim 6 , wherein the second feature comprises one or more of a pin, a registration slot, a socket, a notch, a protrusion, a hole, an interlocking mechanism, a jig, and a pluggable or an attachable feature.

8. The method of claim 6 , further comprising fabricating the physical tooth models having the first features having the selected configurations.

9. The method of claim 1 , further comprising selecting the positions and orientations of second features on a base to prevent interference between the two physical tooth models when they are mounted to a base with the assistance of the second features.

10. The method of claim 9 , wherein the second feature comprises one or more of a pin, a registration slot, a socket, a notch, a protrusion, a hole, an interlocking mechanism, a jig, and a pluggable or attachable feature.

11. The method of claim 9 , further comprising

fabricating the base having the second features having the selected positions and orientations.

12. The method of claim 1 , wherein the mesh is interpolated to produce one or more surfaces to represent the boundaries of one of the two physical tooth models.

13. A method for preventing interference between two physical tooth models in a physical dental arch model, comprising:

acquiring the coordinates of a plurality of points on the surfaces of each of the two physical tooth models;

digitally representing the surfaces of each of the two physical tooth models by a mesh of points in three dimensions using the acquired coordinates, wherein the meshes representing the surfaces of the two physical tooth models intersect at least at one point to form an overlapping portion;

calculating the depth of the overlapping portion between the two meshes; and

adjusting the positions or the orientations of at least one of the two physical tooth models in accordance with the depth of the overlapping portion between the two physical tooth models to prevent the interference between the physical tooth models.

14. The method of claim 13 , further comprising selecting the configurations of a first feature to be affixed to the undersides of the two physical tooth models in accordance with the depth of the overlapping portion between the two physical tooth models to prevent interference between the two physical tooth models when they are mounted to a base with the assistance of the first feature.

15. The method of claim 14 , wherein the second feature comprises one or more of a pin, a registration slot, a socket, a notch, a protrusion, a hole, an interlocking mechanism, a jig, and a pluggable or an attachable feature.

16. The method of claim 14 , further comprising fabricating the physical tooth models having the first features having the selected configurations.

17. A method for preventing interference between two physical tooth models in a physical dental arch model, comprising:

acquiring the coordinates of a plurality of points on the surfaces of each of the two physical tooth models;

digitally representing the surfaces of each of the two physical tooth models by a mesh of points in three dimensions using the acquired coordinates;

interpolating each of the two meshes to produce one or more surfaces to represent the boundaries of one of the two physical tooth models, wherein the interpolated surfaces intersect at least at one point to form an overlapping portion; and

calculating the depth of the overlapping portion between the two interpolated surfaces to quantify the interference of the two physical tooth models.

18. The method of claim 17 , adjusting the positions or the orientations of at least one of the two physical tooth models in accordance with the quantified interference between the two physical tooth models to prevent the interference between the physical tooth models.

19. The method of claim 18 , further comprising selecting the configurations of a first feature to be affixed to the undersides of the two physical tooth models in accordance with the quantified interference between the two physical tooth models to prevent interference between the two physical tooth models when they are mounted to a base with the assistance of the first feature.