Accurately predicting and preventing interference between tooth models

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

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

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

specifying a straight line running through the overlapping portion and intersecting the two interpolated surfaces representing the boundaries of the two physical tooth models; and

calculating the length of the straight line in the overlapping portion to quantify the interference between the two physical tooth models.

2. The method of claim 1 , further comprising

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

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

3. The method of claim 2 , further comprising measuring the positions of points on the surfaces of an impression representing a patient's teeth.

4. The method of claim 1 , further comprising

developing aligned coordinate systems or a common coordinate system for the two interpolated surfaces representing the boundaries of the two physical tooth models wherein the straight line can be quantitative defined.

5. The method of claim 1 , further comprising

calculating the lengths of three orthogonally oriented straight lines in the overlapping portion;

defining three vectors along the three orthogonally oriented straight lines, each of the vectors having a magnitude of the inverse of the length in the overlapping portion; and

calculating a vector sum of the three vectors to determine the direction and the distance required for the interpolated surfaces representing the two physical tooth models to move apart to avoid interference between the two physical tooth models.

6. The method of claim 5 , further comprising

moving apart the interpolated surfaces representing the boundaries of the two physical tooth models in accordance to the vector sum to avoid interference between the two physical tooth models.

7. The method of claim 1 , further comprising adjusting the positions or the orientations of at least one of the two physical tooth models to prevent the interference between the physical tooth models.

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

9. 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 to prevent interference between the two physical tooth models when they are mounted to a base with the assistance of the first feature.

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 an attachable feature.

11. The method of claim 9 , further comprising fabricating the physical tooth models having the first features having the selected configurations.

12. 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.

13. The method of claim 12 , 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.

14. The method of claim 12 , further comprising

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

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

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

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

developing aligned coordinate systems or a common coordinate system for the two interpolated surfaces representing the two physical tooth models;

specifying a straight line running through the overlapping portion and intersecting the two interpolated surfaces representing the boundaries of the two physical tooth models; and

calculating the length of the straight line in the overlapping portion to quantify the interference between the two physical tooth models.

16. The method of claim 15 , further comprising

calculating the lengths of three orthogonally oriented straight lines in the overlapping portion;

defining three vectors along the three orthogonally oriented straight lines, each of the vectors having a magnitude of the inverse of the length in the overlapping portion; and

calculating a vector sum of the three vectors to determine the direction and the distance required for the interpolated surfaces representing the boundaries of the two physical tooth models to move apart to avoid interference between the two physical tooth models.

17. The method of claim 16 , further comprising

moving apart the interpolated surfaces representing the boundaries of the two physical tooth models in accordance to the vector sum to avoid interference between the two physical tooth models.

18. The method of claim 15 , further comprising selecting the configurations of a first feature to be affixed to the undersides of 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.

19. The method of claim 18 , 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.

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

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

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

specifying three orthogonally oriented straight lines each running through the overlapping portion and intersecting the two interpolated surfaces representing the boundaries of the two physical tooth models;

calculating the lengths of three orthogonally oriented straight lines in the overlapping portion;

defining three vectors along the three orthogonally oriented straight lines, each of the vectors having a magnitude of the inverse of the corresponding length of the overlapping portion;

calculating a vector sum of the three vectors to determine the direction and the distance required for the interpolated surfaces representing the boundaries of the two physical tooth models to move apart to avoid interference between the two physical tooth models; and

moving apart the interpolated surfaces representing the boundaries of the two physical tooth models in accordance to the vector sum to avoid interference between the two physical tooth models.