System and method for automatic construction of tooth axes
System and method for automatic construction of the tooth's axes in terms of three orthogonal unit vectors are disclosed. Three dimensional data for a tooth is used to automatically construct the tooth's axes. System and methods for automatic construction of the axes for different types of teeth such as incisors, canines, premolars, and molars are disclosed.
1. A computer-implemented method for automatic construction of a set of axes for an incisor, comprising:
receiving three dimensional data for the incisor by the computer;
calculating an OZ axis for the incisor by calculating an axis that bisects a three dimensional bounding box for the incisor, such that the OZ axis approximates an axis of rotation symmetry for the incisor by the computer without operator intervention, wherein calculating the OZ axis further comprises:
rotating the incisor about the OZ axis by 180 degrees;
pairing a number of vertices in the incisor with a respective number of nearest vertices in the unrotated incisor;
calculating a rigid body transformation from the number of paired vertices; and
calculating a new OZ axis from the transformation; and
calculating, an OY axis for the incisor, such that the OY axis is substantially parallel to the ridge of the incisor by the computer without operator intervention.
2. The computer-implemented method of claim 1 , further comprising:
calculating a first plane that approximates a labial area of the incisor;
calculating a second plane that approximates a lingual area of the incisor;
calculating a YZ plane, for the set of axes, wherein the YZ plane is approximately balanced between the labial area and the lingual area of the incisor;
calculating a Y coordinate for an origin for the set of axes, such that the Y coordinate approximates a mid-point of the ridge of the incisor; and
calculating an X coordinate and a Z coordinate for the origin, such that the X and Z coordinates are located proximate to a front edge of the incisor.
3. The computer-implemented method of claim 2 , wherein the step of calculating a YZ, plane comprises calculating a plane that is approximately balanced between the first plane for the labial area of the incisor and the second plane for the lingual area of the incisor.
4. The computer-implemented method of claim 2 , wherein:
the step of calculating a first plane further comprises utilizing a best fit to match a set of three dimensional points for the labial area of the incisor; and
the step of calculating a second plane further comprises utilizing a best fit to match a set of three dimensional points for the lingual area of the incisor.
5. The computer-implemented method of claim 1 , wherein the step of calculating an OZ axis further comprises repeating the rotating, pairing, and calculating steps to reduce errors in the OZ axis.
6. The computer-implemented method of claim 5 , wherein the step of calculating an OZ axis further comprises:
calculating a second OZ axis balanced between left and right borders of a three dimensional mesh of the incisor;
determining if the OZ axis is more than a configurable amount different than the second OZ axis; and
notifying the operator to determine whether the OZ axis is in an acceptable position.
7. A computer-implemented method for automatic construction of a set of axes for a tooth having a pair of cusps and a crown, comprising:
receiving three dimensional data for the tooth by the computer;
calculating a first plane that approximates a labial area of the tooth by the computer without operator intervention;
calculating a second plane that approximates a lingual area of the tooth by the computer without operator intervention;
calculating a YZ plane, for the set of axes, wherein the YZ plane is approximately balanced between the labial area and the lingual area of the tooth by the computer without operator intervention; and
calculating an OZ axis for the tooth by the computer without operator intervention, such that the OZ axis approximates an axis matching a number of pre-selected points most distal from the YZ plane on the labial area of the tooth.
8. The computer-implemented method of claim 7 , further comprising:
calculating an origin for the set of axes, such that the origin approximates the center of the crown of the tooth.
9. The computer-implemented method of claim 8 , wherein:
the step of calculating a first plane further comprises utilizing a best fit to match a set of three dimensional points for the labial area of the tooth; and
the step of calculating a second plane further comprises utilizing a best fit to match a set of three dimensional points for the lingual area of the tooth.
10. The computer-implemented method of claim 8 , wherein the step of calculating a YZ plane comprises bisecting the first plane that approximates the labial area of the tooth and the second plane that approximates the lingual area of the tooth.
11. A computerized system for automatic construction of a set of axes for an incisor, the computerized system comprising:
a microprocessor;
a memory device; and
wherein the computerized system is configured for:
receiving three dimensional data for the incisor;
calculating a first plane that approximates a labial area of the incisor;
calculating a second plane that approximates a lingual area of the incisor;
calculating a YZ plane, for the set of axes, that is approximately balanced between the first plane for the labial area of the incisor and the second plane for the lingual area of the incisor;
calculating an OZ axis for the set of axes, such that the OZ axis approximates an axis of rotation symmetry for the incisor by calculating an axis that bisects a three dimensional bounding box for the incisor, wherein calculating the OZ axis further comprises:
rotating the incisor about the OZ axis by 180 degrees;
pairing a number of vertices in the tooth with a respective number of nearest vertices in the unrotated tooth;
calculating a rigid body transformation from the number of paired vertices; and
calculating a new OZ axis from the transformation:
calculating an OY axis for the set of axes, such that the OY axis is substantially parallel to the ridge of the incisor;
calculating a Y coordinate for an origin for the set of axes, such that the Y coordinate approximates the cusp of the incisor; and
calculating an X coordinate and a Z coordinate for the origin, such that the X and Z coordinates are located proximate to a front edge of the incisor.