Methods and apparatus for automated part positioning based on geometrical comparisons

A digital computer system of the type including a display, an input-output device, a processor, and a storage device having software code residing therein, the digital computer system configured to perform the steps of:

• receiving a master model comprising a precise definition of a three-dimensional solid;
• receiving a target model comprising a simplified definition of the three-dimensional solid;
• identifying a first set of geometric entities in the master model that have a unique characteristic, including a first set of planar faces in the master model that have a unique area as compared to a set of other first model planar faces, wherein the unique area is unique when the unique area is within a predetermined tolerance, and including a first set of linear edges in the first set of planar faces;
• identifying a second set of geometric entities in the target model that have the unique characteristic, including a second set of planar faces in the target model that have the unique area as compared to a set of other target model planar faces, and including a second set of linear edges in the second set of planar faces;
• determining a best match between a member of the first set of geometric entities and a member of the second set of geometric entities by comparing the unique characteristic of the first set of geometric entities and the second set of geometric entities to form a comparison and minimizing an error function on the comparison, including determining a best planar face match, based on an area measurement, between the first set of planar faces and the second set of planar faces and a best linear edge match, based on a length measurement, between the first set of linear edges and the second set of linear edges;
• and
• computing a rigid body motion to be applied to the first model such that said first model is substantially coincident with the target model, wherein computing the rigid body motion further comprises:
• determining a midpoint and a tangent of matching edges from the best linear edge match:
• determining an outward normal of matching faces from the best planar face match;
• and
• determining a transformation matrix to place the master model based on a coordinate system comprising the midpoint, the tangent, and the outward normal.

A method of automatic spatial matching of a master model comprising a precise definition of a three-dimensional solid with a target model comprising a simplified definition of the three-dimensional solid, the method comprising:

• identifying, using a processor, a first set of planar faces in the master model that have a unique area as compared to a set of other master model planar faces, wherein the unique area is unique when the unique area is within a predetermined tolerance;
• identifying, using the processor, a second set of planar faces in the target model that have the unique area as compared to a set of other target model planar faces;
• determining a best planar face match, based on an area measurement, between the first set of planar faces and the second set of planar faces;
• identifying a first set of linear edges in the first set of planar faces and a second set of linear edges in the second set of planar faces;
• determining a best linear edge match, based on a length measurement, between the first set of linear edges and the second set of linear edges;
• and
• determining a rigid body motion, based on the best linear edge match between the first and second set of linear edges, to be applied to the master model such that the master model is substantially coincident with the target model, wherein the rigid body motion comprises a position and an orientation of the master model that moves the master model into a target model location, and wherein determining the rigid body motion further comprises:
• determining a midpoint and a tangent of matching edges from the best linear edge match:
• determining an outward normal of matching faces from the best planar face match;
• and
• determining a transformation matrix to place the master model based on a coordinate system comprising the midpoint, the tangent, and the outward normal.