Abstract: A system and method is disclosed for determining an optimal direction and a minimum directional negative distance between two objects. The system and method uses an iterative process involving rotating a vector about two or more axes to obtain a group of new vectors, determining which one of the new group of vectors has the smallest directional negative distance, comparing the vector having the smallest directional negative distance to a preset value, and repeating the above operations as needed until a vector is obtained which does not exceed the preset value, and which is then identified as the optimum directional vector having a minimal directional negative value.

Abstract: A system and method is disclosed for determining an optimal direction and a minimum directional negative distance between two objects. The system and method uses an iterative process involving rotating a vector about two or more axes to obtain a group of new vectors, determining which one of the new group of vectors has the smallest directional negative distance, comparing the vector having the smallest directional negative distance to a preset value, and repeating the above operations as needed until a vector is obtained which does not exceed the preset value, and which is then identified as the optimum directional vector having a minimal directional negative value.

Abstract: A method for determining a mated portion of an object can include receiving design data defining a three-dimensional object having a first member mated with a second member. Each member can be represented by a plurality of triangles. The method can include determining an outer layer of the three-dimensional object and a mated surface of the three-dimensional object. The mated surface may be determined by utilizing a recursive process to analyze each specific triangle of the plurality of triangles. The recursive process can classify a triangle as: (i) on the outer layer when all of its vertices are on the outer layer, and (ii) in the mated surface when none of its vertices are on the outer layer. When a triangle has at least one but not all of its vertices on the outer layer, the triangle can be subdivided into sub-triangles, which are then analyzed individually.

Abstract: A system and method for generating a representation of an outer layer of a three-dimensional object is disclosed. The object may be represented by a data structure that defines a plurality of triangles that collectively represent the object. The method comprises receiving the data structure and determining a bounding box that can encapsulate the object, the bounding box being comprised of a plurality of voxels. The method further comprises determining an intersecting set of voxels of the plurality of voxels. A member of the intersecting set of voxels intersects with at least one triangle of the plurality of triangles. The method also includes determining an outer set of voxels from the intersecting set of voxels, wherein a member of the outer set of voxels shares a face with a voxel that is not a member of the intersecting set of voxels. The method further includes determining an outer layer set of triangles from the plurality of triangles to obtain a modified data structure.

Abstract: An iterative process for determining an aperture in a representation of an object is disclosed. The object is received and a bounding box corresponding thereto is determined. The bounding box includes a plurality of initial voxels and the object is embedded therein. An intersecting set of initial voxels is determined, as well as an internal set and an external set of initial voxels. The resolution of the voxels is iteratively decreased until the ratio of internal voxels to external voxels exceeds a predetermined threshold. The voxels corresponding to the final iteration are the final voxels. An internal set of final voxels is determined. A union set of initial voxels is determined indicating an intersection between the external set of initial voxels and the internal set of final voxels. From the union set of initial voxels and the external set of initial voxels, a location of an aperture is determined.

Abstract: A method for determining a mated portion of an object can include receiving design data defining a three-dimensional object having a first member mated with a second member. Each member can be represented by a plurality of triangles. The method can include determining an outer layer of the three-dimensional object and a mated surface of the three-dimensional object. The mated surface may be determined by utilizing a recursive process to analyze each specific triangle of the plurality of triangles. The recursive process can classify a triangle as: (i) on the outer layer when all of its vertices are on the outer layer, and (ii) in the mated surface when none of its vertices are on the outer layer. When a triangle has at least one but not all of its vertices on the outer layer, the triangle can be subdivided into sub-triangles, which are then analyzed individually.

Abstract: A system and method for generating a representation of an outer layer of a three-dimensional object is disclosed. The object may be represented by a data structure that defines a plurality of triangles that collectively represent the object. The method comprises receiving the data structure and determining a bounding box that can encapsulate the object, the bounding box being comprised of a plurality of voxels. The method further comprises determining an intersecting set of voxels of the plurality of voxels. A member of the intersecting set of voxels intersects with at least one triangle of the plurality of triangles. The method also includes determining an outer set of voxels from the intersecting set of voxels, wherein a member of the outer set of voxels shares a face with a voxel that is not a member of the intersecting set of voxels. The method further includes determining an outer layer set of triangles from the plurality of triangles to obtain a modified data structure.

Abstract: An iterative process for determining an aperture in a representation of an object is disclosed. The object is received and a bounding box corresponding thereto is determined. The bounding box includes a plurality of initial voxels and the object is embedded therein. An intersecting set of initial voxels is determined, as well as an internal set and an external set of initial voxels. The resolution of the voxels is iteratively decreased until the ratio of internal voxels to external voxels exceeds a predetermined threshold. The voxels corresponding to the final iteration are the final voxels. An internal set of final voxels is determined. A union set of initial voxels is determined indicating an intersection between the external set of initial voxels and the internal set of final voxels. From the union set of initial voxels and the external set of initial voxels, a location of an aperture is determined.