System and method for determining minimal negative distance between two objects

A method for electronically determining an optimal vector and a minimal negative distance between overlapping first and second 3D models to translate the overlapping first and second 3D models with respect to each other so that they don't overlap each other, the method comprising:

• using a controller to determine a starting vector V that defines a direction of movement of the second 3D model relative to the first 3D model;
• using the controller to rotate the vector V about each one of X, Y and Z axes, to define vectors V1 through V6, where:
• vector V1 represents the vector V rotated by a first predetermined X value about an X axis of the three dimensional coordinate space;
• vector V2 represents the vector V rotated by a second predetermined X value about the three dimensional coordinate space;
• vector V3 represents the vector V rotated by a first predetermined Y value about the three dimensional coordinate space;
• vector V4 represents the vector V rotated by a second predetermined Y value about the three dimensional coordinate space;
• vector V5 represents the vector V rotated by a first predetermined Z value about the three dimensional coordinate space;
• vector V6 represents the vector V rotated by a second predetermined Z value about the three dimensional coordinate space;
• using the controller to determine a directional negative distance D1-D6 for vectors V1-V6, respectively;
• using the controller to determine which one of distances D1-D6 represents a smallest distance value, and designating the one of vectors V1-V6 having the smallest distance value as distance D′ and vector V′;
• using the controller to compare distance D′ to a preset value to determine if D′ exceeds the preset value, and when distance D′ exceeds the preset value, then resetting distance D equal to D′;
• using the controller to repeat the rotations of vector V to generate a new groups of vectors V1-V6 having new distances D1-D6, until a smallest one of the new distances D1-D6 does not exceed the preset value, and then using the controller to identify the smallest one of the new distances as an optimal directional negative distance Dopt and its associated vector as an optimal vector Vopt;
• and
• using the controller to translate the first and second 3D models with respect to each other along the optimal vector Vopt the minimal directional negative distance Dopt.

A system for electronically determining an optimal vector and a minimal negative distance between overlapping first and second 3D models to translate the overlapping first and second 3D models with respect to each other so that they don't overlap each other, the system comprising:

• a controller to determine a starting vector V that defines a direction of movement of the second 3D model relative to the first 3D model;
• the controller being configured to:
• a) determine a directional negative distance D for vector V;
• b) rotate vector V in a plurality of directions about each one of X, Y and Z axes, to define a plurality of additional vectors;
• c) compare directional negative distances defined by each one of the plurality of additional vectors with one another to determine which represents a smallest directional negative distance, and identifying the one of the plurality of additional vectors having the smallest directional negative distance as vector V′ and its associated directional negative distance as D′;
• d) obtain a difference between D and D′;
• e) determine if the difference between D and D′ is no greater than a set value, and if not, then again setting vector V equal to vector V′ and distance D equal to distance D′, and again using the controller to rotate vector V in a plurality of directions;
• and
• repeat operations b) through e) until it is determined that distance D is no greater than the set value, and then identifying V as an optimal vector Vopt having a minimal directional negative distance Dmin;
• and
• translate the first and second 3D models with respect to each other along the optimal vector Vopt the minimal directional negative distance Dmin.