New formulation for the minimum directed distances between 3D convex polyhedra

The minimal directed distance function has been shown to have greater freedom in hypothesizing trajectories to be relaxed into admissibility. The minimum directed Euclidean distance (MDED) between two objects is the shortest relative translated Euclidean distance that results in the objects being just in contact. The MDED is also defined for intersecting objects and it then returns a measure of penetration. Given two disjointed objects we define the minimum directed L^∞ distance (MDLD) between them to be the shortest size either object needs to grow proportionally that results in the objects being in contact. The MDLD is equivalent to MDED for two intersecting objects and is the shortest relative translated distance so as to separate them. The computation of MDLD and MDED can be recast as a configuration space problem and finished in one routine