On the quantification of penetration between general objects

Abstract

In this article, we study the characterization, properties, and limitations of a variety of measures of penetration between two general object models. Measures of penetration between convex objects have appeared in the literature. We introduce new measures of penetration for general objects, which are generalizations of those for convex objects. We illustrate by example that these new measures are more accurate estimates of penetration in the case of nonconvex objects. Several properties of the new measures are derived. These include continuity of the measures with respect to rotational and translational parameters of the two objects, and invariance with respect to the choice of coordinate system. Since these measures are generalizations of the measures of penetration between convex objects, properties of the new measures are also properties of the traditional measures. An important property of these new penetration measures is established: the new penetration measures and the traditional penetration measures are the same in the case of convex objects.