Introducing the interaction distance in the context of distance geometry for human motions

The dynamical Distance Geometry Problem (dynDGP) is a recently introduced subclass of the distance geometry where problems have a dynamical component. The graphs
$$G=(V \times T,E,\{\delta,\pi\})$$
of dynDGPs have a vertex set that is the set product of two sets: the set $V$, containing the objects to animate, and the set $T$, representing the time. In this article, the focus is given to special instances of the dynDGP that are used to represent human motion adaptation problems, where the set $V$ admits a skeletal structure $(S,\chi)$.
The “interaction distance” is introduced as a possible replacement of the Euclidean distance which is able to capture the information about the dynamics of the problem, and some initial properties of this new distance are presented.