Geodesic
Introducing the interaction distance in the context of distance geometry for human motions
Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 273-283

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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.
Keywords: dynamical distance geometry, interaction distance, human motion adaptation, retargeting, animated skeletal structures, symmetric quasi-distance. 
@article{CHEB_2019_20_2_a20,
     author = {A. Mucherino},
     title = {Introducing the interaction distance in the context of distance geometry for human motions},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {273--283},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/}
}
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A. Mucherino. Introducing the interaction distance in the context of distance geometry for human motions. Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 273-283. http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/