  In arXiv:2107.05714 the concept of the Voronoi diagram was investigated
closely from a theoretical point of view. Then, a physics-driven kinematical
method was introduced to produce an improved model for dominance space in
soccer. Remaining faithful to the deterministic approach, we extend the
original work by the introduction of (a) an asymmetric influence of the players
in their surrounding area, (b) the frictional forces to the players' motion,
and (c) the simultaneous combination of both effects. The asymmetric influence
is fairly intuitive; players have more control in the direction they are
running than any other direction. The sharper the turn they must make to reach
a point on the pitch, the weaker their control of that point will be. From
simple kinematical laws, this effect can be quantified explicitly. For the
frictional force, a portion comes from air resistance, and so will be
proportional to the square of the player's speed, as is well known from fluid
dynamics. There are no other external frictional forces, but, at the suggestion
of biokinematics, there is an internal frictional force, relating to the
consumption of energy by the muscles, which is proportional to the player's
speed.
  Although these additions are intuitively understood, mathematically they
introduce many analytical complexities. We establish exact analytical solutions
of the dominance areas of the pitch by introducing a few reasonable simplifying
assumptions. Given these solutions the new Voronoi diagrams are drawn for the
publicly available data by Metrica Sports. In general, it is not necessary
anymore for the dominance regions to be convex, they might contain holes, and
may be disconnected. The fastest player may dominate points far away from the
rest of the players.
