Limit of Voronoi diagrams in soccer analysis, 2, simple numerical calculation

In this article, shown is simple numerical calculation for estimating players' occupying regions, with velocities of the players' movement.

("Player's occupying region" means a region where a player can cover without being disturbed by the other players. These regions are similar to Voronoi cells in a Voronoi diagram, if all players are in stationary state at a certain moment.)

The contents of the numerical calculation may be meaningless to inexperienced people.

I recommend them only to look at images.

The numerical calculation is not complicated.

The calculation scheme used is the 2D version of the 4th order Runge-Kutta method. (undergraduate level?)



Again I write, considering the velocity of the players, player's occupying region is far from Voronoi cell.

As an alternative to the Voronoi diagram, I suggest to illustrate regions (boundary lines) that players will cover a few seconds later.



The contents of this article are as follows.

• Reproduction of a Voronoi diagram 
• When there is initial velocity
• Calculation of collision boundary line from model speed
• Practical figure?

Figures in this articles is made with this program (jupiter notebook) on google colaboratory.

Limit of Voronoi diagrams in soccer analysis, 1, essence

My claim in this article is that "do not rely on Voronoi diagrams unlimitedly in soccer."

I am concerned about criticism to players by using Voronoi diagrams under blind reliance.

As a fact, when 22 players do not move, a Voronoi diagram indicates regions that the players can cover.

On the other hand, when some players move fast, a Voronoi diagram is far from regions that the players can cover.

I think, Voronoi diagrams are not compatible with soccer.

This is because the essence of soccer is in the movement of players.



The reason why Voronoi diagrams are used in soccer analysis is because "likely regions are obtained only from players' positions."



In this article, I roughly explain what the Voronoi diagram is.

In the next article, I will show difficulties in applying Voronoi diagrams when players move, with simple numerical calculation.



The contents of this article are as follows.

• Why are Voronoi diagrams used?
• Questionable scenes.
• Scenes where Voronoi diagrams can be applied, during a game.
• Scenes where Voronoi diagrams can be applied, in our lives.