Sport Informatics and Analytics/Audiences and Messages/Visualising Data/Voronoi

Introduction
Theme 4 of this course is Audiences and Messages. In our discussion of the visualisation of data aspects of the theme, we noted "At some point in the sport analytics process we share our findings with an audience".

This page introduces one form of visualising and sharing data, namely, a Voronoi diagram.

Adrienne Kemp describes the features of a Voronoi diagram: Given a set of n points in m-dimensional Euclidean space, a Voronoi diagram partitions the space into n convex polygons, each containing one of the points, in such a way that all locations within the polygon are closer to that point than to any other.

The name of the diagram comes from the mathematician, Georgy Voronoi, who defined it in a paper published in 1908. There is a copy of the original paper, in French, in the Gottinger Digitalisierungszentrum archive.

In addition to Georgy Voronoi's paper, you can find a great deal of information about pre-Voronoi use of diagrams (including by Johannes Kepler and Rene Descarte) in Thomas Liebling and Lionel Pournin's (2012) paper.

You might also see reference to a Voronoi tessellation in the literature. In this case the word 'tessellation' is synonomous with 'diagram'.

Definition
Thomas Lieling and Lionel Fournin note: A Voronoi diagram induced by a finite set A of sites is a decomposition of the plane into possibly unbounded (convex) polygons called Voronoi regions, each consisting of those points at least as close to some particular site as to the others.

These Voronoi regions change continuously over time and in sport reflect the dynamic nature of team play and spatial configuration.

Franz Aurenhammer states a Voronoi diagram: ... divides the plane according to the nearest-neighbour rule: Each point is associated with the region of the plane closest to it.

Franz's paper provides a most comprehensive computational geometry account of Voronoi diagrams and shares an extensive bibliography. If you have a particular interest in mathematics, we recommend Franz's paper to you. The original mathematics conventions are contained in Gregory Voronoi's 1908 paper.

The literature also makes mention of a centroidal Voronoi tessellation 38 (2014): 268-276. . Qiang Du, Vance Faber and Max Gunzburger point out that a centroid Voronoi tesselation is: a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions.

Voronoi diagrams in sport
Voronoi diagrams have attracted the attention of researchers in sport. Examples include:


 * Association football (motion analysis), (passing networks and player movement dynamics) , (classification of passes) ,  (measuring tactical success) , (changes in space control)   (probabilistic movement models) , (player identification for transfers) (spatial dynamics)
 * Football computer game (accurate measurement of player position)
 * Field hockey (evaluating teamwork)
 * Indoor sports (basketball, handball, squash), (basketball) , (handball)
 * Fencing (classification of complex motion patterns)
 * Futsal (to identify and investigate the spatial dynamics of players’ behavior)
 * Basketball (rebounding), (tactical behaviour) , (NBA court realty)
 * RoboCup Football (cooperation), (group behaviour) , (tactical decision making)
 * Netball