VORONOI DIAGRAM Meaning and
Definition
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A Voronoi diagram is a geometric concept in mathematics that divides a plane into regions based on the proximity of points. It is named after the Russian mathematician Georgy Voronoi, who introduced the concept in 1908. The diagram is also known as Voronoi tessellation, Dirichlet tessellation, or Thiessen polygons.
In a Voronoi diagram, given a set of points (known as seeds or generators) in a plane, each point creates a region that encompasses all the locations that are closer to it than any other point. These regions, called Voronoi cells or Voronoi polygons, are defined by the perpendicular bisectors of the line segments connecting each pair of neighboring seeds. Every point within a cell is closer to its seed than any other seed in the set.
This diagram helps to visualize and analyze the spatial distribution of points or locations. It has numerous applications in various fields such as computer graphics, geographic information systems (GIS), pattern recognition, physics, biology, and urban planning.
The Voronoi diagram is often represented graphically as a collection of convex polygons, although it can also be represented through graphs or mathematical equations. It provides a powerful tool for understanding proximity and spatial relationships, allowing researchers and analysts to gain insights into cluster patterns, nearest neighbor analysis, and optimal location determination.
Etymology of VORONOI DIAGRAM
The word "Voronoi" in "Voronoi diagram" is derived from the name of Ukrainian mathematician Georgy Voronoy, who introduced this mathematical concept in 1908.
