What are Voronoi Diagrams?

Voronoi diagrams, also known as Voronoi tessellations or Thiessen polygons, are a mathematical concept that describes how to divide space into regions based on the distance to a set of points. In a Voronoi diagram, each region corresponds to a point in the set, and consists of all the points in space that are closer to that point than to any other point in the set.

Here's an example: Imagine you have a map of a city, and you want to divide the city into regions based on which hospital is closest to each location. You would start by placing a point at the location of each hospital. Then, you would draw the boundaries of each region such that every point within a given boundary is closer to the corresponding hospital than to any other hospital.

Another example of Voronoi diagrams is in the field of cellular biology. Scientists use Voronoi diagrams to describe the distribution of cells in a tissue. They place a point at the center of each cell, and then draw boundaries such that each region includes all of the space closer to that cell than to any other cell. This allows them to analyze the geometry and distribution of cells in the tissue, which can provide insights into the development and behavior of cells.

Voronoi diagrams also have applications in computer science, where they are used in algorithms for image processing, pattern recognition, and data analysis. For example, a Voronoi diagram can be used to cluster data points into groups based on their proximity to certain reference points, such as the centroids of clusters in k-means clustering.

What are Voronoi Diagrams?