The world of Voronoi diagrams (2021)

10 months ago

Voronoi diagrams, also known as Dirichlet tessellation or Thiessen polygons, are natural patterns found in various fields like cartography, biology, and architecture.
A Voronoi diagram divides a plane into cells around points, where each cell contains the area closest to its point.
These diagrams are common in nature, seen in structures like onion skins, jackfruit shells, and giraffe coats due to efficient space usage and uniform growth patterns.
Voronoi patterns are used in human-made structures, such as the 'Water cube' in Beijing and crackled glazes in Song dynasty ceramics.
They are also popular in graphic arts for creating abstract patterns and backgrounds.
Voronoi diagrams can be generalized to n-dimensional spaces and use different distance metrics, like Euclidean or Manhattan distances.
They are closely related to the k-nearest neighbors algorithm and Delaunay triangulation, which is useful in modeling surfaces and objects.
Lloyd’s algorithm, used in k-means clustering, iteratively improves Voronoi diagrams by moving points to cell centroids, leading to more uniform cells.
Efficient algorithms for constructing Voronoi diagrams include the Sweep line algorithm and methods based on Delaunay triangulation.
Voronoi diagrams have diverse applications, from modeling forest trees to planning robot paths and procedural map generation in games.

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