The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other.The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other.

A Voronoi diagram is sometimes also known as a Dirichlet tessellation. The cells are called Dirichlet regions, Thiessen polytopes, or Voronoi polygons.

Voronoi diagrams were considered as early as 1644 by René Descartes and were used by Dirichlet (1850) to investigate positive quadratic forms.

They were also studied by Georgy Voronoi (1868-1908), the inventor of an original method of diagrams, who extended the investigation of Voronoi diagrams to higher dimensions.

They find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology.

A particularly notable use of a Voronoi diagram was the analysis of the 1854 cholera epidemic in London, in which physician John Snow determined a strong correlation of deaths with proximity to a particular (and infected) water pump on Broad Street (Snow 1854, Snow 1855).

In his analysis, Snow constructed a map on which he drew a line labeled “Boundary of equal distance between Broad Street Pump and other Pumps.”

This line indicated the Broad Street Pump’s Voronoi cell (Austin 2006). However, for an analysis highlighting some of the oversimplifications and misattributions in this folklore history account of the events surrounding Snow and the London cholera incident, see Field (2020).

Text Source: Voronoi Diagram / wolfram

 

 

Video Source:

Voronoi Pattern (Grasshopper Tutorial) / Youtube / Rhino Grasshopper

 

Corollaria generation / Vimeo / Nervous System

 

Generating a New Balance 3D-printed midsole from pressure data / Vimeo / Nervous System

Animated 3D Voronoi diagram / Youtube / Spherical Tools

CSCEC just took 20 days to transform the Water Cube into the Ice Cube / Youtube / China State Construction

The Water Cube / Youtube / Sean D

Delaunay Triangulation & Voronoi Diagram / Youtube/ 3u54e4f5

Colloidal Voronoi bubble / Youtube/ Chemical bouillon

Dragonfly Wings in Slow Motion – Smarter Every Day 91/ Youtube/ SmartEveryDay

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ASMR Triggers Visual Macro Photography of Soap Bubbles look like Distant Galaxies / Youtube/ Stereokroma

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Giraffes Animals Collection in 8K HDR 60FPS ULTRA HD / Youtube/ 8K VIDEOS ULTRA HD

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How to shoot stunning macro leaf photos (with a surprise visitor!) / Youtube / Adaptalux