Voronoi diagram (nonfiction)

Approximate Voronoi diagram of a set of points. Notice the blended colors in the fuzzy boundary of the Voronoi cells.

In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.

It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet).

Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.

In the News

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  Fantasy Voronoi diagram color commentators discussing recent scores from hotly contested Voronoi diagrams.

Fiction cross-reference

• Gnomon algorithm
• Gnomon Chronicles
• Fantasy Voronoi diagram
• Mathematics
• Voronoia - a pathological mental condition characterized by delusions of Voronoi diagrams.

Nonfiction cross-reference

• Centroidal Voronoi tessellation (nonfiction)
• Delaunay triangulation (nonfiction) - a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles.
• Lloyd's algorithm (nonfiction)
• Mathematics (nonfiction)
• Mathematical diagram (nonfiction)
• Wigner–Seitz cell (nonfiction) - a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. It is used in the study of crystalline materials in solid-state physics.

External links:

• Voronoi diagram @ Wikipedia

• Very nice Voronoi

• Jump Flood Voronoi for WebGL
  • Online demo
• Voronoi Tessellation
• Voronoi Tesselation - Paper.js
• Voronator - upload 3D model, download your voroni tesselated version
• Voronoi experiment @ karljones.com
• Fortune's algorithm for Voronoi diagrams
• Javascript implementation of Steven J. Fortune's algorithm to compute Voronoi diagrams
• Lloyd’s Relaxation - generates a centroidal Voronoi tessellation, which is where the seed point for each Voronoi region is also its centroid
• Voronoi diagram in JavaScript
• Spherical Voronoi Diagram
• Interactive Voronoi Diagram Generator with WebGL

• Voronoi diagram code examples @ rosettacode.org

• Robot Path Planning Using Generalized Voronoi Diagrams