The Math Meridian
Back to 3D Geometry, Voronoi Diagrams and Graphs

Voronoi diagrams and nearest neighbours

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Useful for: IB Math AI SL & HL

Learn it A Voronoi diagram splits a map into cells: every point in a cell is closer to that cell's site than to any other. The edges are parts of perpendicular bisectors between sites. Used to find the nearest hospital, school or phone tower.

Example: Sites A(0, 0) and B(6, 0). Which point is in A's cell: (2, 5) or (4, 1)?

  1. The boundary is the perpendicular bisector x = 3.
  2. (2, 5) has x < 3, so it is in A's cell.

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