Interpreting Voronoi Diagrams (DP IB Applications & Interpretation (AI)): Revision Note

Interpreting Voronoi Diagrams

What is a Voronoi diagram used for?

• Voronoi diagrams are often used in land management to work out where the best location would be according to where sites are already situated

• They can show where to put something to make sure that it is

  • Closest to a particular site

  • Closer to one site than another

  • Equidistant from two or three specific sites

  • As far as possible from any other site

What do I need to know about Voronoi diagrams?

• You may be asked to find the shortest distance from a point to its closest site

  • Use Pythagoras’ Theorem to find the distance between the given coordinate and the site in the same region as it

  • If the coordinate is on an edge then there will be two sites equidistant from it

• You may be asked to find the point which is furthest from any of the sites

  • This will be one of the vertices

  • To choose which vertex look at which is the centre of the largest empty circle

• You may be asked to estimate the success of a new site

  • This is done by looking at the data for the nearest site

  • The prediction for the new site would be assumed to be the same

    • This is called nearest neighbour interpolation