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Voronoi Diagrams

Voronoi Diagrams. Given a set of points S in the plane, which are the Voronoi sites. Each site s has a Voronoi cell, also called a Dirichlet cell, V(s) consisting of all points closer to s than to any other site.

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Voronoi Diagrams

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  1. Voronoi Diagrams Given a set of points S in the plane, which are the Voronoi sites. Each site s has a Voronoi cell, also called a Dirichlet cell, V(s) consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi nodes are the points equidistant to three (or more) sites.

  2. Ten shops in a flat city and their Voronoicells Based on this model, what is the assumption regarding how customers are choosing which shop to go to? Where should the shops be built? Distance is only consideration Euclidean Distance is used. Customers travel by most efficient path Point A to Point B

  3. Ten shops in a flat city and their Voronoicells Based on this model, what is the assumption regarding how customers are choosing which shop to go to and the path they take? Where should the shops be built? Distance is only consideration Manhattan Distance is used. Customers only go to the shops by a vehicle and the traffic paths are parallel to the and axes Note: Voronoicells depend significantly on the metric used.

  4. Uniform Triangle Mass Center Fractal Pattern

  5. Input Output

  6. Voronoi tessellation based on world population density

  7. Voroni Map of United States based on state capital. It pretty much mirrors existing state boundaries; supports that the state capitals were located in the center of each state

  8. As long as I stay on the black lines, I will be as far away from the surrounding houses as I possibly can be.

  9. What if more houses?

  10. Pizza Parlor Proximity

  11. You are the owner…. • …of five pizzerias in the town of Squaresville. • To ensure minimal delivery times, you devise a system in which customers call a central phone number and are then transferred to the pizzeria that is closest to them. • The map of Squaresville shows the position of the five pizzerias. • You need to divide the town into five regions so that customers order their pizza from the closest pizzeria.

  12. Workers Needed to Service a Given Area

  13. Workers Needed to Service a Given Area

  14. Workers Needed to Service a Given Area

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