Why it matters

Voronoi models nearest-neighbor problems. Understanding shapes spatial computing.

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The architecture

Each site owns cell of nearest points.

Cell boundaries: perpendicular bisectors.

Voronoi structureSitespointsCellsnearest regionBoundariesperp bisectorsFortune's sweep line algorithm O(n log n); Delaunay dual can also produce
Voronoi.
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How it works end to end

Fortune's algorithm: parabolic front.

Beach line + events.

Applications: k-NN, meshing, biology.