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Lecture 7: Voronoi Diagrams

Lecture 7: Voronoi Diagrams

Lecture 7: Voronoi Diagrams. Presented by Allen Miu 6.838 Computational Geometry September 27, 2001. p i : site points. q : free point. e : Voronoi edge. v : Voronoi vertex. v. q. e. p i. Post Office: What is the area of service?. Definition of Voronoi Diagram.

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Voronoi Diagrams

Voronoi Diagrams

Voronoi Diagrams. Voronoi Diagram. Input: A set of points locations ( sites ) in the plane. Output: A planar subdivision into cells. Each cell contains all the points for which a certain site is the closest. Application: Nearest-neighbor queries (by point location in the diagram).

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Computational Geometry

Computational Geometry

Computational Geometry. Lecture 8 Voronoi Diagrams. Voronoi Diagram. Input: A set of points locations ( sites ) in the plane. Output: A planar subdivision into cells. Each cell contains all the points for which a certain site is the closest.

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Computational Geometry

Computational Geometry

Computational Geometry. Chapter 7 Voronoi Diagrams. Definition. Input: A set S of n point locations ( sites ) in the plane. Output: Vor( S ), a planar subdivision into cells. Each cell contains all the points for which a certain site is the closest.

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Computing Voronoi Diagram

Computing Voronoi Diagram

Computing Voronoi Diagram. For each site p i , compute the common inter-section of the half-planes h(p i , p j ) for i ? j , using linear programming: O ( n 2 log n ) The worst case time bound is O ( n log n )

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Joshua Fuerst

Joshua Fuerst

Joshua Fuerst. Initial idea. What it is, is a piece of driftwood wedged in the sand. Project area. Where I am going to be during my spring break is a typical beach.

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