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Unformatted text preview: Motivation Voronoi diagrams Voronoi diagrams Computational Geometry Lecture 10: Voronoi diagrams Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Given some trees, seen from above, which region will they occupy? Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Given some trees, seen from above, which region will they occupy? Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Given ambulance posts in a country, in case of an emergency somewhere, where should the ambulance come from? Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Given ambulance posts in a country, in case of an emergency somewhere, where should the ambulance come from? Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Voronoi diagram induced by a set of points (called sites): Subdivision of the plane where the faces correspond to the regions where one site is closest Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Voronoi diagram Question: Why is the Voronoi diagram not really a subdivision? Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Spatial interpolation Suppose we tested the soil at a number of sample points and classified the results sand clay chalk limestone clay clay sand chalk Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Spatial interpolation Suppose we tested the soil at a number of sample points and classified the results sand clay chalk limestone clay clay sand chalk Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Spatial interpolation Suppose we tested the soil at a number of sample points and classified the results sand clay chalk limestone clay clay sand chalk Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Spatial interpolation Suppose we measured the lead concentration at a number of sample points 14 13 22 6 7 15 18 11 20 Computational Geometry Lecture 10: Voronoi diagrams Motivation Voronoi diagrams Voronoi diagrams Spatial interpolation Spatial interpolation Suppose we measured the lead concentration at a number of sample points 14 13 22 6 7 15 18 11 20 ?...
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 Fall '08
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