# 2023 1 Theorem 7 3 For n 3 the number of vertices in the | Assignment Collections

Computer Science 2023 Voronoi Diagram–Computer Geographics

2023 1 Theorem 7 3 For n 3 the number of vertices in the | Assignment Collections

1.

Theorem 7.3 For n 3, the number of vertices in the Voronoi diagram of a set of n point sites in the plane is at most 2n − 5 and the number of edges is at most 3n−6.

Show that Theorem 7.3 implies that the average number of vertices of a Voronoi cell is less than six.

2.

Suppose you are given a set, S, of n > 3 points in the plane such that no three lie on the same line. Show that a point, p, in S, is on the convex hull of S if and only if p has an unbounded cell in the Voronoi diagram of S.

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