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CHAPTER 13

# Hulls and Diagrams

The convex hull of a set can be regarded as a “domain of influence” of the set. Similarly, the Voronoi diagram of a set of points defines “domains of influence” of the points. This chapter discusses hulls and diagrams in Euclidean space or in a grid, with emphasis on 2D. We discuss definitions of digital convexity and digital Voronoi diagrams and give algorithms based on adjacency grid models. We also discuss “domains of influence” in pictures.

## 13.1 Hulls

Let S be a class of subsets of a set S. A function H that takes sets in S into sets in S is called a hull operator iff it has the following properties:

H1: MH (M) for all M ∈ S.

H2: M1M2 implies H(M1) ⊆ H(M2) for all M1,M2S.

H3: H (H (M)) ⊆ H (M) for ...

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